Observation of the diphoton decay mode of the recently discovered Higgs boson and measurement of some of its properties are reported. The analysis uses the entire dataset collected by the CMS experiment in proton-proton collisions during the 2011 and 2012 LHC running periods. The data samples correspond to integrated luminosities of 5.1fb-1\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}$$\end{document} . A clear signal is observed in the diphoton channel at a mass close to 125GeV\documentclass[12pt]{minimal}
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\begin{document}$$5.2\,\sigma $$\end{document} is expected for the standard model Higgs boson. The mass is measured to be 124.70±0.34GeV=124.70±0.31(stat)±0.15(syst)GeV\documentclass[12pt]{minimal}
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\begin{document}$$124.70\pm 0.34\,\text {GeV} \,=124.70\pm 0.31\,\text {(stat)}\,\pm 0.15\,\text {(syst)}\,\,\text {GeV} \,$$\end{document} , and the best-fit signal strength relative to the standard model prediction is 1.14-0.23+0.26=1.14±0.21(stat)\documentclass[12pt]{minimal}
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\begin{document}$$1.14^\mathrm{+0.26}_{-0.23}=1.14\pm 0.21\,\text {(stat)}\,$$\end{document}-0.05+0.09(syst)\documentclass[12pt]{minimal}
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\begin{document}$$^\mathrm{+0.13}_{-0.09}\,\text {(theo)}\,$$\end{document}. Additional measurements include the signal strength modifiers associated with different production mechanisms, and hypothesis tests between spin-0 and spin-2 models.
volume-issue-count12issue-article-count53issue-toc-levels0issue-typeRegularissue-online-date-year2014issue-online-date-month11issue-online-date-day28issue-pricelist-year2014issue-copyright-holderSIF and Springer-Verlag Berlin Heidelbergissue-copyright-year2014article-contains-esmNoarticle-numbering-styleContentOnlyarticle-toc-levels0article-registration-date-year2014article-registration-date-month9article-registration-date-day16article-grants-typeOpenChoicemetadata-grantOpenAccessabstract-grantOpenAccessbodypdf-grantOpenAccessbodyhtml-grantOpenAccessbibliography-grantOpenAccessesm-grantOpenAccessIntroduction
In 2012 the ATLAS and CMS Collaborations announced the observation [1, 2] of a new boson with a mass, mH\documentclass[12pt]{minimal}
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\begin{document}$$m_\text {H}$$\end{document}, of about 125GeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {GeV} \, $$\end{document}and properties consistent, within uncertainties, with expectations for a standard model (SM) Higgs boson. The Higgs boson is the particle predicted to exist as a consequence of the spontaneous symmetry breaking mechanism acting in the electroweak sector of the SM [3–5]. This mechanism was first suggested nearly fifty years ago [6–11], and introduces a complex scalar field, which also gives masses to the fundamental fermions through a Yukawa interaction. Results using the full available dataset have recently been published by CMS [12–19], and by ATLAS [20–25].
The diphoton decay channel provides a clean final-state topology that allows the mass of the decaying object to be reconstructed with high precision. Having in mind the discovery of a low mass Higgs boson in the diphoton channel, the electromagnetic calorimeter performance was a design priority for CMS. The diphoton decay is mediated by loop diagrams containing charged particles. The top quark loop and the W boson loop diagrams dominate the decay amplitude, though they contribute with opposite sign. The branching fraction is small, reaches a maximum value of 0.23 % at mH=125GeV\documentclass[12pt]{minimal}
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\begin{document}$$m_\text {H}=125\,\text {GeV} \, $$\end{document} and falls steeply to values less than 0.1 % above 150GeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {GeV} \, $$\end{document} [26]. As a consequence the search reported in this paper is limited to the mass range, 110<mH<150GeV\documentclass[12pt]{minimal}
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\begin{document}$$110<m_\text {H}<150\,\text {GeV}\, $$\end{document} . Despite the small branching fraction and the presence of a large diphoton continuum background, the diphoton decay mode provides an expected signal significance for the 125GeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {GeV}\, $$\end{document}SM Higgs boson that is one of the highest among all the decay modes.
This paper presents the analysis performed on the full dataset collected in 2011 and 2012, reconstructed with the final detector calibration values, in pp\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}(herein referred to as the “7TeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document} dataset”). The results supersede those previously reported by CMS for this decay mode [27, 28].
The primary production mechanism of the Higgs boson at the LHC is gluon-gluon fusion (ggH) [29] with additional smaller contributions from vector boson fusion (VBF) [30] and production in association with a W\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} ) [32, 33]. Events from specific production mechanisms are identified and classified by the presence of additional objects in the final state. Requiring the presence of two forward jets, in addition to the photon pair, favours events produced by the VBF mechanism, while event classes designed to preferentially select VH or tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} production require the presence of muons, electrons, missing transverse energy from neutrinos, or jets arising from the hadronization of b quarks. To achieve the best sensitivity, the remaining events, and also the dijet events selected as having a VBF signature, are further separated using multivariate classifiers that provide measures of their probability to be signal rather than background. The signal is measured performing a simultaneous fit to the diphoton invariant mass distributions in the various event classes. The signal model is derived from simulation, while the background is obtained from the fit to data. A very large sample of events is available in which a Z\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}$$\end{document} boson decays to a pair of electrons; treating the electron showers in these events as if they were from photons allows precise and detailed knowledge to be obtained concerning the accuracy of the simulation of the signal, specifically the simulation of the energy reconstruction and selection of photons, and the simulation of the selection and classification of diphoton events.
With respect to analyses of this decay mode previously reported by CMS there are refinements in methodology, which are described in the main body of the paper. In addition, the analysis uses an improved intercalibration of the electromagnetic calorimeter channels and an improved energy regression algorithm to correct the clustered energy, resulting in better energy resolution. The simulation of the signal and Z boson samples is also improved. The changes in the energy-equivalent noise in the electromagnetic calorimeter during the data-taking period are simulated, and a significantly increased time window is used to simulate the effect of deposited energy coming from interactions in earlier bunch crossings.
The paper is organized as follows. After a brief description of the CMS detector and event reconstruction in Sect. 2 and of the data and simulated samples in Sect. 3, the reconstruction and identification of photons is detailed in Sect. 4. The issue of identifying the diphoton vertex is covered in Sect. 5. In Sect. 6 the event classification is described. The section first describes the construction of a multivariate event classifier which takes as input quantities associated with the two photons, and then goes on to describe the tagging of events by the presence of objects in the final state, in addition to the photon pair, that give the event a signature characteristic of one of the production processes. It concludes by detailing the use of two multivariate event classifiers to additionally subdivide into classes both the untagged events, and the events tagged as coming from the VBF process. Sections 7 and 8 describe, respectively, the signal and background models used in the statistical procedures which provide the results of the analysis, and Sect. 9 discusses the systematic uncertainties taken into account in those procedures. Section 10 outlines three alternative analyses that use specific variations of methodology that provide corroboration of particular aspects of the main analysis. Finally, in Sect. 11 the results of the measurements of the Higgs boson production and its properties are presented and discussed.
CMS detector
The central feature of the CMS apparatus is a superconducting solenoid, 13 \,m\documentclass[12pt]{minimal}
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A more detailed description of the CMS detector can be found in Ref. [35].
Reconstruction of the photons used in this analysis is described in Sect. 4, and uses a clustering of the energy recorded in the ECAL, known as a “supercluster”, which may be extended in the ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document} direction to form an extended cluster or group of clusters.
The global event reconstruction (also called particle-flow event reconstruction) consists of reconstructing and identifying each particle with an optimized combination of all subdetector information [36, 37]. In this process, the identification of the particle type (photon, electron, muon, charged hadron, neutral hadron) plays an important role in the determination of the particle direction and energy. Photons are identified as ECAL energy clusters not linked to the extrapolation of any charged-particle trajectory to the ECAL. Electrons are identified as a primary charged-particle track associated with ECAL energy clusters corresponding to this track’s extrapolation to the ECAL and to possible bremsstrahlung photons emitted along the way through the tracker material. Muons are identified as a track in the central tracker consistent with either a track or several hits in the muon system, associated with less energy in the calorimeters than would be deposited by a charged hadron or electron. Charged hadrons are identified as charged-particle tracks neither identified as electrons, nor as muons. Finally, neutral hadrons are identified as HCAL energy clusters not linked to any charged hadron trajectory, or as ECAL and HCAL energy excesses with respect to the expected energy deposited by a matching charged hadron.
The energy of photons used in the global event reconstruction is directly obtained from the ECAL measurement. The energy of electrons is determined from a combination of the track momentum at the main interaction vertex, the corresponding ECAL cluster energy, and the energy sum of all bremsstrahlung photons attached to the track. The energy of muons is obtained from the corresponding track momentum. The energy of charged hadrons is determined from a combination of the track momentum and the corresponding ECAL and HCAL energy, calibrated for the nonlinear response of the calorimeters. Finally, the energy of neutral hadrons is obtained from the corresponding calibrated ECAL and HCAL energies.
For each event, hadronic jets are clustered from these reconstructed particles using the infrared- and collinear-safe anti-kT\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {GeV}\, $$\end{document} , to be compared to about 40 % (12 %) obtained when the calorimeters alone are used for jet clustering.
To identify jets originating from the hadronization of bottom quarks, the combined secondary vertex b-tagging algorithm [40] is employed. The algorithm tags jets from b-hadron decays by identifying their displaced decay vertex. The working point of the tagging algorithm used provides an efficiency for identifying b-quark jets of about 70 % and a misidentification probability for jets from light quarks and gluons of about 1 %.
The missing transverse energy vector is taken as the negative vector sum of all reconstructed particle candidate transverse momenta in the global event reconstruction, and its magnitude is referred to as ETmiss\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}^{\text {miss}}\,$$\end{document}.
Data sample and simulated events
The events used in the analysis were selected by diphoton triggers with asymmetric transverse energy thresholds and complementary photon selections. One selection requires a loose calorimetric identification based on the shape of the electromagnetic shower and loose isolation requirements on the photon candidates, while the other requires only that the photon candidate has a high value of the R9\documentclass[12pt]{minimal}
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\begin{document}$$R_\mathrm {9}$$\end{document} shower shape variable. High trigger efficiency is maintained by allowing both photons to satisfy either selection. The R9\documentclass[12pt]{minimal}
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\begin{document}$$99.4~\%$$\end{document} for events satisfying the diphoton preselection required for events entering the analysis, as described in Sect. 4.
The Monte Carlo (MC) simulation of detector response employs a detailed description of the CMS detector, and uses GEANT4\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}samples, respectively [43]. Simulated Higgs boson signal events are used both for training of multivariate discriminants and to construct the signal model used in the statistical procedures employed to extract the results. Sufficient samples have been produced to ensure that the samples of simulated signal events used for construction of the signal model (Sect. 7) are not used for training the multivariate discriminants. The MC signal event samples for the ggH and VBF processes are obtained using the next-to-leading order (NLO) matrix-element generator powheg (version 1.0) [44–48] interfaced with pythia. For the 7TeV\documentclass[12pt]{minimal}
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Simulated samples of Z→e+e-\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {\mu ^+}\mathrm {\mu ^-}\mathrm {\gamma }$$\end{document} events used for comparison with data, and for the derivation of energy scale and resolution smearing corrections are generated with MadGraph, sherpa, and powheg [57], allowing comparisons to be made between the different generators.
Simulated background samples are used only for training multivariate discriminants and defining selection and classification criteria. The background is simulated using a combination of samples. At s=7TeV\documentclass[12pt]{minimal}
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Photon reconstruction and identification
Photon candidates for the analysis are reconstructed from energy deposits in the ECAL using algorithms that constrain the superclusters in η\documentclass[12pt]{minimal}
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\begin{document}$$\approx $$\end{document}95 %) collection of the energy of photons and electrons, even those that undergo conversion and bremsstrahlung in the material in front of the ECAL. In the barrel region, superclusters are formed from five-crystal-wide strips in η\documentclass[12pt]{minimal}
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About half of the photons convert in the material upstream of the ECAL. If the resulting charged particle tracks originate sufficiently close to the interaction point so as to pass through three or more tracking layers, conversion track pairs may be reconstructed and matched to the photon candidate.
Photon energy
The photon energy is computed from the signals recorded by the ECAL. In the region covered by the preshower detector (|η|>1.65\documentclass[12pt]{minimal}
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\begin{document}$$|\eta | > 1.65$$\end{document}) the signals recorded in it are also considered. In order to obtain the best energy resolution, the calorimeter signals are calibrated and corrected for several detector effects [34]. The variation of crystal transparency during the run is continuously monitored and corrected for using a factor based on the measured change in response to the light from the laser system, with the response for each crystal being computed approximately every 40 minutes. The single-channel response of the ECAL is equalized exploiting the ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}$$\end{document}-boson decays. Finally, the containment of the shower in the clustered crystals, the shower losses for photons that convert in the material upstream of the calorimeter, and the effects of pileup, are corrected using a multivariate regression technique. The photon energy response distribution is parameterized by a function with a Gaussian core and two power law tails, an extended form of the Crystal Ball function [62]. The regression provides a per-photon estimate of the parameters of the function, and therefore a prediction of the distribution of the ratio of true energy to uncorrected supercluster energy. The most probable value of this distribution is taken as the corrected photon energy. The width of the Gaussian core is further used as a per-photon estimator of the energy uncertainty. The regression input variables are a collection of shower shape variables including R9\documentclass[12pt]{minimal}
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A multistep procedure has been implemented to correct the energy scale in data, and to determine the parameters of Gaussian smearing to be applied to showers in simulated events so as to reproduce the energy resolution seen in data. First, the energy scale in data is equalized with that in simulated events, and residual long-term drifts in the response are corrected, using Z→e+e-\documentclass[12pt]{minimal}
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Figure 1 shows the invariant mass of electron pairs reconstructed in Z→e+e-\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}data and in simulated events in which the electron showers are reconstructed as photons, and the full set of corrections to the data, and smearings of the simulated energies, are applied. The selection applied to the diphoton candidates is the same, apart from the inversion of the electron veto, as is applied to diphoton candidates entering the analysis (as described in Sect. 6). There is excellent agreement between the data and the simulation in the core of the distributions. A slight discrepancy is present in the low-mass tail in the endcaps, where the Gaussian smearing is not enough to account for some noticeable non-Gaussian energy loss. The mass peaks are shifted from the true Z\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}$$\end{document}-boson mass, both in data and simulation, because the electron showers are reconstructed as photons.
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\begin{document}$$\,\text {TeV}\ $$\end{document}data (points), and in simulated events (histogram), in which the electron showers are reconstructed as photons, and the full set of photon corrections and smearings are applied. The comparison is shown for (left) events with both showers in the barrel, and (right) the remaining events. For each bin, the ratio of the number of events in data to the number of simulated events is shown in the lower main plot
Photon preselection
The continuum background to the H→γγ\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}$$\end{document} and are thus relatively isolated from hadronic activity in the detector. In the transverse momentum range of interest, the photons from neutral pion decays are rather collimated and are reconstructed as a single photon. In the events used for the analysis, i.e. after all selection and classification criteria are applied, MC simulation predicts that about 70 % of the total background is due to the irreducible prompt diphoton production.
The photons entering the analysis are required to satisfy preselection criteria similar to, but slightly more stringent than, the trigger requirements. These consist of
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a selection on the hadronic leakage of the shower, measured as the ratio of energy in HCAL cells behind the supercluster to the energy in the supercluster,
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\begin{document}$$\text {Z}\rightarrow \mathrm {e}^+\mathrm {e}^-\,$$\end{document} events.
The selection requirements are applied with different stringency in four categories defined to match the different selections used in the trigger. The four categories are shown in Table 1.
Photon preselection efficiencies for both the 7 and 8TeV\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {e}^+\mathrm {e}^-\,$$\end{document} events, where the electrons are reconstructed as photons, in four photon categories. The statistical uncertainties in the efficiencies found in simulated events are negligible, and the uncertainties measured in data are discussed in the text
The efficiency of the photon preselection is measured in data using a “tag-and-probe” technique [64]. The efficiency of all preselection criteria, except the electron veto requirement, is measured using Z→e+e-\documentclass[12pt]{minimal}
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\begin{document}$$\epsilon _\text {data}/\epsilon _\mathrm {MC}$$\end{document} ratios are used to correct the simulated signal sample, and the associated uncertainties are taken into account as systematic uncertainties in the signal extraction procedure. For photons in simulated Higgs boson events the efficiency of the preselection criteria in the four categories ranges from 92 to 99 %.
Photon identification
A boosted decision tree (BDT), implemented using the tmva [65] framework, is trained to separate prompt photons from photon candidates resulting from misidentification of jet fragments passing the preselection requirements. The following variables are used as inputs to the photon identification BDT:
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Figure 2 shows the photon identification BDT score of the lower-scoring photon in diphoton pairs with an invariant mass, mγγ\documentclass[12pt]{minimal}
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Diphoton vertex
The mean number of pp\documentclass[12pt]{minimal}
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Diphoton vertex identification
No charged particle tracks result from photons that do not convert, so the diphoton vertex is identified indirectly, using the kinematic properties of the diphoton system and its correlations with the kinematic properties of the recoiling tracks. If either of the photons converts, the direction of the resulting tracks can provide additional information.
Three discriminating variables are calculated for each reconstructed primary vertex: the sum of the squared transverse momenta of the charged particle tracks associated with the vertex, and two variables that quantify the vector and scalar balance of pT\documentclass[12pt]{minimal}
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\begin{document}$$z_\mathrm {e}\,$$\end{document}. The variables are used as the inputs to a multivariate system based on a BDT to choose the reconstructed vertex to be associated with the diphoton system.
The vertex finding efficiency, defined as the efficiency that the chosen vertex is within 10mm\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {\mu ^+}\mathrm {\mu ^-}\,$$\end{document} events. The performance of the algorithm is evaluated after re-reconstruction of the vertices following removal of the muon tracks, so that the event mimics a diphoton event. The use of tracks from a converted photon to locate the vertex is validated in γ+jet\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}^{\gamma \gamma }\,$$\end{document}. Also shown is a band, the centre of which is the mean prediction, from the vertex probability BDT (described in Sect. 5.2), of the probability of correctly locating the vertex. The mean is calculated in pTγγ\documentclass[12pt]{minimal}
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Per-event vertex probability
A second vertex-related multivariate discriminant has been designed to estimate, event-by-event, the probability for the vertex assignment to be within 10mm\documentclass[12pt]{minimal}
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the values of the vertex identification BDT output for the three most likely vertices in the event,
the total number of reconstructed vertices in the event,
the transverse momentum of the diphoton system, pTγγ\documentclass[12pt]{minimal}
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the distances between the chosen vertex and the second- and third-best vertices,
the number of photons with an associated conversion track or tracks.
The vertex probability BDT is tested with simulated signal events as shown in Fig. 4, and the performance in data is tested using Z→μ+μ-\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {\mu ^+}\mathrm {\mu ^-}\,$$\end{document} events. The charged particle tracks belonging to the muon pair are used to identify the vertex, and are then removed from the event before re-reconstructing the vertices and passing them to the vertex identification and the vertex probability BDTs. The pT\documentclass[12pt]{minimal}
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Distribution of the vertex probability estimate in Z→μ+μ-\documentclass[12pt]{minimal}
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Event classification
The analysis uses events with two photon candidates satisfying the preselection requirements (described in Sect. 4.3) with an invariant mass, mγγ\documentclass[12pt]{minimal}
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\begin{document}$$-0.2$$\end{document} (see Fig. 2). This requirement retains more than 99 % of simulated signal events fulfilling the other analysis selection requirements, while removing about 24 % of events in data. The requirements listed above are referred to as the “full diphoton preselection”.
To achieve the best analysis performance, the events are separated into classes based on both their mass resolution and their relative probability to be due to signal rather than background. The first step in the classification of the events involves the extraction of those tagged by the presence of objects in the final state, in addition to the photon pair, that give the event a signature characteristic of one of the production processes. The remaining untagged events, which constitute the majority (≈\documentclass[12pt]{minimal}
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\begin{document}$$\approx $$\end{document}99 %) of the events used in the analysis, are classified according to a variable constructed using multivariate techniques.
The classification procedure, which is described in detail below, results in 11 event classes for the 7TeV\documentclass[12pt]{minimal}
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Multivariate event classifier
A multivariate event classifier, the diphoton BDT, is constructed to satisfy the following criteria:
The diphoton BDT should assign a high score to events that have
good diphoton mass resolution,
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The classifier should not select events according to the mass of the diphoton system relative to the particular mass of the Higgs boson signal used for training.
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\begin{document}$$m_\text {H}=125\,\text {GeV} \, $$\end{document} , and on data satisfying the full diphoton preselection. The classifier score has been transformed such that the sum of signal events from all processes has a uniform, flat, distribution. This transformation assists visualization of the performance of the BDT. The outlined histogram, following the data points, is for simulated background events. The vertical dashed lines indicate the boundaries of the untagged event classes, the determination of which is described in Sect. 6.3. Given that the data are completely dominated by background events, it can be seen that the signal-to-background ratio increases substantially with the classifier score, and that the VBF, VH, and tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}^{\gamma \gamma }$$\end{document} spectrum [66, 67].
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\begin{document}$$\,\text {TeV}\ $$\end{document}data (points with error bars, left axis), and for simulated signal events from the four production processes (solid filled histograms, right axis). The outlined histogram, following the data points, is for simulated background events. The vertical dashed lines show the boundaries of the untagged event classes, with the leftmost dashed line representing the score below which events are discarded and not used in the final analysis (described in Sect. 6.3)
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\begin{document}$$\text {Z}\rightarrow \mathrm {e}^+\mathrm {e}^-\,$$\end{document} data and for MC simulated events, in which for both cases the electrons are reconstructed as photons. The electron showers in the events satisfy the full diphoton preselection requirements with the electron veto condition inverted. The classifier score has been subjected to the same transformation as was used for Fig. 6. The score for Z→e+e-\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {e}^+\mathrm {e}^-\,$$\end{document} events peaks at low values whilst Higgs boson signal events have a flat distribution, reflecting the differences between the two types of event, but it can be seen that sufficient numbers of Z→e+e-\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {e}^+\mathrm {e}^-\,$$\end{document} events are present even at high values of the classifier score to enable the agreement between data and MC simulation to be adequately tested there. The good agreement between MC simulation and data for Z→e+e-\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {e}^+\mathrm {e}^-\,$$\end{document} events constitutes an important check that the modeling of the BDT input variables and their correlations in the simulation of the Higgs boson signal is accurate. The simulated events have been weighted so that the Z\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {e}^+\mathrm {e}^-\,$$\end{document} data. The band indicates the systematic uncertainty resulting from propagating to the diphoton BDT event classifier both the uncertainty associated with the photon identification BDT score (which corresponds to a shift of ±\documentclass[12pt]{minimal}
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\begin{document}$$\pm $$\end{document}0.01 of the score) and the uncertainty in the per-photon estimate of the energy resolution (which amounts to a scaling of its value by ±\documentclass[12pt]{minimal}
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\begin{document}$$\pm $$\end{document}10 %). Since the magnitudes of these two uncertainties were chosen to cover the discrepancies between data and simulation in the tails of the distributions of the two variables, the resulting uncertainty in the diphoton BDT event classifier appears to be slightly overestimated.
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\begin{document}$$\,\text {TeV}\ $$\end{document}data, and in MC simulation, in which the electrons are reconstructed as photons. The distribution of simulated events is represented by a histogram, and the data by points with error bars. For each bin, the ratio of the number of events in data to the number of simulated events is shown in the lower plot. The bands in the two plots indicate the systematic uncertainty related to the MC cluster shape uncertainty (see text). The vertical dashed lines show the boundaries of the untagged event classes, with the leftmost dashed line representing the score below which events are discarded and not used in the final analysis (described in Sect. 6.3)
Events tagged by exclusive signatures
Selections enriched in Higgs boson production mechanisms other than ggH can be made by requiring, in addition to the diphoton pair, the presence of other objects which provide signatures of the production mechanism. Higgs bosons produced by VBF are accompanied by a pair of jets separated by a large rapidity gap. Those resulting from the VH production mechanism may be accompanied by one or more charged leptons, large ETmiss\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} production are, as a result of the decay of the top quarks, accompanied by b quarks, and may be accompanied by charged leptons or additional jets.
The tagging of dijet events, targeting VBF production, significantly increases the overall sensitivity of the analysis and precision on the measured signal strength, and increases the sensitivity to deviations of the Higgs boson couplings from their expected values. The tagging aimed at the VH process increases the sensitivity to deviations of the couplings, and the tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} tagging further probes the compatibility of the observed signal with a SM Higgs boson.
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} processes is significantly harder than that of Higgs bosons produced by ggH, or of background diphotons. This results in a harder leading-photon pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}$$\end{document} requirement on the leading photon.
Dijet-tagged event selection and BDT classifiers for VBF production
Vector boson fusion production results in two forward jets, originating from the two scattered quarks. Separating events tagged by the presence of dijets compatible with the VBF process into specific event classes not only increases the separation between signal and background, it also increases the separation between signal production processes. In the purest VBF dijet-tagged class the signal is expected to have a contribution of only 18 % from ggH production. A loose preselection of dijet events is defined and a dijet BDT is trained to separate VBF signal from diphoton background using samples of MC events satisfying this dijet preselection. Signal events from ggH satisfying the dijet preselection are included as background in the training. Details of the dijet preselection and the BDT input variables are given below. A further, “combined”, BDT is then trained. This BDT has only three input variables: the score of the dijet BDT, the score of the diphoton BDT, and the transverse momentum of the diphoton system divided by its mass, pTγγ/mγγ\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}^{\gamma \gamma }\,/m_{\gamma \gamma }$$\end{document}. Events for the VBF dijet-tagged classes are selected, from those satisfying the loose dijet preselection, by placing a minimum requirement on their combined BDT score, and the selected events are then classified using that score.
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The selection requirements for the classes aimed at selecting events produced by the VH process have been obtained by minimizing the expected uncertainty in the measurement of signal strength of the process, using data in control regions to estimate the background and MC signal samples to estimate the signal efficiency. Four classes are defined: events with a muon or an electron are separated into two classes, according to whether there is significant ETmiss\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}$$\end{document}-boson mass. In addition, a conversion veto is applied to the electrons to reduce the number of electrons originating from photon conversions.
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\begin{document}$$p_{\mathrm {T}}^{\gamma \gamma }\,>13m_{\gamma \gamma }/12$$\end{document}. The selection also exploits the expected angular distribution of the diphoton pair with respect to the dijet pair from the vector boson decay. The angle, θ⋆\documentclass[12pt]{minimal}
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\begin{document}$$\theta ^\star $$\end{document}, that the diphoton system makes, in the diphoton-dijet centre-of-mass frame, with respect to the direction of motion of the diphoton-dijet system in the lab frame is computed. The distribution of cosθ⋆\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}^{\text {miss}}\,$$\end{document} tag, additional selection criteria are applied on the azimuthal angular separation between the diphoton system and the ETmiss\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}^{\text {miss}}\,$$\end{document} vector have been studied in detail and a set of corrections derived, some of which need to be applied to simulated events, and others to data. The corrected ETmiss\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}^{\text {miss}}\,>70\,\text {GeV} \, $$\end{document} .
In addition to the requirements described above, a minimum requirement is also made on the diphoton BDT classifier score for entry into the event classes tagging VH production. The severity of the requirement is optimized for each class: 0.17 for the two lepton-tagged classes, 0.62 for the ETmiss\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}^{\text {miss}}\,$$\end{document}-tagged class, and 0.76 for the VH dijet-tagged class, where the numerical scale is the classifier score shown in Figs. 6 and 7.
The production of Higgs bosons in association with top quarks has a small cross section, and so the overall cross section times branching fraction of the decay to photons is only 0.3 \,fb\documentclass[12pt]{minimal}
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\begin{document}$$\text {\,fb}$$\end{document} at NLO. Therefore, in the full dataset only a handful of events are expected. To maximize signal efficiency we devise event selections that collect both leptonic and hadronic decays of the top quarks, defining both a lepton-tagged and a multijet-tagged event class.
As for the VH event classes, the selection requirements for the classes aimed at selecting events produced by the tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} process have been obtained by minimizing the expected uncertainty in the measurement of signal strength of the process, using data in control regions to estimate the background, and MC signal samples to estimate the signal efficiency. The leading photon is required to have pTγ1>mγγ/2\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}\,>25\,\text {GeV}\, $$\end{document} and both classes require the presence of at least one b-tagged jet. The lepton tag is then defined by requiring at least one more jet in the event and at least one electron or muon with pT>20GeV\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}\,>20\,\text {GeV} \, $$\end{document} , and the multijet tag is defined by the requirement of at least four more jets in the event and no lepton. Requirements are also made on the minimum diphoton BDT classifier score for entry into the two classes tagging tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}\,$$\end{document}: 0.17 for the lepton class, and 0.48 for the multijet class, where the numerical scale is the classifier score shown in Figs. 6 and 7. For the 7TeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}dataset the events in the two classes are combined after selection to form a single tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}\,$$\end{document} event class.
Classification of VBF dijet-tagged and untagged events
Classes for the VBF dijet-tagged events and the untagged events are defined using the scores of the classification BDTs: the combined dijet-diphoton BDT score is used to select and define the dijet-tagged classes, and the diphoton BDT score defines the untagged class into which the untagged events are placed. The BDT score requirements that constitute the event class boundaries are set by an optimization procedure, using simulated event samples, aimed at minimizing the expected uncertainty in the signal strength. To avoid biases, the simulated events are divided into three non-overlapping sets, which are then used only for the training of the BDTs, or the optimization of event class boundaries, or to model the signal in the extraction of the final results. The number of available simulated events limits the statistical precision in the optimization procedure. The small number of simulated events for some background processes where one or more of the photon candidates result from misidentified jet fragments, results in a very uneven and spikey distribution of the event classifier scores for the simulated background in the range of BDT scores in which there is some contribution from these processes, but it is rare. So, for the event class boundary optimization procedure, the event classifier BDT scores are smoothed, using an adaptive-width Gaussian smoothing in the RooFit package [74]. Differences in performance of less than about 2 % are indistinguishable from statistical fluctuations and are regarded as insignificant.
As a result of the optimization procedure, four untagged event classes and two VBF dijet-tagged classes are defined for the 7TeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}dataset. For the 8TeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}dataset five untagged and three dijet-tagged classes are defined. Events that fail the requirement on the combined dijet-diphoton BDT score to enter the VBF dijet-tagged classes may enter other event classes. Untagged events that have a diphoton BDT score less than the lower boundaries of the untagged classes in the two datasets are not used in the final statistical analysis. The goal of the optimization setting the diphoton BDT score requirements, which define the untagged classes, is to minimize the expected uncertainty in the overall signal strength measurement. The goal of the optimization for the setting of the combined dijet-diphoton BDT score boundaries, which define the VBF dijet-tagged classes, is to minimize the expected uncertainty in the signal strength associated with the VBF production mechanism. When optimizing the boundaries for the 7TeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}dataset, for which the number of MC background events available is particularly limited, the number of dijet-tagged classes is limited to two and the lower boundary of the lowest dijet-tagged class is fixed so that the same efficiency times acceptance is obtained for VBF signal events as in the 8TeV\documentclass[12pt]{minimal}
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Figure 8 shows the combined dijet-diphoton BDT score for events satisfying the dijet preselection in 8TeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}data, and for simulated signal events from the four production processes. The outlined histogram is for simulated background events; the shaded error bands on the histogram show the statistical uncertainty in the simulation. The VBF dijet-tagged class boundaries used for the 8TeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}dataset are shown by vertical dashed lines. The classifier score is transformed such that signal events produced by the VBF process have a uniform, flat, distribution across the full range of the score. This allows the visualization of the extent to which signal events produced by the VBF process are favoured over background (which predominates in the data), and signal events produced by other processes. Events with scores below the lower boundary fail the VBF dijet-tagged selection, but remain candidates for inclusion in other classes.
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\begin{document}$$\,\text {TeV}\ $$\end{document}data (points with error bars, left axis) and for simulated signal events from the four production processes (histograms, right axis). The outlined histogram is for simulated background events; the shaded error bands on the histogram show the statistical uncertainty in the simulation. The vertical dashed lines show the boundaries of the event classes, with the leftmost dashed line representing the score below which events are not included in the VBF dijet-tagged classes, but remain candidates for inclusion in other classes. The classifier score is transformed such that signal events produced by the VBF process have a uniform, flat, distribution
The lower boundary on the untagged event class with the lowest signal-to-background ratio controls the total number of events used in the analysis and the overall signal efficiency times acceptance of the analysis (see Fig. 6). The boundary excludes events with very low score in the diphoton BDT for which the background is poorly modelled by MC simulation. Exclusion of these events has the advantage of allowing a better assessment of the expected sensitivity of the analysis, but the exact placement of the boundary is of little consequence.
It is found that, within the statistical uncertainty described above, it makes no difference if the optimization goal is the expected overall uncertainty in signal strength, the expected significance of the signal, or the expected uncertainty in the measured signal strength associated with the VBF production mechanism. It is also found that the performance maxima that fix the event class boundaries are rather shallow, so that the boundaries can be moved without significantly changing the expected performance. Adding further event classes for either the untagged or the VBF dijet-tagged events does not significantly improve the expected performance.
The overall efficiency times acceptance for SM Higgs boson events with mH=125GeV\documentclass[12pt]{minimal}
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\begin{document}$$m_\text {H}=125\,\text {GeV}\, $$\end{document} is 49.3 % (48.6 %) in the 8 (7)TeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}analysis. Investigating the properties of the simulated signal events in the untagged classes reveals, as expected, that the best untagged class (“untagged 0”) contains events in which the diphoton system has high pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}^{\gamma \gamma }\,>80\,\text {GeV}$$\end{document}), while the second best class (“untagged 1”) is dominated by events in which both photons are unconverted and situated in the central barrel region of the ECAL.
Procedure of classification
In total there are 14 event classes for the analysis of the 8TeV\documentclass[12pt]{minimal}
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Event classes for the 7 and 8TeV\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} lepton tag and multijet tag classes are selected first, and combined to form a single event class
Signal model
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\begin{document}$$\,\text {GeV}\, $$\end{document}intervals. The two possible cases regarding diphoton vertex identification, correct vertex and wrong (misidentified) vertex, are fitted separately. Good descriptions of the distributions, including the tails, can be achieved using a sum of Gaussian functions, where the means are not required to be identical. The fits are first performed for the mH=125GeV\documentclass[12pt]{minimal}
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\begin{document}$$m_\text {H}=125\,\text {GeV}\, $$\end{document} MC sample to determine the number of Gaussian functions to be used and the starting values of their parameters for the further fits to the other eight samples. As many as five Gaussian functions are used, although in most cases the use of two or three results in a good fit. Signal models for intermediate values of mH\documentclass[12pt]{minimal}
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Table 3 shows the number of expected signal events from a SM Higgs boson with mH=125GeV\documentclass[12pt]{minimal}
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\begin{document}$$m_{\gamma \gamma }=125\,\text {GeV} \, $$\end{document} . The table also shows the fraction of each Higgs boson production process (as predicted by MC simulation) as well as the mass resolution, measured both by half the width of the narrowest interval containing 68.3 % of the invariant mass distribution, σeff\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}datasets. The composition of the SM Higgs boson signal in terms of the production processes and its mass resolution is also given. The number corresponding to the production process making the largest contribution to each event class is highlighted in boldface. Numbers are omitted for production processes representing less than 0.05 % of the total signal. The variables used to characterize the resolution, σeff\documentclass[12pt]{minimal}
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\begin{document}$$\sigma _\text {eff}$$\end{document} and σHM\documentclass[12pt]{minimal}
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\begin{document}$$\sigma _\mathrm {HM}$$\end{document}, are defined in the text
It can be seen that in all classes σeff>σHM\documentclass[12pt]{minimal}
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\begin{document}$$\sigma _\text {eff}>\sigma _\mathrm {HM}$$\end{document} since the tails of the signal mass distribution are always somewhat larger relative to the width of the core of the distribution than would be the case for a Gaussian distribution. Untagged events with the best mass resolution are selected to the best event classes, and even ignoring the improving mass resolution, and considering a wide window to include all the signal events, the signal-to-background ratio improves by an order of magnitude going from the worst to the best untagged class—a significantly larger variation than the change in resolution. The highest signal-to-background ratio is achieved in the tagged classes, many of which manage to also achieve high levels of purity with respect to contamination from the ggH process.
The mass resolution achieved has improved significantly with respect to analyses of this decay mode previously reported by CMS [28], due to improved intercalibration of the ECAL, complemented by the improved supercluster energy correction regression described in Sect. 4.1. For events in which both photons are in the barrel the σeff\documentclass[12pt]{minimal}
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\begin{document}$$\sigma _\mathrm {HM}$$\end{document}, representing the core of the distribution, is slightly larger, generally an additional 5 % better, when compared to σeff\documentclass[12pt]{minimal}
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Statistical methodology
To extract a result or measurement a simultaneous binned maximum-likelihood fit to the diphoton invariant mass distributions in all the event classes is performed over the range 100<mγγ<180GeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {MeV}$$\end{document} , is sufficiently small compared to the mass resolution that no information is lost. It has been verified that a binned fit with this bin size gives the same result as an unbinned fit. The signal model is derived from MC simulation after applying the corrections determined from data/MC comparisons of Z→e+e-\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {\mu ^+}\mathrm {\mu ^-}\mathrm {\gamma }\,$$\end{document} events, as described in the previous section. The background is evaluated by fitting the mγγ\documentclass[12pt]{minimal}
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\begin{document}$$m_{\gamma \gamma }$$\end{document} distribution in data, without reference to the MC simulation. Thus the likelihood to be evaluated in a signal-plus-background fit isL=L(data|s(p,mγγ)+f(mγγ)),\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \mathcal {L}\,=\mathcal {L}\,(\text {data}|s(p,m_{\gamma \gamma })+f(m_{\gamma \gamma })), \end{aligned}$$\end{document}where p\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document} comprises those parameters of the signal, such as mH\documentclass[12pt]{minimal}
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\begin{document}$$m_\text {H}$$\end{document} or the signal strength, that are allowed to vary in the fit, s(p,mγγ)\documentclass[12pt]{minimal}
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\begin{document}$$f(m_{\gamma \gamma })$$\end{document} the background fit function.
The chosen test statistic, used to determine how signal- or background-like the data are, is based on the profile likelihood ratio. Systematic uncertainties are incorporated into the analysis via nuisance parameters and treated according to the frequentist paradigm. A description of the general methodology can be found in Refs. [75, 76]. Unless stated otherwise, the results presented here are obtained using asymptotic formulae [77], including updates introduced in the RooStats package [78].
It is important that the choice of background fit function does not bias the estimate of background obtained from the fit for any signal mass hypothesis, mH\documentclass[12pt]{minimal}
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\begin{document}$$m_\text {H}$$\end{document}, in the range of the search.
A change has been made with respect to the method used to obtain previous results, which is described in Ref. [28]. Previously, a single fit function was chosen for each class after a study of the potential bias on the estimated background. The potential bias using the chosen function was required to be negligible. The number of degrees of freedom of the fit was increased until the bias became at least five times smaller than the statistical uncertainty in the number of fitted events in a mass window corresponding to the full width at half maximum of the corresponding signal model, for any mass in the range 110≤mH≤150GeV\documentclass[12pt]{minimal}
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\begin{document}$$110\le m_\text {H}\le 150\,\text {GeV} \, $$\end{document} .
For the results reported in this paper a method, the discrete profiling method, has been developed [79] to treat the uncertainty associated with the choice of the function used to fit the background, in a similar way to systematic uncertainties associated with the measurements. The choice of the function used to fit the background, in any particular event class, is included as a discrete nuisance parameter in the likelihood function used to extract the result. All reasonable families of functions should be considered, although in practice it is found that the choice needs to be made between functions in the same families as were previously considered: exponentials, power-law functions, polynomials in the Bernstein basis, and Laurent series. When performing either a background-only fit, or a signal-plus-background fit, by minimizing the value of twice the negative logarithm of the likelihood all functions in these families are tried, with a penalty term added to account for the number of free parameters in the fitting function.
The penalized likelihood function, L~f\documentclass[12pt]{minimal}
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\begin{document}$$\widetilde{\mathcal {L}}\,_f$$\end{document}, for a single fixed background fitting function, f\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} -2\ln \widetilde{\mathcal {L}}\,_f=-2\ln \mathcal {L}\,_f+kN_{f}, \end{aligned}$$\end{document}where Lf\documentclass[12pt]{minimal}
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\begin{document}$$q(p)$$\end{document}, is used:q(p)=-2lnL~(data|p,θ^p,f^p)L~(data|p^,θ^,f^),\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} q(p)=-2\ln \frac{\widetilde{\mathcal {L}}\,(\text {data}|p,\hat{\theta }_p,\hat{f}_p)}{\widetilde{\mathcal {L}}\,(\text {data}|\hat{p},\hat{\theta },\hat{f})}, \end{aligned}$$\end{document}where the numerator represents the maximum of L~\documentclass[12pt]{minimal}
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\begin{document}$$k=1$$\end{document} the method gives consistently good coverage and negligible bias.
In order to test coverage and bias we generate pseudo-data. To do that we need first to fit the data, thus facing a problem similar to, but not to be confused with, the original problem of choosing the background fit function to model the background in the analysis. The method used to generate pseudo-data is as follows. For each event class in turn, functions from each of the families used in the discrete profiling method, and listed above, are fit to the data. In each family, the number of degrees of freedom (number of exponentials, number of terms in the series, degree of the polynomial, etc.) is increased until the χ2\documentclass[12pt]{minimal}
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\begin{document}$$p\text {-value}<0.05$$\end{document} obtained from the F-distribution [81]). At that point the function with N degrees of freedom is retained as representative of that family of functions. For each event class, the fits to the data with the retained representative functions for that class, are used to generate pseudo-background distributions.
The discrete profiling method is applied to pseudo-experiments in which signals having a range of strengths, from half to twice that of the SM, are added to the pseudo-background. The tests have demonstrated that the discrete profiling method provides good coverage of the uncertainty associated with the choice of the function, for all the functions considered as generators of background, and provides an estimate of the signal strength with negligible bias. The criterion used for this is similar and approximately equivalent to that used previously [28], the median of the distribution of the pull on the signal strength, (μmeas.-μtrue)/σμmeas.\documentclass[12pt]{minimal}
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\begin{document}$$(\mu _\text {meas.}-\mu _\text {true})/\sigma _{\mu _\text {meas.}}$$\end{document}, should be less than 0.14. This value is chosen because satisfaction of this criterion ensures that any underestimation of the uncertainty in the signal strength is less than 1 %.
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\begin{document}$$\,\text {TeV}\ $$\end{document}data samples, together with the results of a simultaneous fit of the signal-plus-background model, are shown in Figs. 9–16. The mγγ\documentclass[12pt]{minimal}
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\begin{document}$$m_{\gamma \gamma }$$\end{document}distribution of the combined event classes is shown in Sect. 11. The distributions are labeled with the s\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s}$$\end{document} and integrated luminosity of the combined datasets, reflecting the fact that the signal-plus-background fit is a simultaneous fit to the 25 event classes. Data points are drawn for all bins, including those in which there are no events. The error bars are calculated using the Garwood procedure [82] to provide correct coverage of the Poisson uncertainty. The 1σ\documentclass[12pt]{minimal}
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\begin{document}$$2\sigma $$\end{document} uncertainty bands shown for the background component of the fit include the uncertainty due to the choice of function and the uncertainty in the fitted parameters, and are computed from the variation in pseudo-experiments on the fitted background yield in bins corresponding to those used to display the data. These bands do not contain the Poisson uncertainty that must be included when the full uncertainty in the number of background events in any given mass range is estimated. The fit is performed on the data from all event class distributions simultaneously, with a single overall value of the signal strength free to vary in the fit.
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Systematic uncertainties
The uncertainty related to the background modelling, and how it is handled, has been discussed in the previous section. The systematic uncertainties related to the signal model are described below. A useful measure of the relative importance of the various systematic uncertainties can be obtained by tabulating their contributions to the total uncertainty in the final results for the best-fit signal strength and the best-fit mass. This is done in Tables 7 and 8 in Sect. 11 where the results of the analysis are discussed.
The systematic uncertainties assigned to all events are
PDF, and theory uncertainties: the theory systematic uncertainties in the production cross section and the diphoton branching fraction follow the recommendations of the LHC Higgs Cross Section Working Group [54, 83]. As can be seen in Table 7, these uncertainties make up the largest contribution to the uncertainty in the signal strength, and are dominated by the uncertainty in the ggH process cross section, coming from both uncertainties due to the missing higher orders and uncertainties related to the parton distribution functions. The effect of these theory uncertainties on the overall acceptance and on the classification of the accepted events is included by varying the pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}\,$$\end{document} and rapidity distributions of the simulated Higgs boson events as they are changed by the theory uncertainties.
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Vertex finding efficiency: the uncertainty in the vertex finding efficiency is taken from the uncertainty in the measurement of the corresponding data/MC scale factor obtained using Z→μ+μ-\documentclass[12pt]{minimal}
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\begin{document}$$R_\mathrm {9}$$\end{document} distributions of electrons and photons. The uncertainty value obtained is slightly less than 1 %, but an uncertainty of 1 % has been assigned.
The systematic uncertainties related to individual photons are
Photon energy scale uncertainty resulting from electron/photon differences: an important source of uncertainty in the energy scale of photons is the imperfect modelling of the difference between electrons and photons by the MC simulation, the most important cause of which is an imperfect description of the material between the interaction point and the ECAL. Studies of electron bremsstrahlung, photon conversion vertices, and the multiple scattering of pions suggest a deficit of material in the simulation. Although the deficit is almost certainly in specific structures and localized regions—and this hypothesis is supported by the studies—the data/MC discrepancies are slightly smaller than what would be caused by a 10 % uniform deficit of material in the region |η|<1.0\documentclass[12pt]{minimal}
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\begin{document}$$R_\mathrm {9}$$\end{document}) as are used to derive the scale corrections and the resolution smearings for simulated events. The uncertainties range from 0.05 % for unconverted photons in the ECAL central barrel, to 0.1 % for converted photons in the ECAL outer endcaps. In addition, for the barrel region, the uncertainty in the energy dependence of the Gaussian smearing applied to the simulation, is also accounted for. The energy dependence of the smearing is controlled by a parameter that shares the smearing between a constant term and a term proportional to 1/ET\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {e}^+\mathrm {e}^-\,$$\end{document} line-shape in simulation.
Photon identification BDT score, and estimate of the per-photon energy resolution: the uncertainties in these two quantities are discussed together since they are studied in the same way, and the dominant underlying cause of the observed differences between data and simulation is, almost certainly, the imperfect simulation of the shower shape—despite the fact that no obvious differences between data and simulation can be observed when the shower shape variables are examined individually. The combined contribution of the uncertainties in these two quantities dominates the experimental contribution to the systematic uncertainty in the signal strength, and has been labeled “shower shape modelling” in Table 7. The agreement between data and simulation is examined when the photon candidates are electron showers reconstructed as photons in Z→e+e-\documentclass[12pt]{minimal}
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\begin{document}$$\text {Z}\rightarrow \mathrm {\mu ^+}\mathrm {\mu ^-}\mathrm {\gamma }\,$$\end{document} events, and leading photons in preselected diphoton events where mγγ>160GeV\documentclass[12pt]{minimal}
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\begin{document}$$\pm $$\end{document}0.01 on the photon identification BDT score, together with an uncertainty in the per-photon energy resolution estimate, parameterized as a rescaling of the resolution estimate by ±\documentclass[12pt]{minimal}
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\begin{document}$$\pm $$\end{document}10 % about its nominal value, fully covers the differences observed in all three of the above data samples.
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\begin{document}$$\text {Z}\rightarrow \mathrm {e}^+\mathrm {e}^-\,$$\end{document} events with a tag-and-probe technique (see Table 1).
The effect of the single photon uncertainties is propagated to the diphoton quantities: diphoton efficiency, diphoton mass scale, and diphoton mass resolution. For instance, to obtain the magnitude of the mass-scale uncertainty resulting from a particular photon energy uncertainty, which may relate only to certain photons (such as barrel photons with R9>0.94\documentclass[12pt]{minimal}
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\begin{document}$$R_\mathrm {9}>0.94$$\end{document}), the energy of photons in simulated signal events to which the uncertainty applies is shifted by the 1σ\documentclass[12pt]{minimal}
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\begin{document}$$1\,\sigma $$\end{document} single photon uncertainty. The resulting shift of the mean of the diphoton mass distribution in each event class is determined. This shift corresponds to the effect of the single photon energy uncertainty in the diphoton mass scale and may be different for each event class. The effect of single photon uncertainties on the diphoton selection efficiency and diphoton resolution are determined in a similar way.
The sources of systematic uncertainty for the event classes targeting specific production modes are
Uncertainties in jet requirements: the largest uncertainty related to the tagging of production processes comes from a theory uncertainty and concerns the probability of producing additional jets in gluon-fusion Higgs boson production. The Stewart–Tackmann procedure [72] recommended by the LHC Higgs Cross Section Working Group [54] has been used to quantify the uncertainty in the yield of ggH events in the VBF dijet-tagged classes. The resulting uncertainty agrees comfortably with our previous estimation [28] derived by varying the underlying event tunes in ggH events produced by pythia, and that method is retained to estimate the uncertainty associated with additional jet production in the yield of ggH events in the tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} multijet-tagged class. There is a further contribution to the uncertainty in the yield of ggH events in the tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} multijet-tagged class, there is a contribution due to the limited sample size. For the VBF dijet-tagged classes, the VH dijet-tagged class, and the tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}dataset only). Further small contributions are due to the uncertainties in the jet energy scale and resolution corrections.
Lepton identification efficiency: for both electrons and muons, the uncertainty in the identification efficiency is computed by varying the data/simulation efficiency scale factor by its uncertainty. The resulting differences in the selection efficiency for the event classes tagged by leptons, range from 0.2 to 0.5 % depending on the event category, and are taken as systematic uncertainties.
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Alternative analyses
Three alternative analyses are performed using particular variations of methodology, which help to provide verification of different aspects of the analysis described in the previous sections.
Cut-based analysis
The first of these, the “cut-based” analysis described in Ref. [28], does not use multivariate techniques for selection or classification of events. Photon identification is performed by dividing photons into four mutually exclusive categories depending on whether the photon is in the barrel or endcap, and on whether or not it has R9>0.94\documentclass[12pt]{minimal}
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\begin{document}$$R_\mathrm {9}$$\end{document} are also less likely to arise from misidentification of jet fragments. Similarly, photons in the barrel have both better energy resolution and are more likely to be signal photons. Thus, the classification serves a similar purpose to the one using the BDT event classifier: events with good diphoton mass resolution, resulting from photons with good energy resolution, and with better signal-to-background ratio are grouped together. Each of the four event classes is then split into two according to the transverse momentum of the diphoton system. Since the pTγγ\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} production are also included in the cut-based analysis. The event classes tagged for VH and tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} production are defined in exactly the same way as described in Sect. 6.2, with the exception that the minimum requirements on the diphoton BDT scores are replaced by the cut-based photon identification requirements. A dijet tag is defined to select signal events produced by the VBF process by requiring a pair of jets satisfying requirements on the same variables as are used by the main analysis in the dijet BDT described in Sect. 6.2.1. These selection requirements are listed in Table 4. The tagged events are subdivided into two classes depending on whether they additionally satisfy tighter requirements on the pT\documentclass[12pt]{minimal}
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Selection requirements for the VBF dijet tag in the cut-based and dijet 2D analyses. The variables are defined in Sect. 6.2.1
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Dijet 2D analysis
The third alternative analysis, the “dijet 2D” analysis, uses a different method for extracting the signal produced by the VBF production process. The dijet invariant mass, mjj\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}datasets are divided in two and four event classes, respectively, based solely on the estimated diphoton mass resolution. The remaining events, not selected for the VBF dijet-tagged classes, are classified in the same way as in the main analysis. The 2D fit is applied to the events in the dijet-tagged classes using parametric 2D signal and background models. The signal in the other event classes is extracted using a one-dimensional fit to the mγγ\documentclass[12pt]{minimal}
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\begin{document}$$m_{\gamma \gamma }$$\end{document} distribution, as in the main analysis. This analysis provides an alternative approach to extracting the VBF signal, which provides most of the sensitivity in the measurement of vector-boson-initiated production.
Results
Figure 17 shows the mγγ\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {TeV}\ $$\end{document}samples, together with the sum of the signal-plus-background fits to the 25 event classes which results in a best-fit mass mH=124.7GeV\documentclass[12pt]{minimal}
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\begin{document}$$m_\text {H}=124.7\,\text {GeV}\, $$\end{document}. The uncertainty bands shown on the background component of the fit include the uncertainty due to the choice of function and the uncertainty in the fitted parameters. These bands do not contain the Poisson uncertainty which must be included when the full uncertainty in the number of background events in any given mass range is estimated. The excess of events over the background expectation visible near mγγ=125GeV\documentclass[12pt]{minimal}
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\begin{document}$$m_{\gamma \gamma }=125\,\text {GeV}\, $$\end{document} can be seen more clearly after subtraction of the background component, shown in the lower plot.
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\begin{document}$$2\sigma $$\end{document} uncertainty bands shown for the background component of the fit are computed from the fit uncertainty in the background yield in bins corresponding to those used to display the data. These bands do not contain the Poisson uncertainty that must be included when the full uncertainty in the number of background events in any given mass range is estimated. The lower plot shows the residual data after subtracting the fitted background component
Significance of the signal and its strength
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\begin{document}$$p$$\end{document}-value quantifies the probability for the background to produce a fluctuation as large, or larger, than the apparent signal observed, within a specified search range and uncorrected for the “look-elsewhere effect” [89]. Figure 18 shows the local p\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}-values expected for a SM Higgs boson, for the three cases, are also shown. The values of expected significance have been calculated using the background expectation obtained from the signal-plus-background fit, the so-called post-fit expectation. The post-fit model corresponds to the parametric bootstrap described in the statistics literature [90, 91], and includes information gained in the fit regarding the values of all parameters, including the best-fit mass.
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\begin{document}$$\sigma $$\end{document} is expected from the SM Higgs boson. To better visualize the excess of events, with respect to the background expectation, and its significance, the diphoton mass spectrum is plotted with each event used in the analysis weighted by a factor depending on the category in which it falls. The weight is proportional to S/(S+B)\documentclass[12pt]{minimal}
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\begin{document}$$m_{\gamma \gamma }=124.7\,\text {GeV}$$\end{document} . The background is calculated from the signal-plus-background fit. The motivation for this choice of weights is explained in Ref. [92]. The weighted data, the weighted signal model, and the weighted background model are normalized such that the integral of the weighted signal model matches the number of signal events obtained from the best fit. The resulting distribution, and the corresponding background subtracted spectrum, are shown in Fig. 19.
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The signal strength is quantified by μ=σ/σSM\documentclass[12pt]{minimal}
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\begin{document}$$\hat{\mu }\,$$\end{document}, is shown as a function of the Higgs boson mass hypothesis, both for the standard analysis (top) and for the cut-based analysis (bottom). The two analyses agree well across the entire mass range. In addition to the signal around 125GeV\documentclass[12pt]{minimal}
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\begin{document}$$m_\text {H}=151\,\text {GeV}\, $$\end{document}—slightly beyond the mass range of our analysis.
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Expected and observed best-fit values of the signal strength for a SM Higgs boson signal in the alternative analyses, together with their uncertainties, indicating the expected uncertainty in the measurement at the best-fit values of mH\documentclass[12pt]{minimal}
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The uncertainty in the signal strength may be separated into statistical and systematic contributions, with the latter further divided into those having, or not, a theoretical origin: μ^=1.14±0.21(stat)-0.05+0.09(syst)-0.09+0.13(theo)\documentclass[12pt]{minimal}
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Values of μ^\documentclass[12pt]{minimal}
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Mass measurement
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\begin{document}$$(\widehat{m}_\text {H}\,, \hat{\mu }\,)=(124.70\,\text {GeV}\, \!\!, 1.14)$$\end{document}
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\begin{document}$$\text {Z}$$\end{document}-boson mass to the Higgs boson mass. A further contribution comes from the uncertainties in the setting of the energy scale itself, that is, in the procedure and methodology of using measurement of the invariant mass in Z→e+e-\documentclass[12pt]{minimal}
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Magnitude of the uncertainty in the best fit mass induced by the systematic uncertainties in the signal model. These numbers have been obtained by quadratic subtraction of the statistical uncertainty. The statistical uncertainty includes all uncertainties in the background modelling
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\begin{document}$$\hat{\mu }\,_{\text {g}\text {g}\text {H}, \text {t}\overline{\text {t}}\text {H}\,}\!\!, \hat{\mu }\,_\text {VBF, VH})=(1.13, 1.16)$$\end{document}, and the diamond represents the SM expectation
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\begin{document}$$\sigma /\sigma _\mathrm {SM}\,$$\end{document} measured for each process are compatible with the expectations for a SM Higgs boson, as shown in Fig. 24. The signal mass, common to all four processes, is treated as an unconstrained parameter in the fit. The horizontal bars indicate ±1σ\documentclass[12pt]{minimal}
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\begin{document}$${\pm }1\,\sigma $$\end{document} uncertaintiesin the values. For comparison, the dijet 2D analysis obtains the value μ^VBF=1.6-0.7+0.9\documentclass[12pt]{minimal}
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\begin{document}$$\hat{\mu }\,_\text {VBF}=1.6^{+0.9}_{-0.7}$$\end{document}, whereas the result of the main analysis, shown in the plot, is μ^VBF=1.6-0.7+0.8\documentclass[12pt]{minimal}
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\begin{document}$$\hat{\mu }\,_\text {VBF}=1.6^{+0.8}_{-0.7}$$\end{document}. Table 10 shows the four signal strengths observed, with the contributions to their uncertainties separated into statistical and systematic components. The systematic uncertainty has been separated, where feasible, into the contributions from theoretical uncertainties, and other (experimental) uncertainties.
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\begin{document}$$\hat{\mu }\,$$\end{document}, measured for each of the production processes in a combined fit where the signal strengths of all four processes have been allowed to vary independently in the fit. The signal mass, common to all four processes, is treated as an unconstrained parameter in the fit. The horizontal bars indicate ±1σ\documentclass[12pt]{minimal}
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Decay width
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\begin{document}$$\,\text {GeV}\, $$\end{document}at a 95 % CL
Search for additional Higgs-boson-like states
To search for a possible additional Higgs-boson-like state, H′\documentclass[12pt]{minimal}
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A further particular case of interest is when the second state couples only to fermions, for example in the alignment limit of some two-Higgs-doublet models [97]. We also examine the case where the second state couples only to bosons at the tree level. Figure 28 shows the exclusion limits obtained when the observed signal near 125GeV\documentclass[12pt]{minimal}
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The shaded regions in Figs. 27 and 28, where the expected sensitivity to a second Higgs boson is severely degraded due to the presence of the already observed state, are probed by a dedicated search using the high resolution of the diphoton channel to provide sensitivity to a pair of states separated by only a few GeV\documentclass[12pt]{minimal}
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\begin{document}$$A\times \epsilon $$\end{document} for SM is shown below, where the bands indicate the spread of values among the four diphoton classes. It can be seen that the ratio is flat, independent of |cosθCS∗|\documentclass[12pt]{minimal}
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\begin{document}$$|{\cos \theta ^{*}_{\text {\tiny {CS}}}}|$$\end{document} , except at the highest values of |cosθCS∗|\documentclass[12pt]{minimal}
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\begin{document}$$|{\cos \theta ^{*}_{\text {\tiny {CS}}}}|$$\end{document} where the relative contribution from SM VBF production is significant. The events in the region where the ratio falls from its flat level, 0.75<|cosθCS∗|<1.0\documentclass[12pt]{minimal}
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\begin{document}$$0.75<|{\cos \theta ^{*}_{\text {\tiny {CS}}}}|\,<1.0$$\end{document}, are collected in a separate bin, and the |cosθCS∗|\documentclass[12pt]{minimal}
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\begin{document}$$|{\cos \theta ^{*}_{\text {\tiny {CS}}}}|$$\end{document} bin boundaries for the remaining events are chosen to maintain approximately the same event yield in each bin.
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\begin{document}$$A\times \epsilon $$\end{document} for SM is shown below, where the bands indicate the spread of values among the four diphoton classes. The |cosθCS∗|\documentclass[12pt]{minimal}
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\begin{document}$$|{\cos \theta ^{*}_{\text {\tiny {CS}}}}|$$\end{document} bin boundaries are shown by vertical dashed lines
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\begin{document}$$\text {q}\overline{\text {q}}$$\end{document}). The expected values in the five bins are obtained by constructing a representative pseudo-data model in which the overall signal strength has been set to be that obtained from fitting the model in question, plus background, to the data. When generating pseudo-experiments for a particular model, the value of all the free parameters, including the signal nuisance parameters, the background shape parameters, and the overall signal strength, are set to their best-fit values obtained by fitting the model in question to the data with a single overall value of the signal strength. The post-fit expected value of the signal strength for the SM signal model is thus that which is observed when simultaneously fitting the 40 event classes with a single signal strength, i.e. 1.31-0.31+0.33\documentclass[12pt]{minimal}
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\begin{document}$$\mu $$\end{document} values in the five bins shown in the figure are obtained from a simultaneous fit of the SM-signal-plus-background model to the 40 event classes, with five signal strength variables (one for each |cosθCS∗|\documentclass[12pt]{minimal}
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\begin{document}$$\text {q}\overline{\text {q}}$$\end{document}. The signal strength observed in the data is shown by the black points
The separation between the two models is extracted using a test statistic defined as twice the negative logarithm of the ratio of the likelihoods for the 0+\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} f(m_\text {H})&= \mu [(1-f_{\text {q}\overline{\text {q}}}\,)\times S_{\text {g}\text {g}}^{2^{+}_{m}\,}(m_\text {H})\nonumber \\&+f_{\text {q}\overline{\text {q}}}\,\times S_{\text {q}\overline{\text {q}}}^{2^{+}_{m}\,}(m_\text {H})]+B(m_\text {H}), \end{aligned}$$\end{document}where Sgg2m+(mH)\documentclass[12pt]{minimal}
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\begin{document}$$1-\mathrm {CL}_\mathrm {s}\,$$\end{document} value of 85 % (83 % expected). Intermediate mixtures, where there is less sensitivity to distinguish between the models, are somewhat less disfavoured.
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We report the observation of the diphoton decay mode of the recently discovered Higgs boson and measurement of some of its properties. The analysis uses the entire dataset collected by the CMS experiment in proton-proton collisions during the 2011 and 2012 LHC running periods. The data samples correspond to integrated luminosities of 5.1fb-1\documentclass[12pt]{minimal}
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\begin{document}$$1.14^{+0.26}_{-0.23}=1.14\pm 0.21\,\text {(stat)}\,^{+0.09}_{-0.05}\,\text {(syst)}\,^{+0.13}_{-0.09}\,\text {(theo)}$$\end{document}. The best-fit values for the signal strength modifiers associated with the ggH and tt¯H\documentclass[12pt]{minimal}
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\begin{document}$$\text {t}\overline{\text {t}}\text {H}$$\end{document} production mechanisms, and with the VBF and VH mechanisms are found to be μ^ggH,tt¯H=1.13-0.31+0.37\documentclass[12pt]{minimal}
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\begin{document}$$\hat{\mu }\,_{\text {g}\text {g}\text {H}, \text {t}\overline{\text {t}}\text {H}\,}=1.13^{+0.37}_{-0.31}$$\end{document} and μ^VBF,VH=1.16-0.58+0.63\documentclass[12pt]{minimal}
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\begin{document}$$\hat{\mu }\,_\text {VBF, VH}= 1.16^{+0.63}_{-0.58}$$\end{document}.
A direct upper limit on the natural width of the state is set at 2.4GeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {GeV}\, $$\end{document}(3.1GeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {GeV}\, $$\end{document}expected) at a 95 % confidence level, and additional SM-like Higgs bosons are excluded at a 95 % confidence level in a large fraction of the mass range between 110 and 150GeV\documentclass[12pt]{minimal}
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\begin{document}$$\,\text {GeV}\, $$\end{document}. The SM spin-0 hypothesis for the observed state is compared to a graviton-like spin-2 hypothesis with minimal couplings. The hypothesis of the signal being 2m+\documentclass[12pt]{minimal}
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\begin{document}$$2^{+}_{m}\,$$\end{document} is disfavoured. When produced entirely by gluon fusion, it is disfavoured with a 1-CLs\documentclass[12pt]{minimal}
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\begin{document}$$1-\mathrm {CL}_\mathrm {s}\,$$\end{document} value of 94 % (92 % expected).
All the results are compatible with the expectations from a standard model Higgs boson.
Acknowledgments
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 centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: the Austrian Federal Ministry of Science, Research and Economy and the Austrian Science Fund; the Belgian Fonds de la Recherche Scientifique, and Fonds voor Wetenschappelijk Onderzoek; the Brazilian Funding Agencies (CNPq, CAPES, FAPERJ, and FAPESP); the Bulgarian Ministry of Education and Science; CERN; the Chinese Academy of Sciences, Ministry of Science and Technology, and National Natural Science Foundation of China; the Colombian Funding Agency (COLCIENCIAS); the Croatian Ministry of Science, Education and Sport, and the Croatian Science Foundation; the Research Promotion Foundation, Cyprus; the Ministry of Education and Research, Estonian Research Council via IUT23-4 and IUT23-6 and European Regional Development Fund, Estonia; the Academy of Finland, Finnish Ministry of Education and Culture, and Helsinki Institute of Physics; the Institut National de Physique Nucléaire et de Physique des Particules / CNRS, and Commissariat à l’Énergie Atomique et aux Énergies Alternatives / CEA, France; the Bundesministerium für Bildung und Forschung, Deutsche Forschungsgemeinschaft, and Helmholtz-Gemeinschaft Deutscher Forschungszentren, Germany; the General Secretariat for Research and Technology, Greece; the National Scientific Research Foundation, and National Innovation Office, Hungary; the Department of Atomic Energy and the Department of Science and Technology, India; the Institute for Studies in Theoretical Physics and Mathematics, Iran; the Science Foundation, Ireland; the Istituto Nazionale di Fisica Nucleare, Italy; the Korean Ministry of Education, Science and Technology and the World Class University program of NRF, Republic of Korea; the Lithuanian Academy of Sciences; the Ministry of Education, and University of Malaya (Malaysia); the Mexican Funding Agencies (CINVESTAV, CONACYT, SEP, and UASLP-FAI); the Ministry of Business, Innovation and Employment, New Zealand; the Pakistan Atomic Energy Commission; the Ministry of Science and Higher Education and the National Science Centre, Poland; the Fundação para a Ciência e a Tecnologia, Portugal; JINR, Dubna; the Ministry of Education and Science of the Russian Federation, the Federal Agency of Atomic Energy of the Russian Federation, Russian Academy of Sciences, and the Russian Foundation for Basic Research; the Ministry of Education, Science and Technological Development of Serbia; the Secretaría de Estado de Investigación, Desarrollo e Innovación and Programa Consolider-Ingenio 2010, Spain; the Swiss Funding Agencies (ETH Board, ETH Zurich, PSI, SNF, UniZH, Canton Zurich, and SER); the Ministry of Science and Technology, Taipei; the Thailand Center of Excellence in Physics, the Institute for the Promotion of Teaching Science and Technology of Thailand, Special Task Force for Activating Research and the National Science and Technology Development Agency of Thailand; the Scientific and Technical Research Council of Turkey, and Turkish Atomic Energy Authority; the National Academy of Sciences of Ukraine, and State Fund for Fundamental Researches, Ukraine; the Science and Technology Facilities Council, UK; the US Department of Energy, and the US National Science Foundation. Individuals have received support from the Marie-Curie programme and the European Research Council and EPLANET (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 Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Science and Industrial Research, India; the HOMING PLUS programme of Foundation for Polish Science, cofinanced from European Union, Regional Development Fund; the Compagnia di San Paolo (Torino); and the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF.
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