Even though the top quark was discovered over 20 years ago [1,2] and its mass has been measured with a subpercent precision [3], direct measurements of its width Γt have an uncertainty of 50% or worse [4–6]. Indirect measurements of Γt using single top-quark production are more precise, but also require additional modeling assumptions [7,8]. In the context of the standard model (SM), the relationship between the top-quark mass and Γt is known at next-to-next-to-leading order (NNLO) in the strong coupling constant with an uncertainty of a few percent [9–11]. Improving the precision of Γt can therefore provide a stringent test of the SM.

The current methods for measuring Γt perform template fits to invariant mass spectra that peak near the top-quark mass. Because of their cleaner event signatures, the lepton+jets and dilepton decays from tt¯ production are used for the fits and the most sensitive observable is mlb: the invariant mass of a charged lepton and a jet originating from a b quark (b jet). While the location of the mlb peak is linearly sensitive to the top-quark mass, the measured width around the peak depends sublinearly on Γt. This is because the measured width is dominated by the unmeasured neutrino momentum and the fragmentation of the b quark, not by Γt.

We propose a new method for measuring Γt that is linearly sensitive to Γt [12]. The idea is motivated by recent proposals to measure the Higgs boson width from nonresonant production [17–20], which has interesting beyond the standard model (BSM) sensitivity [21–28] and has lead to measurements by the CMS [29–32] and ATLAS [33] Collaborations. Similarly, we propose to study the WWbb cross section far from the tt¯ resonance peak, using a method that can be linearly sensitive to Γt. Furthermore, this approach may be sensitive to BSM physics that only affects the nonresonant part of the spectrum. Such modifications could be due to interference effects from complex phases or from new decay channels that are kinematically inaccessible at the resonance peak.

Calculations of the top-quark width at next-to-leading order (NLO) in the strong coupling constant were first performed in Refs. [34–36]. More recently, the NNLO computation of the total width has been completed [9–11], followed by fully differential calculations of the decay rate [37,38]. At leading order (LO), the dependence of the width on the top-quark mass is given by ΓtLO=GFmt382π(1-mW2mt2)2(1+2mW2mt2),(1)assuming |Vtb|=1 and neglecting the b-quark mass [34]. For a top-quark mass of 172.5 GeV the predicted width is 1.322 GeV, including NNLO QCD, finite b-quark and W masses, and NLO electroweak corrections [37].

The width of the top quark has been measured at the Tevatron and the Large Hadron Collider (LHC) using several approaches. Direct measurements, based on the reconstructed top-quark mass distribution in events with top-quark pairs were made by the CDF [4], ATLAS [5], and CMS [6] Collaborations, with Ref. [5] obtaining the most precise value of Γt=1.76±0.33(stat)-0.68+0.79(syst) using this method. The D0 [7] and CMS [8] Collaborations have each determined the width indirectly, via a combination of the t-channel single-top cross section and measurement of the branching fraction ratio BR(t→Wb)/BR(t→Wq). The most precise estimate from Ref. [8] finds Γt=1.36±0.02(stat)-0.11+0.14(syst), with the restrictive assumption that BR(t→Wq)=1.

Recently, the ATLAS Collaboration reported a differential cross section measurement of events with two charged leptons (ℓ=e, μ) and two b jets, in an observable sensitive to both top-quark pair (tt¯) and single top-quark (tWb) production [39]. The measurement probed the interference between tt¯ and tWb by comparing the data with state-of-the-art interference models [40–43]. The target observable was the minimax pairing of lepton-jet invariant masses mbℓ, mbℓminimax=min{max(mb1ℓ1,mb2ℓ2),max(mb1ℓ2,mb2ℓ1)},(2)where the labeling of leptons and b-tagged jets is arbitrary. For values of mbℓminimax>mt2-mW2, the top-quark pair process at LO enters only through off-shell effects and tWb contributions become important. In this high-mbℓminimax region, the NLO calculation of bbℓ+νℓl-ν¯l including interference effects [44–49] and parton showering [43], provides an excellent description of the data.

The advent of such calculations enables these data to constrain other properties of the top quark. Specifically, modifications to the top-quark width impact the mbℓminimax spectrum. The origin of this dependence is twofold.

First, the cross section of events with mbℓminimax considerably greater than mt2-mW2 has a contribution from top-quark pair production diagrams, where at least one of the top (anti-)quarks is produced far off shell. The width impacts the size of this contribution directly through the top-quark line shape, which can be described as a Breit-Wigner distribution: dσdmWb2∼1(mWb2-mt2)2+mt2Γt2.(3)Integrating over both top-quark resonances, the fraction of off-shell events is found to be linearly dependent on the width [50].

Second, the “tail” cross section is also enhanced by tWb diagrams containing only one top-(anti-)quark propagator. While this is a smaller overall contribution than that of top-quark pairs, the W boson and b quark not originating from a top quark often satisfy mWb>mt, so that a comparatively large fraction of such events have mbℓminimax>mt2-mW2. For this reason, width variations affect the relative importance of these two classes of diagrams and thus the shape itself of the mbℓminimax observable.

In Ref. [39], the fractional contribution of WWbb events to 15 bins of mbℓminimax was reported, including many measurements with mbℓminimax>mt2-mW2. These data enable an extraction of the top-quark width, assuming that BSM effects modifying the width do not also modify nonresonant production. Despite the measurement not considering a width uncertainty, the unfolded result would only be impacted through migrations in the response matrix, and the effect is thus expected to be negligible. For comparison, the uncertainty due to unfolding with different interference schemes is <5% in most bins, despite the predictions leading to raw differences of 50% or more for large values of mbℓminimax.

The primary calculation used to model the W+W-bb¯ signal is the b_bbar_41 [43] generator implemented in powheg box res [51]. It includes NLO QCD corrections and matching with the parton shower (PS) based on the Powheg method [52,53]. The process is described in terms of exact matrix elements for pp→ℓ+νℓl-ν¯lbb¯, dominated by top-pair topologies with leptonic W-boson decays, with massive b quarks provided by the OpenLoops program [54]. The b_bbar_41 generator combines for the first time consistent NLO+PS treatment of top-quark resonances, including quantum corrections to top-quark propagators and off-shell top-quark decay chains; exact spin correlations at NLO, interference between NLO radiation from top-quark production and decays, full NLO accuracy in tt¯ production and decays; NLO accuracy in b-quark kinematics; access to phase-space regions with unresolved b quarks and/or jet vetoes.

The nominal event sample was obtained using the NNPDF30_nlo_as_0118 parton distribution function (PDF) set and the input top-quark mass value mt=172.5  GeV. Additional samples were generated with a range of top-quark widths Γt∈{0.66,1,ΓtSM,1.66,2}  GeV (with mt=172.5 and ΓtSM=1.3328  GeV) [55] to enable the extraction of the best-fit value from data, with a range of top-quark mass values mt∈{171.5,172.5,173.5}  GeV (with Γt=ΓtSM) in order to estimate the uncertainty due to the top-quark mass, and a range of αS values in the PDF αS∈{0.115,0.118,0.121} (with mt=172.5  GeV and Γt=ΓtSM) to explore the uncertainty due to variation of scale of the shower evolution. The central renormalization and factorization scales are set to the geometric average of transverse masses of the top quark and antitop quark, and the value of hdamp is always set equal to the input value of the top-quark mass. The samples include all possible combinations of different family final state leptons (corresponding to the channel 7 setting). Events also feature additional weights due to standard 7-point scale variation and due to PDF variation. Up to three hardest emissions are kept with the allrad 1 setting, one from the production process and one from each of the top-quark resonances, and matching to Pythia 8.2 [56] makes use of both the PowhegHooks and PowhegHooksBB4L [57] vetoes, and A14 set of tuned parameters [58]. In the samples with αS∈{0.115,0.121} the SpaceShower:alphaSValue parameter of shower evolution in Pythia 8.2 is set correspondingly.

In addition, a LO calculation of the W+W-bb¯ process is examined, calculated by Madgraph5_aMC@NLO 2.6.4 (MG5_aMC@NLO) [59] with up to 2 extra jets, matched to a parton shower implemented in Pythia 8.240. This sample of events was simulated using the NNPDF23_nlo_as_0118 PDF set, the A14 set of tuned parameters, mt=172.5  GeV, and Γt∈{0.66,1,1.33,1.66,2}  GeV. Alternative samples were produced with αS varied as described above, as well as with alternative top-quark mass hypotheses mt∈{170,175}  GeV.

Event samples are analyzed and compared to data using the selection criteria of Ref. [39] as implemented in the Rivet toolkit [60]. Briefly, leptons and jets are reconstructed at particle-level with selections based upon the acceptance of the ATLAS detector. Leptons are dressed with nearby photons and are required to have transverse momentum pT>28  GeV and pseudorapidity |η|<2.47 (2.5) for electrons (muons). Jets are reconstructed with the anti-kT algorithm using a radius parameter of R=0.4 [61–63] and considered in the analysis only if pT>25  GeV and |η|<2.5. They are b tagged if a B hadron with pT>5  GeV is found within the jet cone. Events are selected that have two leptons, two b-tagged jets, with same-flavor lepton events vetoed if the dilepton mass mℓℓ<10  GeV or satisfies |mℓℓ-mZ|<15  GeV.

The b_bbar_41 simulation produces events with different-flavor leptons and must be corrected to account for same-flavor contributions. The ee and μμ contribution is obtained by reweighting the generated eμ events that satisfy same-flavor mℓℓ requirements. Good closure of this technique is found using the LO MG5_aMC@NLO simulation, which includes all leptonic decays of the W boson. Further, the contribution of di-τ events (with fully leptonic τ decays) is found to be negligible and is not considered.

Using the experimental data of Ref. [39] and the signal models described above, the top-quark width is extracted by minimizing the following χ2 statistic: χ2=∑i,j(di-mi)Vij-1(dj-mj),(4)where di is the measured, normalized, differential cross section indexed by bins of mbℓminimax and mi is the corresponding prediction. The covariance matrix Vij gives the uncertainty on the unfolded data, including bin-to-bin correlations. The measurements with mbℓminimax<160  GeV are only weakly sensitive to variations in Γt and are thus excluded from Eq. (4).

For each systematic uncertainty, the differential cross section is computed separately for a set of test widths Γt. To interpolate between generated samples, the calculated yields are fit as a function of the top-quark width to obtain a parametrized prediction mi=Fi(Γt), individually for each bin i. Choosing the functions Fi to be quadratic in Γt is found to fit the calculated predictions well for each bin of mbℓminimax. Thus, given the data and choice of signal model, the statistic may be written explicitly as a function of the width χ2=χ2(Γt|d,m). By minimizing this function with respect to Γt, the best-fit value of the width may be extracted.

Uncertainties stemming from the precision of the experimental measurement, from choices in signal modeling, and from the limited number of generated events are each considered. Pseudoexperiments are used to assess the experimental uncertainty, where pseudodata are drawn from a multivariate Gaussian distribution with mean and covariance matrix given by di and Vij. For each pseudoexperiment a random dataset dipseudo is drawn from this distribution and a new value of Γt is extracted by minimizing χ2(Γt|dipseudo,mi). The experimental uncertainty is calculated as the 1σ range of extracted widths from the pseudoexperiment distribution.

Theoretical uncertainties are assessed on the b_bbar_41 signal model by generating event samples with alternative input parameters. The nominal simulated sample with alternative weight sets is used to estimate the uncertainty due to the choice of PDF as well as renormalization and factorization scales. The PDF uncertainty is assessed as the standard deviation of widths extracted over the set of 100 eigenvector variations of the NNPDF30_nlo_as_0118 PDF set. The scale uncertainty is the maximum pairwise difference between the widths extracted with the nominal and varied scales.

For top-quark mass and αs variations, independent samples of events are generated. To minimize the impact of statistical variations across samples and make optimal use of all generated events, the systematic uncertainty dependence is extracted in a fit, writing mi(αs,mt)=m^i(αsSM,mtSM)+a^i(αs-αsSM)+b^i(mt-mtSM).(5)Further, the fitted coefficients a^i, b^i are constrained to vary quadratically in mbℓminimax to reduce unphysical, statistical fluctuations. The postfit yields for mt and αs variations are then used to reweight the nominal mbℓminimax spectra for each value of the top-quark width and to extract the χ2-minimizing value for each variation.

An uncertainty due to the finite number of simulated events is estimated from an ensemble of pseudoexperiments where the predicted yields for all bins of each value of the top-quark width are varied within their uncertainties. A width is obtained for each trial to assess the impact on the final extracted parameter.

For the MG5_aMC@NLO signal model, an identical set of uncertainties are assessed, employing the same estimation methods, with the following modification: the NNPDF23_nlo_as_0119 PDF set is used as the nominal value for this sample. The top-quark mass uncertainty is assessed using samples with mt=170, 175 GeV, interpolating to obtain the same 1 GeV variations as used above.

The nominal b_bbar_41 prediction is compared to ATLAS data in Fig. 1. Predictions for alternate values of the top-quark width are also shown, as well as the theoretical uncertainty on the nominal estimate. A summary of the uncertainties on the width extracted using both signal models is presented in Table I. Changes to the top-quark width are found to produce larger variations in the relative fraction of events in the mbℓminimax tail for samples generated using MG5_aMC@NLO than b_bbar_41. As a result, the impact of uncertainties on the extracted width parameter is generally smaller when using the LO simulation, despite the impact on the normalized differential cross section being similar. This effect leads to a smaller uncertainty due to scale variations, among others, in the LO sample than in the more accurate b_bbar_41 calculation.

Using the b_bbar_41 signal description, a top-quark width of 1.28±0.30  GeV is extracted (1.33±0.29  GeV expected), as shown in Fig. 2. A width is also extracted using the leading order MG5_aMC@NLO simulation, obtaining 1.18±0.22  GeV (1.33±0.23  GeV expected). These measurements are more precise than the previously most precise direct measurement of (1.76-0.76+0.86  GeV) [5].

These results can also be interpreted into a limit on the BSM decays of the top-quark through the relation BR(t→BSM)<Γext+95%-Γt→bWSMΓext+95%,(6)where Γt→bWSM is the SM partial width for t→Wb and Γext+95% is the (one-sided) upper limit on the top-quark width at the 95% confidence level. The limit is BR(t→BSM)<29% using the b_bbar_41 model (30% expected) and 18% using the MG5_aMC@NLO model (26% expected). Model-specific BSM constraints are also possible for processes which have a significant effect in the off-shell region defined by high mbℓminimax. For example, a charged Higgs H+ produced via its btH+ coupling and then decaying via τν would preferentially enhance this region. However, limits from this measurement are not as strong as direct searches [64–66] because of the penalties from the τ decay to e/μ.

In conclusion, we present a novel method to directly measure the top-quark width and have provided a first estimate using the technique based on a recent measurement of top-quark properties by the ATLAS Collaboration. The estimate of 1.28±0.31  GeV obtained using the powheg box res calculation is in good agreement with the standard model prediction of 1.32 GeV and more precise than existing direct measurements. Future measurements with more data and in combination with other extractions will be able to provide robust constraints on the top sector of the SM.