PRDPRVDAQPhysical Review DPhys. Rev. D2470-00102470-0029American Physical Society10.1103/PhysRevD.99.112003ARTICLESParticle Physics ExperimentsMeasurements of the Higgs boson width and anomalous HVV couplings from on-shell and off-shell production in the four-lepton final stateMEASUREMENTS OF THE HIGGS BOSON WIDTH AND …A. M. 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BarbaroP.¹⁷⁵DeminaR.¹⁷⁵DuhY. t.¹⁷⁵DulembaJ. L.¹⁷⁵FallonC.¹⁷⁵FerbelT.¹⁷⁵GalantiM.¹⁷⁵Garcia-BellidoA.¹⁷⁵HanJ.¹⁷⁵HindrichsO.¹⁷⁵KhukhunaishviliA.¹⁷⁵RankenE.¹⁷⁵TanP.¹⁷⁵TausR.¹⁷⁵ChiaritoB.¹⁷⁶ChouJ. P.¹⁷⁶GershteinY.¹⁷⁶HalkiadakisE.¹⁷⁶HartA.¹⁷⁶HeindlM.¹⁷⁶HughesE.¹⁷⁶KaplanS.¹⁷⁶Kunnawalkam ElayavalliR.¹⁷⁶KyriacouS.¹⁷⁶LaflotteI.¹⁷⁶LathA.¹⁷⁶MontalvoR.¹⁷⁶NashK.¹⁷⁶OshersonM.¹⁷⁶SakaH.¹⁷⁶SalurS.¹⁷⁶SchnetzerS.¹⁷⁶SheffieldD.¹⁷⁶SomalwarS.¹⁷⁶StoneR.¹⁷⁶ThomasS.¹⁷⁶ThomassenP.¹⁷⁶AcharyaH.¹⁷⁷DelannoyA. G.¹⁷⁷HeidemanJ.¹⁷⁷RileyG.¹⁷⁷SpanierS.¹⁷⁷BouhaliO.^178,vvvCelikA.¹⁷⁸DalchenkoM.¹⁷⁸De MattiaM.¹⁷⁸DelgadoA.¹⁷⁸DildickS.¹⁷⁸EusebiR.¹⁷⁸GilmoreJ.¹⁷⁸HuangT.¹⁷⁸KamonT.^178,wwwLuoS.¹⁷⁸MarleyD.¹⁷⁸MuellerR.¹⁷⁸OvertonD.¹⁷⁸PernièL.¹⁷⁸RathjensD.¹⁷⁸SafonovA.¹⁷⁸AkchurinN.¹⁷⁹DamgovJ.¹⁷⁹De GuioF.¹⁷⁹DuderoP. R.¹⁷⁹KunoriS.¹⁷⁹LamichhaneK.¹⁷⁹LeeS. W.¹⁷⁹MengkeT.¹⁷⁹MuthumuniS.¹⁷⁹PeltolaT.¹⁷⁹UndleebS.¹⁷⁹VolobouevI.¹⁷⁹WangZ.¹⁷⁹WhitbeckA.¹⁷⁹GreeneS.¹⁸⁰GurrolaA.¹⁸⁰JanjamR.¹⁸⁰JohnsW.¹⁸⁰MaguireC.¹⁸⁰MeloA.¹⁸⁰NiH.¹⁸⁰PadekenK.¹⁸⁰RomeoF.¹⁸⁰SheldonP.¹⁸⁰TuoS.¹⁸⁰VelkovskaJ.¹⁸⁰VerweijM.¹⁸⁰XuQ.¹⁸⁰ArentonM. W.¹⁸¹BarriaP.¹⁸¹CoxB.¹⁸¹HiroskyR.¹⁸¹JoyceM.¹⁸¹LedovskoyA.¹⁸¹LiH.¹⁸¹NeuC.¹⁸¹SinthuprasithT.¹⁸¹WangY.¹⁸¹WolfeE.¹⁸¹XiaF.¹⁸¹HarrR.¹⁸²KarchinP. E.¹⁸²PoudyalN.¹⁸²SturdyJ.¹⁸²ThapaP.¹⁸²ZaleskiS.¹⁸²BuchananJ.¹⁸³CaillolC.¹⁸³CarlsmithD.¹⁸³DasuS.¹⁸³De BruynI.¹⁸³DoddL.¹⁸³GomberB.^183,xxxGrotheM.¹⁸³HerndonM.¹⁸³HervéA.¹⁸³HussainU.¹⁸³KlabbersP.¹⁸³LanaroA.¹⁸³LongK.¹⁸³LovelessR.¹⁸³RugglesT.¹⁸³SavinA.¹⁸³SharmaV.¹⁸³SmithN.¹⁸³SmithW. H.¹⁸³WoodsN.¹⁸³(CMS Collaboration)^*1Yerevan Physics Institute, Yerevan, Armenia²Institut für Hochenergiephysik, Wien, Austria³Institute for Nuclear Problems, Minsk, Belarus⁴Universiteit Antwerpen, Antwerpen, Belgium⁵Vrije Universiteit Brussel, Brussel, Belgium⁶Université Libre de Bruxelles, Bruxelles, Belgium⁷Ghent University, Ghent, Belgium⁸Université Catholique de Louvain, Louvain-la-Neuve, Belgium⁹Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil¹⁰Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil^11aUniversidade Estadual Paulista, São Paulo, Brazil^11bUniversidade Federal do ABC, São Paulo, Brazil¹²Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria¹³University of Sofia, Sofia, Bulgaria¹⁴Beihang University, Beijing, China¹⁵Institute of High Energy Physics, Beijing, China¹⁶State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China¹⁷Tsinghua University, Beijing, China¹⁸Universidad de Los Andes, Bogota, Colombia¹⁹University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia²⁰University of Split, Faculty of Science, Split, Croatia²¹Institute Rudjer Boskovic, Zagreb, Croatia²²University of Cyprus, Nicosia, Cyprus²³Charles University, Prague, Czech Republic²⁴Escuela Politecnica Nacional, Quito, Ecuador²⁵Universidad San Francisco de Quito, Quito, Ecuador²⁶Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt²⁷National Institute of Chemical Physics and Biophysics, Tallinn, Estonia²⁸Department of Physics, University of Helsinki, Helsinki, Finland²⁹Helsinki Institute of Physics, Helsinki, Finland³⁰Lappeenranta University of Technology, Lappeenranta, Finland³¹IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France³²Laboratoire Leprince-Ringuet, Ecole polytechnique, CNRS/IN2P3, Université Paris-Saclay, Palaiseau, France³³Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France³⁴Centre de Calcul de l’Institut National de Physique Nucleaire et de Physique des Particules, CNRS/IN2P3, Villeurbanne, France³⁵Université de Lyon, Université Claude Bernard Lyon 1, CNRS-IN2P3, Institut de Physique Nucléaire de Lyon, Villeurbanne, France³⁶Georgian Technical University, Tbilisi, Georgia³⁷Tbilisi State University, Tbilisi, Georgia³⁸RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany³⁹RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany⁴⁰RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany⁴¹Deutsches Elektronen-Synchrotron, Hamburg, Germany⁴²University of Hamburg, Hamburg, Germany⁴³Karlsruher Institut fuer Technologie, Karlsruhe, Germany⁴⁴Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece⁴⁵National and Kapodistrian University of Athens, Athens, Greece⁴⁶National Technical University of Athens, Athens, Greece⁴⁷University of Ioánnina, Ioánnina, Greece⁴⁸MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary⁴⁹Wigner Research Centre for Physics, Budapest, Hungary⁵⁰Institute of Nuclear Research ATOMKI, Debrecen, Hungary⁵¹Institute of Physics, University of Debrecen, Debrecen, Hungary⁵²Indian Institute of Science (IISc), Bangalore, India⁵³National Institute of Science Education and Research, HBNI, Bhubaneswar, India⁵⁴Panjab University, Chandigarh, India⁵⁵University of Delhi, Delhi, India⁵⁶Saha Institute of Nuclear Physics, HBNI, Kolkata,India⁵⁷Indian Institute of Technology Madras, Madras, India⁵⁸Bhabha Atomic Research Centre, Mumbai, India⁵⁹Tata Institute of Fundamental Research-A, Mumbai, India⁶⁰Tata Institute of Fundamental Research-B, Mumbai, India⁶¹Indian Institute of Science Education and Research (IISER), Pune, India⁶²Institute for Research in Fundamental Sciences (IPM), Tehran, Iran⁶³University College Dublin, Dublin, Ireland^64aINFN Sezione di Bari, Bari, Italy^64bUniversità di Bari, Bari, Italy^64cPolitecnico di Bari, Bari, Italy^65aINFN Sezione di Bologna, Bologna, Italy^65bUniversità di Bologna, Bologna, Italy^66aINFN Sezione di Catania, Catania, Italy^66bUniversità di Catania, Catania, Italy^67aINFN Sezione di Firenze, Firenze, Italy^67bUniversità di Firenze, Firenze, Italy⁶⁸INFN Laboratori Nazionali di Frascati, Frascati, Italy^69aINFN Sezione di Genova, Genova, Italy^69bUniversità di Genova, Genova, Italy^70aINFN Sezione di Milano-Bicocca, Milano, Italy^70bUniversità di Milano-Bicocca, Milano, Italy^71aINFN Sezione di Napoli’, Napoli, Italy^71bUniversità di Napoli ’Federico II’’, Napoli, Italy^71cUniversità della Basilicata, Potenza, Italy^71dUniversità G. Marconi, Roma, Italy^72aINFN Sezione di Padova, Padova, Italy^72bUniversità di Padova, Padova, Italy^72cUniversità di Trento, Trento, Italy^73aINFN Sezione di Pavia, Pavia, Italy^73bUniversità di Pavia, Pavia, Italy^74aINFN Sezione di Perugia, Perugia, Italy^74bUniversità di Perugia, Perugia, Italy^75aINFN Sezione di Pisa, Pisa, Italy^75bUniversità di Pisa, Pisa, Italy^75cScuola Normale Superiore di Pisa, Pisa, Italy^76aINFN Sezione di Roma, Rome, Italy^76bSapienza Università di Roma, Rome, Italy^77aINFN Sezione di Torino, Torino, Italy^77bUniversità di Torino, Torino, Italy^77cUniversità del Piemonte Orientale, Novara, Italy^78aINFN Sezione di Trieste, Trieste, Italy^78bUniversità di Trieste, Trieste, Italy⁷⁹Kyungpook National University, Daegu, Korea⁸⁰Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea⁸¹Hanyang University, Seoul, Korea⁸²Korea University, Seoul, Korea⁸³Sejong University, Seoul, Korea⁸⁴Seoul National University, Seoul, Korea⁸⁵University of Seoul, Seoul, Korea⁸⁶Sungkyunkwan University, Suwon, Korea⁸⁷Riga Technical University, Riga, Latvia⁸⁸Vilnius University, Vilnius, Lithuania⁸⁹National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia⁹⁰Universidad de Sonora (UNISON), Hermosillo, Mexico⁹¹Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico⁹²Universidad Iberoamericana, Mexico City, Mexico⁹³Benemerita Universidad Autonoma de Puebla, Puebla, Mexico⁹⁴Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico⁹⁵University of Auckland, Auckland, New Zealand⁹⁶University of Canterbury, Christchurch, New Zealand⁹⁷National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan⁹⁸National Centre for Nuclear Research, Swierk, Poland⁹⁹Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland¹⁰⁰Laboratório de Instrumentação e Física Experimental de Partículas, Lisboa, Portugal¹⁰¹Joint Institute for Nuclear Research, Dubna, Russia¹⁰²Petersburg Nuclear Physics Institute, Gatchina (St. Petersburg), Russia¹⁰³Institute for Nuclear Research, Moscow, Russia¹⁰⁴Institute for Theoretical and Experimental Physics, Moscow, Russia¹⁰⁵Moscow Institute of Physics and Technology, Moscow, Russia¹⁰⁶National Research Nuclear University ’Moscow Engineering Physics Institute’ (MEPhI), Moscow, Russia¹⁰⁷P.N. Lebedev Physical Institute, Moscow, Russia¹⁰⁸Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia¹⁰⁹Novosibirsk State University (NSU), Novosibirsk, Russia¹¹⁰Institute for High Energy Physics of National Research Centre ’Kurchatov Institute’, Protvino, Russia¹¹¹National Research Tomsk Polytechnic University, Tomsk, Russia¹¹²University of Belgrade, Faculty of Physics and Vinca Institute of Nuclear Sciences, Belgrade, Serbia¹¹³Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain¹¹⁴Universidad Autónoma de Madrid, Madrid, Spain¹¹⁵Universidad de Oviedo, Oviedo, Spain¹¹⁶Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain¹¹⁷University of Ruhuna, Department of Physics, Matara, Sri Lanka¹¹⁸CERN, European Organization for Nuclear Research, Geneva, Switzerland¹¹⁹Paul Scherrer Institut, Villigen, Switzerland¹²⁰ETH Zurich - Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland¹²¹Universität Zürich, Zurich, Switzerland¹²²National Central University, Chung-Li, Taiwan¹²³National Taiwan University (NTU), Taipei, Taiwan¹²⁴Chulalongkorn University, Faculty of Science, Department of Physics, Bangkok, Thailand¹²⁵Çukurova University, Physics Department, Science and Art Faculty, Adana, Turkey¹²⁶Middle East Technical University, Physics Department, Ankara, Turkey¹²⁷Bogazici University, Istanbul, Turkey¹²⁸Istanbul Technical University, Istanbul, Turkey¹²⁹Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkov, Ukraine¹³⁰National Scientific Center, Kharkov Institute of Physics and Technology, Kharkov, Ukraine¹³¹University of Bristol, Bristol, United Kingdom¹³²Rutherford Appleton Laboratory, Didcot, United Kingdom¹³³Imperial College, London, United Kingdom¹³⁴Brunel University, Uxbridge, United Kingdom¹³⁵Baylor University, Waco, Texas, USA¹³⁶Catholic University of America, Washington, DC, USA¹³⁷The University of Alabama, Tuscaloosa, Alabama, USA¹³⁸Boston University, Boston, Massachusetts, USA¹³⁹Brown University, Providence, Rhode Island, USA¹⁴⁰University of California, Davis, Davis, California, USA¹⁴¹University of California, Los Angeles, California, USA¹⁴²University of California, Riverside, Riverside, California, USA¹⁴³University of California, San Diego, La Jolla, California, USA¹⁴⁴University of California, Santa Barbara - Department of Physics, Santa Barbara, California, USA¹⁴⁵California Institute of Technology, Pasadena, California, USA¹⁴⁶Carnegie Mellon University, Pittsburgh, Pennsylvania, USA¹⁴⁷University of Colorado Boulder, Boulder, Colorado, USA¹⁴⁸Cornell University, Ithaca, New York, USA¹⁴⁹Fermi National Accelerator Laboratory, Batavia, Illinois, USA¹⁵⁰University of Florida, Gainesville, Florida, USA¹⁵¹Florida International University, Miami, Florida, USA¹⁵²Florida State University, Tallahassee, Florida, USA¹⁵³Florida Institute of Technology, Melbourne, Florida, USA¹⁵⁴University of Illinois at Chicago (UIC), Chicago, Illinois, USA¹⁵⁵The University of Iowa, Iowa City, Iowa, USA¹⁵⁶Johns Hopkins University, Baltimore, Maryland, USA¹⁵⁷The University of Kansas, Lawrence, Kansas, USA¹⁵⁸Kansas State University, Manhattan, Kansas, USA¹⁵⁹Lawrence Livermore National Laboratory, Livermore, California, USA¹⁶⁰University of Maryland, College Park, Maryland, USA¹⁶¹Massachusetts Institute of Technology, Cambridge, Massachusetts, USA¹⁶²University of Minnesota, Minneapolis, Minnesota, USA¹⁶³University of Mississippi, Oxford, Mississippi, USA¹⁶⁴University of Nebraska-Lincoln, Lincoln, Nebraska, USA¹⁶⁵State University of New York at Buffalo, Buffalo, New York, USA¹⁶⁶Northeastern University, Boston, Massachusetts, USA¹⁶⁷Northwestern University, Evanston, Illinois, USA¹⁶⁸University of Notre Dame, Notre Dame, Indiana, USA¹⁶⁹The Ohio State University, Columbus, Ohio, USA¹⁷⁰Princeton University, Princeton, New Jersey, USA¹⁷¹University of Puerto Rico, Mayaguez, Puerto Rico¹⁷²Purdue University, West Lafayette, Indiana, USA¹⁷³Purdue University Northwest, Hammond, Indiana, USA¹⁷⁴Rice University, Houston, Texas, USA¹⁷⁵University of Rochester, Rochester, New York, USA¹⁷⁶Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA¹⁷⁷University of Tennessee, Knoxville, Tennessee, USA¹⁷⁸Texas A&M University, College Station, Texas, USA¹⁷⁹Texas Tech University, Lubbock, Texas, USA¹⁸⁰Vanderbilt University, Nashville, Tennessee, USA¹⁸¹University of Virginia, Charlottesville, Virginia, USA¹⁸²Wayne State University, Detroit, Michigan, USA¹⁸³University of Wisconsin - Madison, Madison, Wisconsin, USA^*

Full author list given at the end of the article.

^a

Deceased.

^b

Also at Vienna University of Technology, Vienna, Austria.

^c

Also at IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France.

^d

Also at Universidade Estadual de Campinas, Campinas, Brazil.

^e

Also at Federal University of Rio Grande do Sul, Porto Alegre, Brazil.

^f

Also at Université Libre de Bruxelles, Bruxelles, Belgium.

^g

Also at University of Chinese Academy of Sciences, Beijing, China.

^h

Also at Institute for Theoretical and Experimental Physics, Moscow, Russia.

ⁱ

Also at Joint Institute for Nuclear Research, Dubna, Russia.

^j

Also at Helwan University, Cairo, Egypt.

^k

Also at Zewail City of Science and Technology, Zewail, Egypt.

^l

Also at British University in Egypt, Cairo, Egypt.

^m

Also at Suez University, Suez, Egypt.

ⁿ

Also at Department of Physics, King Abdulaziz University, Jeddah, Saudi Arabia.

^o

Also at Université de Haute Alsace, Mulhouse, France.

^p

Also at Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia.

^q

Also at CERN, European Organization for Nuclear Research, Geneva, Switzerland.

^r

Also at RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany.

^s

Also at University of Hamburg, Hamburg, Germany.

^t

Also at Brandenburg University of Technology, Cottbus, Germany.

^u

Also at Institute of Physics, University of Debrecen, Debrecen, Hungary.

^v

Also at Institute of Nuclear Research ATOMKI, Debrecen, Hungary.

^w

Also at MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary.

^x

Also at IIT Bhubaneswar, Bhubaneswar, India.

^y

Also at Institute of Physics, Bhubaneswar, India.

^z

Also at Shoolini University, Solan, India.

^aa

Also at University of Visva-Bharati, Santiniketan, India.

^bb

Also at Isfahan University of Technology, Isfahan, Iran.

^cc

Also at Plasma Physics Research Center, Science and Research Branch, Islamic Azad University, Tehran, Iran.

^dd

Also at Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Bologna, Italy.

^ee

Also at Università degli Studi di Siena, Siena, Italy.

^ff

Also at Scuola Normale e Sezione dell’INFN, Pisa, Italy.

^gg

Also at Kyunghee University, Seoul, Korea.

^hh

Also at Riga Technical University, Riga, Latvia.

ⁱⁱ

Also at International Islamic University of Malaysia, Kuala Lumpur, Malaysia.

^jj

Also at Malaysian Nuclear Agency, MOSTI, Kajang, Malaysia.

^kk

Also at Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico.

^ll

Also at Warsaw University of Technology, Institute of Electronic Systems, Warsaw, Poland.

^mm

Also at Institute for Nuclear Research, Moscow, Russia.

ⁿⁿ

Also at National Research Nuclear University ’Moscow Engineering Physics Institute’ (MEPhI), Moscow, Russia.

^oo

Also at St. Petersburg State Polytechnical University, St. Petersburg, Russia.

^pp

Also at University of Florida, Gainesville, Florida, USA.

^qq

Also at P.N. Lebedev Physical Institute, Moscow, Russia.

^rr

Also at California Institute of Technology, Pasadena, California, USA.

^ss

Also at Budker Institute of Nuclear Physics, Novosibirsk, Russia.

^tt

Also at Faculty of Physics, University of Belgrade, Belgrade, Serbia.

^uu

Also at University of Belgrade, Faculty of Physics and Vinca Institute of Nuclear Sciences, Belgrade, Serbia.

^vv

Also at INFN Sezione di Pavia, Università di Pavia, Pavia, Italy.

^ww

Also at National and Kapodistrian University of Athens, Athens, Greece.

^xx

Also at Universität Zürich, Zurich, Switzerland.

^yy

Also at Stefan Meyer Institute for Subatomic Physics, Vienna, Austria.

^zz

Also at Adiyaman University, Adiyaman, Turkey.

^aaa

Also at Istanbul Aydin University, Istanbul, Turkey.

^bbb

Also at Mersin University, Mersin, Turkey.

^ccc

Also at Piri Reis University, Istanbul, Turkey.

^ddd

Also at Gaziosmanpasa University, Tokat, Turkey.

^eee

Also at Ozyegin University, Istanbul, Turkey.

^fff

Also at Izmir Institute of Technology, Izmir, Turkey.

^ggg

Also at Marmara University, Istanbul, Turkey.

^hhh

Also at Kafkas University, Kars, Turkey.

ⁱⁱⁱ

Also at Istanbul University, Faculty of Science, Istanbul, Turkey.

^jjj

Also at Istanbul Bilgi University, Istanbul, Turkey.

^kkk

Also at Hacettepe University, Ankara, Turkey.

^lll

Also at Rutherford Appleton Laboratory, Didcot, United Kingdom.

^mmm

Also at School of Physics and Astronomy, University of Southampton, Southampton, United Kingdom.

ⁿⁿⁿ

Also at Monash University, Faculty of Science, Clayton, Australia.

^ooo

Also at Bethel University, St. Paul, Minneapolis, USA.

^ppp

Also at Karamanoğlu Mehmetbey University, Karaman, Turkey.

^qqq

Also at Purdue University, West Lafayette, Indiana, USA.

^rrr

Also at Beykent University, Istanbul, Turkey.

^sss

Also at Bingol University, Bingol, Turkey.

^ttt

Also at Sinop University, Sinop, Turkey.

^uuu

Also at Mimar Sinan University, Istanbul, Istanbul, Turkey.

^vvv

Also at Texas A&M University at Qatar, Doha, Qatar.

^www

Also at Kyungpook National University, Daegu, Korea.

^xxx

Also at University of Hyderabad, Hyderabad, India.

11June20191June201999111120031January2019© 2019 CERN, for the CMS Collaboration2019CERNPublished by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Studies of on-shell and off-shell Higgs boson production in the four-lepton final state are presented, using data from the CMS experiment at the LHC that correspond to an integrated luminosity of 80.2  fb-1 at a center-of-mass energy of 13 TeV. Joint constraints are set on the Higgs boson total width and parameters that express its anomalous couplings to two electroweak vector bosons. These results are combined with those obtained from the data collected at center-of-mass energies of 7 and 8 TeV, corresponding to integrated luminosities of 5.1 and 19.7  fb-1, respectively. Kinematic information from the decay particles and the associated jets are combined using matrix element techniques to identify the production mechanism and to increase sensitivity to the Higgs boson couplings in both production and decay. The constraints on anomalous HVV couplings are found to be consistent with the standard model expectation in both the on-shell and off-shell regions. Under the assumption of a coupling structure similar to that in the standard model, the Higgs boson width is constrained to be 3.2-2.2+2.8  MeV while the expected constraint based on simulation is 4.1-4.0+5.0  MeV. The constraints on the width remain similar with the inclusion of the tested anomalous HVV interactions.

Bundesministerium für Wissenschaft, Forschung und Wirtschaft10.13039/501100003413Austrian Science Fund10.13039/501100002428Fonds De La Recherche Scientifique - FNRS10.13039/501100002661Fonds Wetenschappelijk Onderzoek10.13039/50110000313030820817Conselho Nacional de Desenvolvimento Científico e Tecnológico10.13039/501100003593Coordenação de Aperfeiçoamento de Pessoal de Nível Superior10.13039/501100002322Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro10.13039/501100004586Fundação de Amparo à Pesquisa do Estado de São Paulo10.13039/501100001807Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul10.13039/501100004263Ministry of Education and Science10.13039/501100005992CERN [Conseil Européen pour la Recherche Nucléaire]Chinese Academy of Sciences10.13039/501100002367Ministry of Science and Technology of the People’s Republic of China10.13039/501100002855National Natural Science Foundation of China10.13039/501100001809Departamento Administrativo de Ciencia, Tecnología e Innovación10.13039/100007637Ministarstvo Znanosti, Obrazovanja i Sporta10.13039/501100006588Hrvatska Zaklada za Znanost10.13039/501100004488Research Promotion Foundation10.13039/501100001810Secretaría de Educación Superior, Ciencia, Tecnología e Innovación10.13039/501100004299MoERH2020 European Research Council10.13039/100010663IUTEuropean Regional Development Fund10.13039/501100008530Academy of Finland10.13039/501100002341Finnish Ministry of Education and Culture (MEC), (Finland)Helsinki Institute of Physics (Finland)Commissariat à l’Énergie Atomique et aux Énergies Alternatives10.13039/501100006489Centre National de la Recherche Scientifique10.13039/501100004794Bundesministerium für Bildung und Forschung10.13039/501100002347Deutsche Forschungsgemeinschaft10.13039/501100001659Helmholtz-Gemeinschaft10.13039/501100001656General Secretariat for Research and Technology10.13039/501100003448NKFIA123842123959124845124850125105Department of Atomic Energy, Government of India10.13039/501100001502Department of Science and Technology, Ministry of Science and Technology10.13039/501100001409Institute for Research in Fundamental Sciences10.13039/501100006115Science Foundation Ireland10.13039/501100001602Instituto Nazionale di Fisica Nucleare10.13039/501100004007Ministry of Science, ICT and Future Planning10.13039/501100003621National Research Foundation of Korea10.13039/501100003725Lietuvos Moksl Akademija10.13039/501100008523Ministry of Higher Education, Malaysia10.13039/501100003093Universiti Malaya10.13039/501100004386Benemérita Universidad Autónoma de Puebla10.13039/501100006348Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional10.13039/501100008688Consejo Nacional de Ciencia y Tecnología10.13039/501100003141Laboratorio Nacional de Supercómputo del Sureste (Mexico)Secretaría de Educación Pública10.13039/100010096Universidad Autónoma de San Luis Potosí10.13039/501100005324Ministry of Science (Montenegro)Ministry of Business, Innovation and Employment10.13039/501100003524Pakistan Atomic Energy Commission10.13039/501100008689Ministerstwo Nauki i Szkolnictwa Wy?szego10.13039/501100004569National Science Center2014/14/M/ST2/004282014/13/B/ST2/025432014/15/B/ST2/039982015/19/B/ST2/02861, Sonata-bis 2012/07/E/ST2/01406Fundação para a Ciência e a Tecnologia10.13039/501100001871Joint Institute for Nuclear Research10.13039/501100003822Ministry of Education and Science of the Russian Federation10.13039/501100003443State Atomic Energy Corporation ROSATOM10.13039/501100008687Russian Academy of Sciences10.13039/501100002674Russian Foundation for Basic Research10.13039/501100002261NRC KIMinistarstvo Prosvete, Nauke i Tehnološkog Razvoja10.13039/501100004564CPANPCTIMinistry of Science,Technology and Research10.13039/501100008981Swiss Funding Agencies (Switzerland)Ministry of Science and Technology, Taiwan10.13039/501100004663Thailand Center of Excellence in Physics10.13039/100012863IPSTSTARNational Science and Technology Development Agency10.13039/501100004192Türkiye Bilimsel ve Teknolojik Ara?tirma Kurumu10.13039/501100004410Türkiye Atom Enerjisi Kurumu10.13039/100010440State Fund for Fundamental Research of Ukraine10.13039/501100008690Science and Technology Facilities Council10.13039/501100000271U.S. Department of Energy10.13039/100000015National Science Foundation10.13039/100000001H2020 Marie Sk?odowska-Curie Actions10.13039/100010665Seventh Framework Programme10.13039/100011102675440A.G. 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The standard model (SM) of particle physics postulates the existence of a Higgs field responsible for the generation of the masses of fundamental particles. The excitation of this field is known as the Higgs boson (H) [1–7]. The observation of an H boson with a mass of around 125 GeV by the ATLAS and CMS Collaborations [8–10] is consistent with the expectations of the SM, but further tests of the properties of this particle, such as its width and the structure of its couplings to the known SM particles, are needed to determine its nature.

The CMS and ATLAS experiments have set constraints of ΓH<13  MeV at 95% confidence level (C.L.) on the H boson total width [11–15] using the off-shell production method [16–18], which relies on the relative measurement of off-shell and on-shell production. The upper bound on ΓH was set considering the gluon fusion and electroweak (EW) production mechanisms in the analysis. The precision on ΓH from on-shell measurements of the width of the resonance peak alone is approximately 1 GeV [19–21], which is significantly worse than the result from the off-shell method. The constraint on the H boson lifetime is equivalent to a lower bound on the width and was derived from the flight distance in the CMS detector as ΓH>3.5×10-9  MeV at 95% C.L. [13]. The SM expectation of the width of the H boson is around 4 MeV [22].

The CMS [13,23–27] and ATLAS [28–33] experiments have set constraints on the spin-parity properties and anomalous couplings of the H boson, finding its quantum numbers to be consistent with JPC=0++, but allowing small anomalous couplings to two EW gauge bosons (anomalous HVV couplings). Off-shell signal production may be enhanced in the presence of these anomalous HVV couplings [11,13,22,34–36]. As a result, the measurement of ΓH using the off-shell technique may be affected by these deviations of the H boson couplings from the SM expectations. An attempt to measure ΓH using the off-shell technique while including anomalous HVV interactions has been made by the CMS experiment [13]. In that previous study, constraints are placed on ΓH and the on-shell cross-section fraction fΛQ that expresses an anomalous coupling contribution sensitive to the invariant mass of the H boson, using a realistic treatment of interference between the H boson signal and the continuum background. Extending the application of the off-shell technique to a wider range of anomalous HVV contributions, studied previously using on-shell H boson production [27], is the goal of this paper.

The presented investigation on the H boson width targets both gluon fusion and EW production mechanisms and tests the effects of possible anomalous HVV couplings in either production or decay. Nevertheless, it still relies on the knowledge of coupling ratios between the off-shell and on-shell production, the dominance of the top quark loop in the gluon fusion production mechanism, and the absence of new particle contributions in the loop. A violation of the last assumption by itself would be a manifestation of physics beyond the SM (BSM), which may become evident if the measured width deviates from the SM expectation. The measured width may also deviate from the SM expectation if the H boson has new BSM decay channels or the known channels have non-SM rates. Therefore, the measurement of the width complements the search for H boson decay to invisible or undetected particles, and the measurement of the H boson couplings to the known SM particles.

The data sample used in this analysis corresponds to integrated luminosities of 35.9  fb-1 collected in 2016 and 41.5  fb-1 collected in 2017 during Run 2 of the CERN LHC at a center-of-mass energy of 13 TeV. These results are combined with results obtained earlier from the data collected at center-of-mass energies of 7 TeV (in 2011), 8 TeV (in 2012), and 13 TeV (in 2015), corresponding to integrated luminosities of 5.1, 19.7, and 2.7  fb-1, respectively [25,27]. The increase in either energy and integrated luminosity leads to substantial improvement in the precision of the width measurement using the off-shell technique, either under the assumption of SM couplings or with BSM effects.

This analysis follows closely the general H→4ℓ (leptons ℓ=e or μ) selection and reconstruction documented in Ref. [21] using the data collected in 2016, and the on-shell study of anomalous HVV couplings with the combined 2015 and 2016 data set in Ref. [27]. Many of the technical details of the search for a scalar resonance X→ZZ at high mass in Run 2 data, documented in Ref. [37], are also shared in the analyses presented here. The rest of the paper is organized as follows. The phenomenology of anomalous HVV interactions is discussed in Sec. II. The CMS detector, reconstruction techniques, and Monte Carlo (MC) simulation methods are introduced in Sec. III. The addition of the 2017 data to that used in Refs. [21,27], and the relevant differences in the detector and reconstruction techniques are also discussed in this section. The details of the analysis are discussed in Secs. IV and V, and the results are presented in Sec. VI. We provide a summary of these results in Sec. VII.

II.

The constraints on ΓH are set using the off-shell production method, which considers the H boson production relationship between the on-shell (105<m4ℓ<140  GeV) and off-shell (m4ℓ>220  GeV) regions. Denoting each production mechanism with vv→H→VV→4ℓ for the H boson coupling to either strong (vv=gg) or EW (vv=WW,ZZ,Zγ,γγ) vector bosons in its production, the on-shell and off-shell H boson signal yields are related by [16] σvv→H→4ℓon-shell∝μvvHandσvv→H→4ℓoff-shell∝μvvHΓH,(1)where μvvH is defined as the on-shell signal strength, the ratio of the observed number of on-shell four-lepton events relative to the SM expectation. This ratio is interpreted as either μF for H boson production via gluon fusion (ggH) or in association with a tt¯ (tt¯H) or bb¯ pair (bb¯H), or μV for H boson production via vector boson fusion (VBF) or in association with an EW vector boson W or Z (VH). There is sizable interference between the H boson signal and the continuum background in the off-shell region [17], contrary to on-shell production, and this formalism scales the interference contribution with μvvHΓH.

This analysis is based on a phenomenological framework [22,38–59] that describes the anomalous couplings of a Higgs-like boson to two gauge bosons, such as WW,ZZ,Zγ,γγ, and gg. These couplings appear in either the production of the H boson or its decay, regardless of the m4ℓ region in which the H boson is produced. The relationship in Eq. (1) is therefore meant to imply concurrent variations in vvH couplings in both on-shell and off-shell regions. The coupling of the H boson to two gluons is assumed to be as in the SM, via quark loops with Yukawa couplings to quarks, where the contribution from the top-quark is dominant. This assumption is valid as long as the production is dominated by the top-quark loop and no new particles contribute to this loop. The Yukawa couplings also appear in direct interactions with fermion-antifermion pairs, such as in tt¯H and bb¯H productions. These interactions are of less importance in this study, since they are highly suppressed at high off-shell mass, but they are included in the analysis of the on-shell H boson production with similar assumptions as in the case of production via gluon fusion. Variation of the HVV couplings, in either the VBF or VH productions, or the H→4ℓ decay, are allowed to depend on anomalous coupling contributions.

In the following, we assume that the H boson couples to two gauge bosons VV, such as WW, ZZ, Zγ or γγ, which in turn couple to fermions, either four leptons in H boson decay, or quarks or leptons in its production or in the decay of associated EW bosons. It is assumed that the H boson does not couple to fermions through a new heavy state, generating a so-called contact interaction [57,58]. However, the inclusion of amplitude terms pertaining to contact interactions is equivalent to the anomalous HVV couplings already tested [25] under the assumption of flavor universality in Vff¯ couplings. Both approaches test three general tensor structures allowed by Lorentz symmetry, with form factors Fi(q12,q22) in front of each term, where q1 and q2 are the four-momenta of the two difermion states, such as (e+e-) and (μ+μ-) in the H→e+e-μ+μ- decay, and equivalent states in production. We also fix all lepton and quark couplings to vector bosons according to SM expectations. Relaxing this requirement would make it equivalent to flavor nonuniversal couplings of the contact terms, but would also introduce too many unconstrained parameters, which cannot be tested with the present data sample. Only the lowest order operators, or lowest order terms in the (qj2/Λ2) form-factor expansion, are tested, where Λ is the energy scale of new physics.

The signal scattering amplitude describing the interaction between a spin-zero H boson and two spin-one gauge bosons VV is written as [54] A∼[a1VV-κ1VVq12+κ2VVq22(Λ1VV)2-κ3VV(q1+q2)2(ΛQVV)2]mV12εV1*εV2*+a2VVfμν*(1)f*(2)μν+a3VVfμν*(1)f˜*(2)μν.(2)In this expression of the scattering amplitude, εi is the polarization vector of gauge boson Vi, f(i)μν=εiμqiν-εiνqiμ is a scalar tensor constructed from this polarization vector and the momentum of the gauge boson, and f˜μν(i)=12εμνρσf(i)ρσ is the pseudoscalar tensor counterpart. When at least one of the gauge bosons V is massive, mV1 is the pole mass of that gauge boson. The scales of BSM physics are denoted with Λ1 and ΛQ, so aiVV, or 1/Λ1 and 1/ΛQ, become the coupling-strength modifiers of the relevant HVV amplitudes, where aiVV may in general be any complex number, and |κ1,2,3VV|=0 or 1 are complex numbers. Under the assumption that the couplings are constant and real, the above formulation is equivalent to an effective Lagrangian notation. Therefore, in this paper, the real coupling constants are tested. The above approach allows a sufficiently general test of the H→4ℓ kinematics in decay and equivalent kinematics in production, as discussed below, including production and decay of virtual intermediate photons. If deviations from the SM are detected, a more detailed study of Fi(q12,q22) could be performed, eventually providing a measurement of the double-differential cross section for each tensor structure tested.

In the above, the only leading tree-level contributions are a1ZZ≠0 and a1WW≠0, and in the following we assume the custodial symmetry a1ZZ=a1WW. The rest of the couplings are considered anomalous contributions, which are either tiny contributions arising in the SM due to loop effects or new BSM contributions. The SM loop contributions are not accessible experimentally with the available data. Among anomalous contributions, considerations of symmetry and gauge invariance require κ1ZZ=κ2ZZ=-exp(iϕΛ1ZZ), κ1γγ=κ2γγ=0, κ1gg=κ2gg=0, κ1Zγ=0, and κ2Zγ=-exp(iϕΛ1Zγ). While not strictly required, the same symmetry is considered in the WW case κ1WW=κ2WW=-exp(iϕΛ1WW).

Neither HZγ nor Hγγ couplings produce a sizable off-shell enhancement, since there is no interplay between the vector bosons or the H boson going off-shell, and there is no off-shell threshold for these couplings. Therefore, off-shell treatment for these couplings can be ignored. While the a2,3Zγ and a2,3γγ terms are tested in the Run 1 analysis [25], the precision of those constraints is still not competitive with the on-shell photon measurements in H→Zγ and γγ. Therefore, we omit those measurements in this paper. The Λ1Zγ coupling, on the other hand, can only be observed with off-shell photons decaying to a pair of fermions, so it is considered in the on-shell analysis. The ΛQ term depends only on the invariant mass of the H boson, so its contribution is not distinguishable from the SM in the on-shell region and is only testable through the off-shell region. Tight constraints are already set on this parameter in the Run 1 analysis [13], so it is also not considered in this paper.

In the following, the ZZ labels for the ZZ interactions are omitted, and we use a generic notation ai to denote a3, a2, 1/Λ1, and 1/Λ1Zγ, which are the four couplings tested in this paper as listed in Table I. Furthermore, the WW measurements are integrated into the ZZ measurements assuming aiZZ=aiWW. The HWW contributions appear in the VBF and WH productions. This assumption does not affect the kinematic analysis of events because there is very little difference in kinematic distributions in events initiated by either WW or ZZ fusion. However, this assumption may affect the interpretation of the results should a different relationship between aiZZ and aiWW be assumed. Therefore, such a scenario is discussed in more detail below by introducing the parameter rai, following Ref. [25], as rai=aiWW/a1WWai/a1.(3)Including the parameter rai in the probability parametrization despite the lack of sensitivity of the data would introduce complexity without a comparable gain in physics content. We proceed with the analysis assuming rai=1, but point out below how results could be reinterpreted should a different value be assumed.

I10.1103/PhysRevD.99.112003.t1TABLE I.

List of the anomalous HVV couplings considered in the measurements assuming a spin-zero H boson. The definition of the effective fractions fai is discussed in the text and the translation constants are the cross-section ratios corresponding to the processes H→2e2μ with the H boson mass mH=125  GeV and calculated using JHUGen [47,50,54].

Anomalous couplingCoupling phaseEffective fractionTranslation constanta3ϕa3fa3σ1/σ3=6.53a2ϕa2fa2σ1/σ2=2.77Λ1ϕΛ1fΛ1σ1/σ˜Λ1=1.47×104  TeV-4Λ1ZγϕΛ1ZγfΛ1Zγσ1/σ˜Λ1Zγ=5.80×103  TeV-4

Most systematic uncertainties cancel when taking ratios to the total cross section, so measurements of ai relative to the dominant SM-like contribution a1 are the preferred approach. For this purpose, the effective fractional ZZ cross sections fai and phases ϕai are defined as fai=|ai|2σi∑j=1,2,3…|aj|2σj,ϕai=arg(aia1),(4)where σi is the cross section for the process corresponding to ai=1, aj≠i=0, while σ˜Λ1 is the effective cross section for the process corresponding to Λ1=1  TeV, given in units of fb TeV4. The cross-section ratios are quoted in Table I. The ai/a1 ratios can be obtained from the ratio fai/fa1, the cross-section ratios, and the phase ϕai as aia1=faifa1σ1σieiϕai.(5)The effective fractions fai are bounded between 0 and 1 and do not depend on the coupling convention. In most cases, uncertainties on these measurements scale with integrated luminosity as 1/L until effects of interference become important. Furthermore, the values of fai have a simple interpretation as the fractional size of the BSM contribution for the H→2e2μ decay. For example, fai=0 indicates a pure SM-like H boson, fai=1 gives a pure BSM particle, and fai=0.5 means that the two couplings contribute equally to the H→2e2μ process.

As mentioned above in application to Eq. (3), the measurement of fai is performed under the rai=1 assumption. Let us denote this to be an effective faieff. Without such an assumption, there is a certain dependence of fai on rai and faieff, such that fai=faieff for rai=1. This dependence is different for different processes, such as VBF production or H→4ℓ decay, where the latter case is in fact independent of rai because the HWW coupling does not affect this decay process. In the former case, let us consider the relative contributions of WW and ZZ fusion on-shell. For example, the ratio of VBF cross sections driven by WW and ZZ fusion is σ1WW/σ1ZZ=2.59 for the SM tree-level couplings under custodial symmetry a1WW=a1ZZ at 13 TeV pp collision energy. The same ratio for the CP-odd couplings is σ3WW/σ3ZZ=3.15, where σ3VV are calculated for a3WW=a3ZZ. The dependence of fai on rai and faieff, as measured in the VBF process, becomes fai=[1+(1/faieff-1)(σiZZ+rai2σiWW)/(σiZZ+σiWW)]-1,(6)where custodial symmetry a1WW=a1ZZ is assumed and the effects of interference between WW and ZZ fusion are negligible and are therefore ignored.

All of the above discussion, including Eq. (2), describes the production of a resonance via gluon fusion, VBF with associated jets, or associated production with an EW vector boson, VH. These mechanisms, along with the tt¯H and bb¯H production, are considered in the analysis of the spin-zero hypothesis of the H boson, where the gluon fusion production is expected to dominate. It is possible to study HVV interactions using the kinematics of particles produced in association with the H boson, such as VBF jets or vector boson daughters in VH production, as we show below. More details can be found in, e.g., Ref. [54] and the experimental application in Refs. [26,27]. While the qi2 range in the HVV process does not exceed approximately 100 GeV because of the kinematic bound, no such bound exists in the associated production, so consideration of more restricted qi2 ranges might be required [54]. However, we only consider that the qi2 range is not restricted in the allowed phase space.

III.

The H→4ℓ decay candidates are reconstructed in the CMS detector [60]. The CMS detector is comprised of a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass/scintillator hadron calorimeter, each composed of a barrel and two end cap sections, all within a superconducting solenoid of 6m internal diameter, providing a magnetic field of 3.8 T. Extensive forward calorimetry complements the coverage provided by the barrel and end cap detectors. Outside the solenoid are the gas-ionization detectors for muon measurements, which are embedded in the steel flux-return yoke. A detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [60].

The JHUGen 7.0.2 [47,50,54,59] Monte Carlo (MC) program is used to simulate anomalous couplings in the H boson production and H→ZZ/Zγ*/γ*γ*→4ℓ decay. The gluon fusion production is simulated with the powheg 2 [61–65] event generator at next-to-leading order (NLO) in QCD, and simulation with the minlo [66] program at NLO in QCD is used for evaluation of systematic uncertainties related to modeling of two associated jets. The kinematics of events produced in gluon fusion with two associated jets are also modified by anomalous Hgg couplings. These effects are studied using JHUGen, and it is found that the kinematic distributions relevant for this analysis are not affected significantly.

The production of the H boson through VBF, in association with a W or Z boson, or with a tt¯ pair, is simulated using both JHUGen at LO in QCD and powheg at NLO in QCD. Production in association with a bb¯ pair is simulated only at LO in QCD via JHUGen. In the VBF, VH, and tt¯H production modes, the JHUGen and powheg simulations are explicitly compared after parton showering in the SM case, and no significant differences are found in kinematic observables. Therefore, the JHUGen simulation is adopted to describe kinematics in the VBF, VH, and tt¯H production modes with anomalous couplings in the on-shell region, with expected yields taken from the powheg simulation. The powheg program is used to simulate wide resonances at masses ranging from 115 GeV to 3 TeV, produced in gluon fusion, VBF, or VH. The events from the powheg simulation are later reweighted using the package for the matrix element likelihood approach (mela) [9,47,50,54,59] to model off-shell H boson production distributions, as discussed below.

The gg→ZZ/Zγ*→4ℓ background process is simulated with mcfm 7.0.1 [18,67–69]. The vector boson scattering and triple-gauge-boson (VVV) backgrounds are obtained by reweighting the powheg simulation with the matrix elements provided by the mela package using the mcfm and JHUGen matrix elements, and the reweighted simulation is checked against the predictions of the phantom 1.3 [70] simulation. Both the mcfm and phantom generators allow one to model the H boson signal, background, and their interference in the off-shell production. However, they do not allow modeling of the anomalous interactions considered in this analysis. Therefore, a combined program has been developed for both gluon fusion and VBF with triple-gauge-boson production based on the modeling of signal and background scattering amplitudes from mcfm and anomalous contributions in the signal scattering amplitude from JHUGen. This program is included within the JHUGen and mela packages, as detailed in Ref. [22]. A large number of MC events with anomalous couplings in the signal and their interference with background have been generated with these packages. The simulated events also include alternative weights to model various anomalous couplings in the signal.

In the gluon fusion process, the factorization and renormalization scales are chosen to be running as m4ℓ/2. In order to include higher-order QCD corrections, LO, NLO, and next-to-NLO (NNLO) signal cross-section calculations are performed using the mcfm and hnnlo 2 programs [71–73] for a wide range of masses using a narrow width approximation. The ratios between the NNLO and LO values (NNLO K factors) are used to reweight [22] the m4ℓ distributions from the mcfm and JHUGen simulation at LO in QCD, and a uniform factor of 1.10 across all of the m4ℓ range is applied to normalize the cross section of the H boson production via gluon fusion to the predictions for m4ℓ≈125  GeV at next-to-NNLO (N3LO) in QCD [22]. The simulated m4ℓ shapes or yields obtained from the powheg simulation of the gluon fusion process are corrected based on the above reweighted distributions. While the NNLO K factor calculation is directly applicable to the signal contribution, it is approximate for the background and its interference with the signal. The NLO calculation with some approximations [74–77] is available for the background and interference. Comparison with this calculation shows that while there is some increase of the NLO K factor for the interference close to the ZZ threshold, the NLO K factors for the background and interference are consistent with the signal within approximately 10% in the mass range m4ℓ>220  GeV relevant for this analysis. We therefore multiply the background and interference contributions by the same NNLO K factor and uniform N3LO correction, both calculated for signal and including associated uncertainties, and introduce an additional unit factor with a 10% uncertainty for the background and the square root of this factor for the interference.

The mela package contains a library of matrix elements from JHUGen and mcfm for the signal, and mcfm for the background, and is used to apply weights to events in any MC sample to model any other set of anomalous or SM couplings in either on-shell or off-shell production. This matrix element library also allows reweighting of the signal powheg simulation of the wide resonances at NLO in QCD in either gluon fusion, VBF, or triple-gauge-boson production to model the signal, background, or their interference.

The main background in this analysis, qq¯→ZZ/Zγ*→4ℓ, is estimated from simulation with powheg. A fully differential cross section has been computed at NNLO in QCD [78], but it is not yet available in a partonic level event generator. Therefore the NNLO/NLO QCD correction is applied as a function of m4ℓ. Additional NLO EW corrections are also applied to this background process in the region m4ℓ>2mZ [79,80]. The parton distribution functions (PDFs) used in this paper belong to the NNPDF 3.0 PDF sets [81]. All MC samples are interfaced to pythia 8 [82] for parton showering, using version 8.212 for the simulation of the 2016 data period and 8.230 for the simulation of the 2017 data period. Simulated events include the contribution from additional pp interactions within the same or adjacent bunch crossings (pileup), and are weighted to reproduce the observed pileup distribution. The MC samples are further processed through a dedicated simulation of the CMS detector based on Geant4 [83].

The selection of 4ℓ events and associated particles closely follows the methods used in the analyses of the Run 1 [24] and Run 2 [21] data sets. The main triggers for the Run 2 analysis select either a pair of electrons or muons, or an electron and a muon. The minimal transverse momentum of the leading electron (muon) is 23 (17) GeV, while that of the subleading lepton is 12 (8) GeV. To maximize the signal acceptance, triggers requiring three leptons with lower pT thresholds and no isolation requirement are also used, as are isolated single-electron and single-muon triggers with thresholds of 27 and 22 GeV in 2016, or 35 and 27 GeV in 2017, respectively. The overall trigger efficiency for simulated signal events that pass the full selection chain of this analysis is larger than 99%. The trigger efficiency is measured in data using a sample of 4ℓ events collected by the single-lepton triggers and is found to be consistent with the expectation from simulation.

Event reconstruction is based on the particle-flow (PF) algorithm [84], which exploits information from all the CMS subdetectors to identify and reconstruct individual particles in the event. The PF candidates are classified as charged hadrons, neutral hadrons, photons, electrons, or muons, and they are then used to build higher-level objects such as jets and lepton isolation quantities. Electrons (muons) are reconstructed within the geometrical acceptance defined by a requirement on the pseudorapidity |η|<2.5(2.4) for transverse momentum pT>7(5)  GeV with an algorithm that combines information from the ECAL (muon system) and the tracker. A dedicated algorithm is used to collect the final-state radiation (FSR) of leptons [21].

The reconstructed vertex with the largest value of summed physics-object pT2 is taken to be the primary pp interaction vertex. The physics objects are the jets and the associated missing transverse momentum, taken as the negative vector sum of the pT of those jets. The jets are clustered using the anti-kT jet finding algorithm [85,86] with a distance parameter of 0.4 and the associated tracks assigned to the vertex as inputs. Jets must satisfy pT>30  GeV and |η|<4.7 and must be separated from all selected lepton candidates and any selected FSR photons with a requirement on the distance parameter ΔR(ℓ/γ,jet)>0.4, where (ΔR)2=(Δϕ)2+(Δη)2. For event categorization, jets are tagged as b-jets using the Combined Secondary Vertex algorithm [87,88], which combines information about impact parameter significance, the secondary vertex, and jet kinematics.

Each lepton track is required to have the ratio of the impact parameter in three dimensions, which is computed with respect to the chosen primary vertex position, and its uncertainty to be less than 4. To discriminate between leptons from prompt Z boson decays and those arising from hadron decays within jets, an isolation requirement for leptons is imposed in the analysis of the 2016 data [21]. For electrons, the isolation variable is included as part of the multivariate training inputs for electron identification in 2017.

We consider three mutually exclusive channels: H→4e, 4μ, and 2e2μ. At least two leptons are required to have pT>10  GeV, and at least one is required to have pT>20  GeV. All four pairs of oppositely charged leptons that can be built with the four leptons are required to satisfy mℓ+ℓ′->4  GeV regardless of lepton flavor. The Z candidates are required to satisfy the condition 12<mℓ+ℓ-<120  GeV, where the invariant mass of at least one of the Z candidates must be larger than 40 GeV. The region between 105 and 140 GeV in the four-lepton invariant mass m4ℓ is identified as the on-shell region, and the region above 220 GeV is identified as the off-shell region.

Different sources of leptons such as the decays of heavy flavor jets or light mesons may produce additional background to the H boson signal in any of these decay channels, or the on-shell and off-shell regions. We denote this background collectively as the Z+X background, and employ a data-driven method for its estimation and m4ℓ dependence. The lepton misidentification rates are first derived using Z+1ℓ control regions with relaxed selection requirements on the third lepton, and the extracted rates are then applied on Z+2ℓ control regions, where the two additional leptons with relaxed selection requirements have the same lepton flavor but may have opposite charge [21,24].

IV.

The full kinematic information from each event using either the H boson decay or associated particles in its production is extracted using discriminants from matrix element calculations. These discriminants use a complete set of mass and angular input observables Ω [47,54,59] to describe kinematics at LO in QCD. The pT of either the combined H boson and two-jet system for the production discriminant (e.g., DVBF/VH), or the H boson itself for the decay discriminants (e.g., Ddec), or for their combination (e.g., DVBF/VH+dec) is not included in the input observables. This information is not used in the analysis of the H boson width and anomalous couplings, as the pT of the overall system is sensitive to QCD, parton shower, and underlying event uncertainties.

The kinematic discriminants used in this study are computed using the same mela package that is utilized in simulation. The signal includes both the four-lepton decay kinematics in the processes H→ZZ/Zγ*/γ*γ*→4ℓ, and kinematics of associated particles in production H+jet, H+2jets, VBF, WH, ZH, tt¯H, tqH, or bb¯H. The background includes gg or qq¯→ZZ/Zγ*/γ*γ*/Z→4ℓ processes, and VBF or associated production with a V boson of the ZZ system. Analytical algorithms are available for the cross-checks of the four-lepton kinematics in H decay and VH associated production within the mela framework and were adopted in the previous CMS analyses [9,10,23].

Kinematic distributions of particles produced in the H boson decay or in association with H boson production are sensitive to the quantum numbers and anomalous couplings of the H boson. In the 1→4 process of the H→4f decay, six observables fully characterize kinematics of the decay products Ωdecay={θ1,θ2,Φ,m1,m2,m4f}, while two other angles relate orientation of the decay frame with respect to the production axis, Ωprod={θ*,Φ1}, as described in Ref. [47]. Moreover, two sets of observables, Ωassoc,VBF={θ1VBF,θ2VBF,ΦVBF,q12,VBF,q22,VBF} for the VBF process and Ωassoc,VH={θ1VH,θ2VH,ΦVH,q12,VH,q22,VH} for the VH process, can also be defined in a similar way to Ωdecay for H boson associated production [54]. As a result, 13 kinematic observables, illustrated in Fig. 1, are defined for the 2→6 associated production process with subsequent H boson decay to a four-fermion final state.

110.1103/PhysRevD.99.112003.f1FIG. 1.

Three topologies of the H boson production and decay: vector boson fusion qq→VV(qq)→H(qq)→VV(qq) (left); associated production qq→V→VH→(ff¯)H→(ff¯)VV (middle); and gluon fusion gg→H→VV→4ℓ (right) representing the topology without associated particles. The incoming particles are shown in brown, the intermediate vector bosons and their fermion daughters are shown in green, the H boson and its vector boson daughters are shown in red, and angles are shown in blue. In the first two cases the production and decay H→VV are followed by the same four-lepton decay shown in the third case. The angles are defined in either the H or V boson rest frames [47,54].

With up to 13 observables, Ω, sensitive to the H boson anomalous couplings in Eq. (2), it is a challenging task to perform an optimal analysis in a multidimensional space of observables. The mela approach introduced earlier is designed to reduce the number of observables to the minimum while retaining all essential information. Two types of discriminants were defined for either the production or decay process, and we also combine them into a joint discriminant for the full 2→6 process where relevant.

These types of discriminants are Dalt(Ω)=Psig(Ω)Psig(Ω)+Palt(Ω)(7)and Dint(Ω)=Pint(Ω)2Psig(Ω)Palt(Ω),(8)where the probability of a certain process P is calculated using the full kinematics characterized by Ω for the processes denoted as “sig” for a signal model and “alt” for an alternative model, which could be an alternative H boson production mechanism (used to categorize events), background (to isolate signal), or an alternative H boson coupling model (to measure coupling parameters). The “int” label represents the interference between the two model contributions. The probabilities P are calculated from the matrix elements provided by the mela package and are normalized to give the same integrated cross sections in the relevant phase space of each process. Such normalization leads to a balanced distribution of events in the range between 0 and 1 of the Dalt discriminants, and between -1 and 1 of Dint. One can apply the Neyman-Pearson lemma to prove that the two discriminants in Eqs. (7) and (8) become the minimal and complete set of optimal observables for the purpose of separating the two processes “sig” and “alt” while including their interference as well [54,59].

The selected events are split into three categories: VBF-tagged, VH-tagged, and untagged. A set of discriminants D2jet is constructed, following Eq. (7), where Psig corresponds to the signal probability for the VBF (WH or ZH) production hypothesis in the VBF-tagged (VH-tagged) category, and Palt corresponds to that of H boson production in association with two jets via gluon fusion. When more than two jets pass the selection criteria, the two jets with the highest pT are chosen for the matrix element calculations. Thereby, the D2jet discriminants separate the target production mode of each category from gluon fusion production, in all cases using only the kinematics of the H boson and two associated jets. Figure 2 illustrates these discriminants, designed for the VBF or VH signal enhancement in the a3 coupling analysis for a pseudoscalar contribution. A selection based on the Dbkg observable, which utilizes information from the 4ℓ decay kinematics and invariant mass, and which is discussed in more detail below, is applied in order to enhance the contribution of the signal over the background.

210.1103/PhysRevD.99.112003.f2FIG. 2.

The distributions of events for max(D2jetVBF,D2jetVBF,0−) (left) and max(D2jetWH,D2jetWH,0−,D2jetZH,D2jetZH,0−) (right) in the on-shell region in the data from 2016 and 2017 from the analysis of the a3 coupling for a pseudoscalar contribution. The requirement Dbkg>0.5 is applied in order to enhance the signal contribution over the background. The VBF signal under both the SM and pseudoscalar hypotheses is enhanced in the region above 0.5 for the former variable, and the WH and ZH signals are similarly enhanced in the region above 0.5 for the latter variable.

The three on-shell and off-shell categories are summarized in Tables II and III, and their sequential selection criteria are as follows: (i)

VBF-tagged requires exactly four leptons, either two or three jets of which at most one is b-quark flavor-tagged, or more if none are b-tagged jets, and D2jetVBF>0.5 using either the SM or BSM signal hypothesis for the VBF production.

(ii)

VH-tagged requires exactly four leptons, either two or three jets, or more if none are b-tagged jets, and D2jetVH=max(D2jetWH,D2jetZH)>0.5 using either the SM or BSM signal hypothesis for the VH production.

(iii)

Untagged consists of the remaining events.

The requirements on the number of b-tagged jets are applied to reduce crossfeed from tt¯H production. Even though VH cross sections are significantly lower with respect to VBF for m4ℓ>220  GeV, the VH cross section becomes comparable to the VBF cross section in the presence of anomalous couplings. Therefore, the off-shell analysis also benefits from featuring the VH-tagged category with hadronic decays of the associated V. In either the on-shell or off-shell regions, events are not tagged for the smaller VH contribution with leptonic V decays explicitly, but this contribution is taken into account in the simulation and parametrization of the VH process in the three different categories. The expected and observed numbers of events are listed in Table IV for the on-shell region and Table V for the off-shell region.

II10.1103/PhysRevD.99.112003.t2TABLE II.

Summary of the three production categories in the on-shell m4ℓ region. The selection requirements on the D2jet discriminants are quoted for each category, and further requirements can be found in the text. Two or three observables (abbreviated as obs.) are listed for each analysis and for each category. All discriminants are calculated with the JHUGen signal matrix elements and mcfm background matrix elements. The discriminants Dbkg in the tagged categories also include probabilities using associated jets and decay in addition to the m4ℓ probability. The VH interference discriminants in the hadronic VH-tagged categories are defined as the simple average of the ones corresponding to the WH and ZH processes.

CategoryVBF-taggedVH-taggedUntaggedSelectionD2jetVBF or D2jetVBF,BSM>0.5D2jetWH or D2jetWH,BSM, orRest of eventsD2jetZH or D2jetZH,BSM>0.5SM obs.m4ℓ, DbkgVBF+decm4ℓ, DbkgVH+decm4ℓ, Dbkgkina3 obs.Dbkg, D0-VBF+dec, DCPVBFDbkg, D0-VH+dec, DCPVHDbkg, D0-dec, DCPdeca2 obs.Dbkg, D0h+VBF+dec, DintVBFDbkg, D0h+VH+dec, DintVHDbkg, D0h+dec, DintdecΛ1 obs.Dbkg, DΛ1VBF+dec, D0h+VBF+decDbkg, DΛ1VH+dec, D0h+VH+decDbkg, DΛ1dec, D0h+decΛ1Zγ obs.Dbkg, DΛ1Zγ,VBF+dec, D0h+VBF+decDbkg, DΛ1Zγ,VH+dec, D0h+VH+decDbkg, DΛ1Zγ,dec, D0h+decIII10.1103/PhysRevD.99.112003.t3TABLE III.

Summary of the three production categories in the off-shell m4ℓ region, listed in a similar manner, as in Table II. All discriminants are calculated with the JHUGen or mcfm/JHUGen signal, and mcfm background matrix elements. The VH interference discriminant in the SM-like analysis hadronic VH-tagged category is defined as the simple average of the ones corresponding to the WH and ZH processes.

CategoryVBF-taggedVH-taggedUntaggedSelectionD2jetVBF or D2jetVBF,BSM>0.5D2jetWH or D2jetWH,BSM, orRest of eventsD2jetZH or D2jetZH,BSM>0.5SM obs.m4ℓ, DbkgVBF+dec, DbsiVBF+decm4ℓ, DbkgVH+dec, DbsiVH+decm4ℓ, Dbkgkin, Dbsigg,deca3 obs.m4ℓ, DbkgVBF+dec, D0-VBF+decm4ℓ, DbkgVH+dec, D0-VH+decm4ℓ, Dbkgkin, D0-deca2 obs.m4ℓ, DbkgVBF+dec, D0h+VBF+decm4ℓ, DbkgVH+dec, D0h+VH+decm4ℓ, Dbkgkin, D0h+decΛ1 obs.m4ℓ, DbkgVBF+dec, DΛ1VBF+decm4ℓ, DbkgVH+dec, DΛ1VH+decm4ℓ, Dbkgkin, DΛ1decIV10.1103/PhysRevD.99.112003.t4TABLE IV.

The numbers of events expected in the SM (or fa3=1 in parentheses) for the different signal and background contributions and the total numbers of observed events are listed across the three a3 analysis categories in the on-shell region for the combined 2016 and 2017 data set.

VBF-taggedVH-taggedUntaggedVBF signal4.7 (3.4)0.3 (0.2)5.7 (0.8)WH signal0.3 (0.6)0.7 (1.9)2.1 (5.3)ZH signal0.2 (0.4)0.5 (1.0)1.5 (2.5)VV background0.20.10.5gg signal5.5 (5.8)3.2 (3.3)98.9 (98.4)gg background0.80.312.7tt¯H signal0.2 (0.2)0.1 (0.1)1.1 (1.2)bb¯H signal0.1 (0.1)0.1 (0.1)1.1 (1.1)qq¯→4ℓ background1.61.5120.3Z+X background5.23.046.3Total expected18.8 (18.2)9.7 (11.4)290.3 (289.1)Total observed199332V10.1103/PhysRevD.99.112003.t5TABLE V.

The numbers of events expected in the SM-like analysis (or fa3=0 in the a3 analysis categorization, divided with a vertical bar) for the different signal and background contributions and the total observed numbers of events are listed across the three SM|a3 analysis categories in the off-shell region for the combined 2016 and 2017 data set. The signal, background, and interference contributions are shown separately for the gluon fusion (gg) and EW processes (VV) under the ΓH=ΓHSM assumption.

VBF-taggedVH-taggedUntaggedVV signal1.0|1.20.3|0.33.3|3.1VV background7.3|9.92.5|2.816.2|13.3VV interference-1.8|-2.10.06|0.03-2.4|-2.2gg signal1.0|1.60.8|1.020.3|19.5gg background10.4|16.48.7|10.4245.9|238.1gg interference-1.6|-2.6-1.4|-1.6-34.4|-33.0qq¯→4ℓ background15.8|33.527.8|31.2992.0|970.8Z+X background2.4|6.42.8|3.345.4|40.8Total expected34.4|64.841.6|47.51286.3|1251.0Total observed36|9246|511325|1264

In each category of events, typically three observables x→ are defined following Eqs. (7) and (8), as summarized in Tables II and III. In the on-shell region, except for the SM-like analysis, these are x→={Dbkg,Dai,Dint}. The first observable, Dbkg, is calculated differently in the three tagged categories. In the untagged category, Pbkg is calculated for the dominant qq¯→4ℓ background process. The signal and background probabilities include both the matrix element probability based on the four-lepton kinematics and the m4ℓ probability parametrization extracted from simulation of detector effects. The signal m4ℓ parametrization assumes mH=125  GeV. In the VBF-tagged and VH-tagged categories, Pbkg and Psig include four-lepton kinematics and the m4ℓ probability parametrization, but they also include kinematics of the two associated jets. The Pbkg probability density represents the EW and QCD background processes 4ℓ+2 jets, while Psig represents EW processes VBF and VH. It was found that jet kinematics in the Dbkg calculation improves separation of the targeted signal production both against background and against the H boson gluon fusion production. However, in the off-shell region and in the SM-like on-shell analysis, the four-lepton invariant mass m4ℓ is one of the most important observables, because the mass parametrization becomes an important feature of the analysis. Therefore, the m4ℓ parametrization is not used in the Dbkg calculation in these cases, and this is reflected with the superscript denoting which information is used, either with decay only information in Dbkgkin or with both decay and production in DbkgVBF+dec and DbkgVH+dec.

The other observable, Dai, separates the SM hypothesis fai=0 as Psig from the alternative hypothesis fai=1 as Palt, following Eq. (7). In the untagged category, the probabilities are calculated using only the decay information, and the Dai observable is called D0− in the a3, Doh+ in the a2, DΛ1 in the Λ1, and DΛ1Zγ in the Λ1Zγ analyses [25]. In the VBF-tagged and VH-tagged categories, both the production and decay probabilities are used, with the matrix elements calculated as the product of the decay component and the component from either VBF production or (WH+ZH) associated production, respectively [27]. The resultant set of Dai discriminants are called in a similar manner to their counterparts in the untagged category but indicating the production assumption in their upper index.

The last observable, Dint defined in Eq. (8), separates the interference of the two amplitudes corresponding to the SM-like H boson coupling and the alternative H boson coupling model, or the SM-like H boson coupling and background as an alternative model in the case of Dbsi for the signal-background interference in the off-shell region. In the case of the a3 analysis, this observable is called DCP because if CP is violated it would exhibit a distinctive forward-backward asymmetry. In the untagged category, decay information is used in the calculation of Dint. In the VBF-tagged and VH-tagged categories, production information with the two associated jets is used. The Dbsi discriminant extends the idea of the Dgg discriminant introduced in Ref. [11] for the H boson width measurement, but allows independent treatment of the interference component. It is used only in the SM-like analysis.

The distributions of events for several of the observables x→ from Tables II and III are illustrated in Fig. 3 for the on-shell and in Fig. 4 for the off-shell regions. In Figs. 3 and 4, cross sections of all background processes are fixed to the SM expectations, except for the Z+X background estimated from the data control regions discussed above. Cross sections of all signal processes, including BSM, are normalized to the SM expectations in the on-shell region.

310.1103/PhysRevD.99.112003.f3FIG. 3.

The distributions of events in the on-shell region in the data from 2016 and 2017. The top row shows Dbkg in the VBF-tagged (left), VH-tagged (middle), and untagged (right) categories of the analysis of the a3 coupling for a pseudoscalar contribution. The rest of the distributions are shown with the requirement Dbkg>0.5 in order to enhance signal over background contributions. The middle row shows D0- in the corresponding three categories. The bottom row shows DCPdec of the a3, D0h+dec of the a2, and DΛ1dec of the Λ1 analyses in the untagged categories.

410.1103/PhysRevD.99.112003.f4FIG. 4.

The distributions of events in the off-shell region in the data from 2016 and 2017. The top row shows m4ℓ in the VBF-tagged (left), VH-tagged (middle), and untagged (right) categories in the dedicated SM-like width analysis where a requirement on DbkgVBF+dec, DbkgVH+dec, or Dbkgkin>0.6 is applied in order to enhance signal over background contributions. The middle row shows DbkgVBF+dec (left), DbkgVH+dec (middle), Dbkgkin (right) of the a3 analysis in the corresponding three categories. The requirement m4ℓ>340  GeV is applied in order to enhance signal over background contributions. The bottom row shows Dbsi in the corresponding three categories in the dedicated SM-like width analysis with both of the m4ℓ and Dbkgkin requirements enhancing the signal contribution. The acronym s+b+i designates the sum of the signal (s), background (b), and their interference contributions (i).

V.

We perform an unbinned extended maximum likelihood fit [89] to the events split into several categories (enumerated with an index k below) according to the three lepton flavor combinations (4e, 4μ, and 2e2μ), three production categories (VBF-tagged, VH-tagged, and untagged), five data periods (2011, 2012, 2015, 2016, and 2017), and two mass ranges (on-shell and off-shell). Therefore, there could be up to 90 categories of events. However, not all categories are used in each independent measurement because of the simpler categorization approach applied to the earlier data. Here we focus on discussion of the 2016 and 2017 data analyses, while treatment of the earlier data can be found in Refs. [13,25,27].

An independent fit is performed for each of the four anomalous HVV coupling parameters faicos(ϕai) using the on-shell region only. These fits avoid any assumptions on how the behavior of each process considered in the analysis changes from the on-shell region to the off-shell region. Four independent joint fits to the on-shell and off-shell regions are performed in order to determine the width of the H boson under the SM-like assumption or in the presence of the three anomalous couplings a3, a2, and Λ1. These fits are also used to constrain the three corresponding anomalous coupling parameters faicos(ϕai). When a certain anomalous coupling is tested, all other anomalous couplings are assumed to be zero, and only real couplings in Eq. (2) are tested, that is with a1≥0 and cos(ϕai)=±1.

The on-shell analysis with the study of the a3, a2, Λ1, and Λ1Zγ couplings has been presented in Ref. [27] using a partial data set. This part of the analysis remains essentially unchanged, except for a small change in the definition of the interference discriminant in Eq. (8) and the inclusion of information from the kinematics of the two associated jets in the Dbkg calculation discussed in Sec. IV. The SM-like on-shell analysis is similar to the one presented in Ref. [21] in methodology, but it uses the observables x→ and categorization k described in Table II and Sec. IV. The on-shell probability density is normalized to the total event yield in each process j and category k according to Pjk(x→;ξ→jk,ζ→)=μjPjksig(x→;ξ→jk,fai,ϕai)+Pjkbkg(x→;ξ→jk),(9)where ζ→=(μF,μV,ΓH,faicos(ϕai)) are the unconstrained parameters of interest, ξ→jk are the constrained nuisance parameters for a particular parametrization, and x→ are the observables listed in Table II, specific to each ai. The on-shell signal strength μj in Eq. (9) is defined in references to Eq. (1) as either μF or μV according to the process type j (gg, VBF, WH, ZH, tt¯H, bb¯H, qq¯→4ℓ, and Z+X). Each process includes both signal (sig) and background (bkg) components, but may contain only signal (tt¯H and bb¯H) or only background (qq¯→4ℓ and Z+X) contributions in the particular cases. The interference between the signal and background components, when both are present, is negligible in the on-shell region because of the very small width ΓH compared to the mass range of interest. This also leads to the on-shell parametrization in Eq. (9) being independent from the width ΓH.

The off-shell probability density follows Eqs. (1) and (9) closely but with the additional contribution of interference (int) between the signal and background amplitudes as Pjk(x→;ξ→jk,ζ→)=μjΓHΓ0Pjksig(x→;ξ→jk,fai,ϕai)+μjΓHΓ0Pjkint(x→;ξ→jk,fai,ϕai)+Pjkbkg(x→;ξ→jk),(10)where the notation remains the same as for Eq. (9). The x→ observables are listed in Table III and are specific to each coupling analysis. They include m4ℓ and two other discriminants. The process type j does not include tt¯H and bb¯H because of their negligible contribution in the off-shell region, while the VBF, WH, and ZH processes are combined into one EW process. The parametrization in Eq. (10) depends on the width ΓH explicitly and the reference value is taken to be Γ0=4.07  MeV, which determines the relative strength of Pjksig and Pjkint with respect to Pjkbkg in the parametrization.

The EW H boson production (VBF and VH) or production via gluon fusion have different dependence on anomalous HVV couplings, equally in the on-shell or off-shell regions. There are two HVV vertices in the former production mechanism with the subsequent H→VV→4ℓ decay while there is only one HVV decay vertex in the latter case. In addition, there is interference with the background in the off-shell region. This leads to the following general expressions for the signal (sig) or interference (int) contributions appearing in Eqs. (9) and (10): Pjksig/int(x→;ξ→jk,fai,ϕai)=∑m=0MPjk,msig/int(x→;ξ→jk)faim2(1-fai)M-m2cosm(ϕai),(11)where the sum over the index m runs up to M=4 in the case of the EW signal process; M=2 in the case of the gluon fusion, tt¯H, and bb¯H signal processes, or the interference between the signal and background in the EW process; and M=1 in the case of the interference between the signal and background in the gluon fusion process. In this expression, the index m corresponds to the exponent of ai in the squared scattering amplitude from Eq. (2), which may contain contributions from production and decay, and the factor cos(ϕai)=±1 affects only the sign of the terms that scale with an odd power of ai.

The Pjk,msig/int and Pjkbkg probability densities are normalized to the expected number of events, and are binned histograms (templates) of the observables x→ listed in Tables II and III, except for the signal m4ℓ parametrization in the on-shell region as discussed below. These templates are obtained by reweighting the existing signal or background samples for different couplings and then finding their linear combination. Since m4ℓ is treated directly as an observable in the on-shell SM-like fit, the signal m4ℓ shape for each process j and category k is parametrized using a double-sided crystal-ball function [90], and the full signal probability density is parametrized as the product of the parametric m4ℓ shape and a template of other discriminants conditional in m4ℓ. In all cases, the H boson mass mH=125  GeV is assumed.

The final constraints on faicos(ϕai) and ΓH are placed using the profile likelihood method using the RooFit toolkit [91] within the root [92] framework. The extended likelihood function is constructed using the probability densities in Eqs. (9) and (10) with each event characterized by the discrete category k and typically three continuous observables x→. The likelihood L is maximized with respect to the nuisance parameters ξ→jk describing the systematic uncertainties discussed below and the yield parameters μF and μV. The allowed 68% and 95% C.L. intervals are defined using the profile likelihood function, -2ΔlnL=1.00 and 3.84, for which exact coverage is expected in the asymptotic limit [93].

Several systematic uncertainties are featured in the vectors of constrained parameters ξ→jk. The template shapes describing probability distributions in Eqs. (9), (10), and (11) are varied separately within either theoretical or experimental uncertainties. In the following, a range of uncertainties affecting the template distributions is given for the m4ℓ values from around 100 GeV (typical for the on-shell range) to around 1 TeV (in the off-shell range), respectively. The factorization (or renormalization) scale uncertainties are evaluated by multiplying the central scale by 2 or 1/2, and the uncertainties range from ±0.7% (+1.2-1.4%) to -1.0+0.6% (+5-4%) in the gg process, from +0.6-0.1% (+5-4%) to ±5% (+30-25%) in the VBF process, from +3-5% (+5-4%) to ±6% (+30-25%) in the processes with an associated EW boson, and from +3.5-5.5% to ±1% (±3%) in the qq¯→4ℓ background. PDF parametrization uncertainties are evaluated by taking the envelope of the 100 alternative NNPDF variations. Variations due to PDF parametrization uncertainties [or due to uncertainties in αS(mZ)=0.1180±0.0015] range from +1.2-1.4% (+2.0-2.5%) to +5-4% (+2.4-1.0%) in the gg process, from +5-4% to about +30-25% in the EW processes, and are approximately ±3% (from +1.0-1.8% to ±0.5%) for the qq¯→4ℓ background. The signal processes, and the backgrounds that interfere with the signal, feature the uncertainties as a function of the multiplicity and kinematics of associated jets due to the hadronization scale used in pythia and the underlying event variations, obtained with the variations of the pythia tune. In the VBF-tagged categories, the correlated template variations for the hadronization scale (underlying event) range from ±11% (±45%) to ∓8% (∓40%) in the gg process, from ±8% (±24%) to ∓6% (∓8%) in the VBF process, and from ±13% (±20%) to ∓10% (∓32%) in the processes with an associated EW boson. In the VH-tagged categories, these correlated template variations instead range from ±15% (±50%) to ∓9% (∓45%) in the gg process, from ±8% (±25%) to ∓7% (∓30%) in the VBF process, and from ±4% (±19%) to ∓4% (∓13%) in the processes with an associated EW boson. Template shapes in the gg processes are also varied to account for a second jet in the hard process, and these correlated variations range from ±18% (±32%) to ∓15% (∓14%) in the VBF-tagged (VH-tagged) category. The qq¯→4ℓ background further features an uncertainty in the NLO EW corrections applied to the simulation [79,80], which are significant at higher m4ℓ values, reaching up to 20% at 1 TeV.

Experimental uncertainties involve jet energy calibration (JEC) uncertainties, which are only relevant when production categories are considered, and lepton efficiency and momentum uncertainties, which are similar for the different processes and categories. Systematic uncertainties in the JEC account for variations in the VBF-tagged (VH-tagged) category, and range from ±13% (±4%) to ±8% (±1%) in the gg process, from ±5% (-10+2%) to about ±11% (±6%) in the VBF process, from ±9% (±4%) to ±12% (±1%) in processes with an associated EW boson, and from ±17% (±8%) to ±15% (+2.0-0.5%) for the qq¯→4ℓ background. The cross-section uncertainties due to electron (muon) efficiency range from +6-7% (+3.0-4.5%) to +3.5-4.5% (+0.8-2.0%) to +7-8% (+0.8-2.0%) in the 2e2μ channel, and roughly double for the 4e (4μ) channel, from m4ℓ∼100  GeV to 230 GeV to around 1 TeV.

In the estimation of the Z+X background, the flavor composition of hadronic jets misidentified as leptons may be different in the Z+1ℓ and Z+2ℓ control regions, and together with the statistical uncertainty in the Z+2ℓ region, this uncertainty accounts for about ±30% variation in the background estimate from the 2017 data set. The uncertainty on the modeling of this misidentification as a function of pT and η, combined with the Z+1ℓ control region statistical uncertainty, leads to a +20-12% to +30-27% variation in the 4e channel, ±(10–20)% variation in the m4ℓ shape in the 2e2μ channel, and ±4% to +14-17% variation in the 4μ channel. Uncertainties in the Z+X background in the 2016 data set are only slightly larger. The normalization of the background processes derived from the MC simulation is affected by the uncertainties in the integrated luminosity of 2.5% [94] and 2.3% [95] in the 2016 and 2017 data sets, respectively. The integrated luminosity is measured using data from the CMS silicon pixel detector, drift tubes, and the forward hadron calorimeters, or from the fast beam conditions monitor and pixel luminosity telescope. All systematic uncertainties are treated as correlated between different time periods except for the luminosity and jet-related uncertainties which originate from statistically independent sources.

VI.

Four faicos(ϕai) parameters sensitive to anomalous HVV interactions, as defined in Eqs. (2) and (6), are tested in the on-shell data sample using the probability densities defined in Eq. (9). Since only the real couplings are tested, cos(ϕai)=±1. Figure 5 shows the results of the likelihood scans of these parameters for the 2016 and 2017 periods of the 13 TeV run and for the full combined data set from collisions at 7, 8, and 13 TeV. The analysis of the 2016 and 2017 data uses the approach presented here with the observables sensitive to anomalous couplings in both production and decay. Because of the smaller numbers of events, the data from the 2015 period of the 13 TeV run and from the 2011 and 2012 periods of the 7 and 8 TeV runs are analyzed using only the decay information as in Refs. [25,27], which is equivalent to having all events in the untagged category of this analysis. The results from on-shell events in the combined data set are listed in Table VI. These results supersede our previous measurements of these parameters in Refs. [25,27].

510.1103/PhysRevD.99.112003.f5FIG. 5.

Observed (solid) and expected (dashed) likelihood scans of fa3cos(ϕa3) (top left), fa2cos(ϕa2) (top right), fΛ1cos(ϕΛ1) (bottom left), and fΛ1Zγcos(ϕΛ1Zγ) (bottom right) using on-shell events only. Results of analysis of the data from 2016 and 2017 only (black) and the combined Run 1 and Run 2 analysis (red) are shown. The dashed horizontal lines show the 68 and 95% C.L. regions.

VI10.1103/PhysRevD.99.112003.t6TABLE VI.

Summary of allowed 68% C.L. (central values with uncertainties) and 95% C.L. (in square brackets) intervals for the anomalous coupling parameters faicos(ϕai) obtained from the analysis of the combination of Run 1 (only on-shell) and Run 2 (on-shell and off-shell) data sets. Three constraint scenarios are shown: using only on-shell events, using both on-shell and off-shell events with the ΓH left unconstrained, or with the constraint ΓH=ΓHSM.

ParameterScenarioObservedExpectedfa3cos(ϕa3)On-shell-0.0001-0.0015+0.0004 [-0.163,0.090]0.0000-0.0019+0.0019 [-0.082,0.082]Any ΓH0.0000-0.0010+0.0003 [-0.0165,0.0087]0.0000-0.0015+0.0015 [-0.038,0.038]ΓH=ΓHSM0.0000-0.0009+0.0003 [-0.0067,0.0050]0.0000-0.0014+0.0014 [-0.0098,0.0098]fa2cos(ϕa2)On-shell0.0004-0.0006+0.0026 [-0.0055,0.0234]0.0000-0.0023+0.0030 [-0.021,0.035]Any ΓH0.0004-0.0006+0.0026 [-0.0035,0.0147]0.0000-0.0017+0.0019 [-0.015,0.021]ΓH=ΓHSM0.0005-0.0006+0.0025 [-0.0029,0.0129]0.0000-0.0016+0.0012 [-0.010,0.012]fΛ1cos(ϕΛ1)On-shell0.0002-0.0009+0.0030 [-0.209,0.089]0.0000-0.0006+0.0012 [-0.059,0.032]Any ΓH0.0001-0.0006+0.0015 [-0.090,0.059]0.0000-0.0007+0.0013 [-0.017,0.019]ΓH=ΓHSM0.0001-0.0005+0.0015 [-0.016,0.068]0.0000-0.0006+0.0013 [-0.015,0.018]fΛ1Zγcos(ϕΛ1Zγ)On-shell0.0000-0.0087+0.3554 [-0.17,0.61]0.0000-0.0100+0.0091 [-0.098,0.343]

The observed and expected 68% C.L. constraints are significantly tighter than in the Run 1 analysis [25] as it is evident from the narrow minima at fai=0 in Fig. 5. This effect comes from utilizing production information because the cross section in VBF and VH production increases quickly with fai. Moreover, the minima of the -2lnL distributions appear rather sharp because of the higher order polynomial of the fai parameters appearing in Eq. (11) in the case of VBF and VH production. At the same time, the constraints above fai∼0.02 are dominated by the decay information from H→4ℓ. The best fit (μF,μV) values in the four analyses under the assumption that fai=0 are as follows: (1.21-0.17+0.21,0.84-0.59+0.71) at fa3=0, (1.19-0.17+0.21,0.91-0.55+0.69) at fa2=0, (1.26-0.18+0.20,0.53-0.50+0.64) at fΛ1=0, and (1.24-0.17+0.19,0.55-0.51+0.64) at fΛ1Zγ=0. The values obtained for the different analyses vary because of the different categorization and observables in each ai analysis.

The combination of on-shell and off-shell regions allows the setting of tighter constraints on faicos(ϕai) using the probability densities defined in Eqs. (9) and (10). As discussed above, the on-shell region is analyzed using the 2015, 2016, and 2017 data, and the earlier Run 1 data. The off-shell region is analyzed using only 2016 and 2017 data because no such analysis of the three anomalous couplings has been performed with the Run 1 or 2015 data in this region. The one-parameter likelihood scans of faicos(ϕai) combining all such available on-shell and off-shell events is shown for two cases in Fig. 6, either with ΓH unconstrained in the fit or with the constraint ΓH=ΓHSM. The corresponding 68% and 95% C.L. constraints are summarized in Table VI. The full two-parameter likelihood scans of faicos(ϕai) and ΓH are likewise shown in Fig. 6. Using the transformation in Eq. (5), the faicos(ϕai) results can be interpreted for the coupling parameters used in Eq. (2), as shown in Table VII.

610.1103/PhysRevD.99.112003.f6FIG. 6.

Constraints on fa3cos(ϕa3) (top), fa2cos(ϕa2) (middle), and fΛ1cos(ϕΛ1) (bottom) from the combined Run 1 and Run 2 data set using both on-shell and off-shell events. Left plots: likelihood scans of the parameters of interest with unconstrained ΓH (red) or assuming ΓH=ΓHSM (blue). The dashed horizontal lines show the 68% and 95% C.L. regions. Right plots: observed two-parameter (ΓH, faicos(ϕai)) likelihood scans. The two-parameter 68% and 95% C.L. regions are indicated with the dashed and solid curves, respectively.

VII10.1103/PhysRevD.99.112003.t7TABLE VII.

Summary of the allowed 95% C.L. intervals for the anomalous HVV couplings using results in Table VI. The coupling ratios are assumed to be real and include the factor cos(ϕΛ1) or cos(ϕΛ1Zγ)=±1.

ParameterScenarioObservedExpecteda3/a1On-shell[-1.13,0.80][-0.76,0.76]Any ΓH[-0.33,0.24][-0.50,0.50]ΓH=ΓHSM[-0.21,0.18][-0.25,0.25]a2/a1On-shell[-0.12,0.26][-0.24,0.31]Any ΓH[-0.098,0.202][-0.21,0.25]ΓH=ΓHSM[-0.089,0.189][-0.17,0.18](Λ1|a1|)cos(ϕΛ1) (GeV)On-shell[-∞,-130]∪[160,∞][-∞,-180]∪[210,∞]Any ΓH[-∞,-160]∪[180,∞][-∞,-250]∪[240,∞]ΓH=ΓHSM[-∞,-250]∪[170,∞][-∞,-260]∪[250,∞](Λ1Zγ|a1|)cos(ϕΛ1Zγ) (GeV)On-shell[-∞,-170]∪[100,∞][-∞,-200]∪[130,∞]

Limits on ΓH are set by combining events from the on-shell and off-shell regions. The left-hand panel of Fig. 7 shows the results of the likelihood scans of ΓH for the 2016 and 2017 period of the 13 TeV run and for the combined data set from collisions at 7, 8 and 13 TeV under the assumption of SM-like couplings. The small contribution from the 2015 data set is not considered in this case, but the Run 1 analysis includes both the on-shell and off-shell regions in the analysis of the H→ZZ→4ℓ decay [11,13]. The combined results are listed in Table VIII. The best fit (μF,μV) values in these results are (1.20-0.16+0.19,0.62-0.43+0.57) when ΓH=ΓHSM, and (1.21-0.17+0.19,0.65-0.45+0.61) when ΓH is unconstrained. The width constraints are also placed with the fa3cos(ϕa3), fa2cos(ϕa2), or fΛ1cos(ϕΛ1) parameters unconstrained, and are shown in Fig. 7 right panel and summarized in Table IX. These results are obtained with the same fit configurations as for the study of anomalous couplings in the combination of the on-shell and off-shell regions.

710.1103/PhysRevD.99.112003.f7FIG. 7.

Observed (solid) and expected (dashed) likelihood scans of ΓH. Left plot: results of the SM-like couplings analysis are shown using the data only from 2016 and 2017 (black) or from the combination of Run 1 and Run 2 (red), which do not include 2015 data. Right plot: results of the combined Run 1 and Run 2 data analyses, with 2015 data included in the on-shell case, for the SM-like couplings or with three unconstrained anomalous coupling parameters, fa3cos(ϕa3) (red), fa2cos(ϕa2) (blue), and fΛ1cos(ϕΛ1) (violet). The dashed horizontal lines show the 68% and 95% C.L. regions.

VIII10.1103/PhysRevD.99.112003.t8TABLE VIII.

Summary of the total width ΓH measurement, showing the allowed 68% C.L. (central values with uncertainties) and 95% C.L. (in square brackets). The limits are reported for the SM-like couplings using the Run 1 and Run 2 combination.

ParameterObservedExpectedΓH (MeV)3.2-2.2+2.8 [0.08, 9.16]4.1-4.0+5.0 [0.0, 13.7]IX10.1103/PhysRevD.99.112003.t9TABLE IX.

Summary of the total width ΓH measurements, showing allowed 68% C.L. (central values with uncertainties) and 95% C.L. (in square brackets). The ΓH limits are reported for the anomalous coupling parameter of interest unconstrained using the Run 1 and Run 2 combination.

ParameterUnconstrained parameterObservedExpectedΓH (MeV)fa3cos(ϕa3)2.4-1.8+2.7 [0.02, 8.38]4.1-4.1+5.2 [0.0, 13.9]ΓH (MeV)fa2cos(ϕa2)2.5-1.8+2.9 [0.02, 8.76]4.1-4.1+5.2 [0.0, 13.9]ΓH (MeV)fΛ1cos(ϕΛ1)2.4-1.6+2.5 [0.06, 7.84]4.1-4.1+5.2 [0.0, 13.9]

The systematic uncertainties mostly cancel in the ratios of cross sections in the measurement of fractional parameters faicos(ϕai), and are therefore negligible. The width constraints are also dominated by the statistical uncertainties, but because of the nontrivial dependence of systematic uncertainties on m4ℓ, their dominant contributions may be worth examination. The two leading theoretical and two leading experimental uncertainties affecting the width constraints (observed and expected at 68% C.L.) are the uncertainty on the NLO EW corrections for the qq¯→4ℓ background (±0.5 and ±1.9  MeV), the variation of renormalization scale in gluon fusion (±0.2 and ±0.4  MeV), the muon efficiency uncertainty (±0.1 and ±0.4  MeV), and the electron efficiency uncertainty (±0.1 and ±0.3  MeV).

The width constraints could also be reinterpreted as an off-shell signal strength with a change of parameters. For this interpretation, we perform an SM-like analysis of only the off-shell events, where the signal strength is modified by the parameter μoff-shell common to all production mechanisms in Eqs. (1) and (10), with ΓH=Γ0=ΓHSM and the SM expectation corresponding to μoff-shell=1. In addition, we also perform a fit of the off-shell events with two unconstrained parameters μFoff-shell and μVoff-shell, which express the signal strengths in the gluon fusion and EW processes, respectively. These constraints are summarized in Table X.

X10.1103/PhysRevD.99.112003.t10TABLE X.

Summary of allowed 68% C.L. (central values with uncertainties) and 95% C.L. (in square brackets) intervals for μoff-shell, μFoff-shell, and μVoff-shell obtained from the analysis of the combination of Run 1 and Run 2 off-shell data sets.

ParameterObservedExpectedμoff-shell0.78-0.53+0.72 [0.02, 2.28]1.00-0.99+1.20 [0.0, 3.2]μFoff-shell0.86-0.68+0.92 [0.0, 2.7]1.0-1.0+1.3 [0.0, 3.5]μVoff-shell0.67-0.61+1.26 [0.0, 3.6]1.0-1.0+3.8 [0.0, 8.4]VII.

Studies of on-shell and off-shell H boson production in the four-lepton final state are presented, using data from the CMS experiment at the LHC that correspond to an integrated luminosity of 80.2  fb-1 at a center-of-mass energy of 13 TeV. Joint constraints are set on the H boson total width and parameters that express its anomalous couplings to two electroweak vector bosons. These results are combined with those obtained from the data collected at center-of-mass energies of 7 and 8 TeV, corresponding to integrated luminosities of 5.1 and 19.7  fb-1, respectively. Kinematic information from the decay particles and the associated jets are combined using matrix element techniques to identify the production mechanism and increase sensitivity to the H boson couplings in both production and decay. The constraints on anomalous HVV couplings are found to be consistent with the standard model expectation in both on-shell and off-shell regions, as presented in Tables VI and VII. Under the assumption of a coupling structure similar to that in the standard model, the H boson width is constrained to be 3.2-2.2+2.8  MeV while the expected constraint based on simulation is 4.1-4.0+5.0  MeV, as shown in Table VIII. The constraints on the width remain similar with the inclusion of the tested anomalous HVV interactions and are summarized in Table IX. The width results are also interpreted in terms of the H boson signal strength in the off-shell region in Table X. The observed off-shell signal strength, or equivalently a nonzero value of the width, is more than 2 standard deviations away from a background-only hypothesis, which provides a new direction to measure H boson properties when more data are available.

We thank Markus Schulze for optimizing the JHUGen Monte Carlo simulation program and matrix element library for this analysis. We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. We also acknowledge the Maryland Advanced Research Computing Center (MARCC) for providing computing resources essential for this analysis. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); NKFIA (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); MES (Latvia); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom, RAS, RFBR, and NRC KI (Russia); MESTD (Serbia); SEIDI, CPAN, PCTI, and FEDER (Spain); MOSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU and SFFR (Ukraine); STFC (United Kingdom); DOE and NSF (USA). Individuals have received support from the Marie-Curie program and the European Research Council and Horizon 2020 Grant, contract No. 675440 (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F. R. S.-FNRS and FWO (Belgium) under the “Excellence of Science—EOS”—be.h project n. 30820817; the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Lendület (“Momentum”) Program and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, the New National Excellence Program ÚNKP, the NKFIA research Grants No. 123842, No. 123959, No. 124845, No. 124850, and No. 125105 (Hungary); the Council of Science and Industrial Research, India; the HOMING PLUS program of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, the Mobility Plus program of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/02861, Sonata-bis 2012/07/E/ST2/01406; the National Priorities Research Program by Qatar National Research Fund; the Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa del Principado de Asturias; the Thalis and Aristeia programs cofinanced by EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand); the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA).

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