Measurements of the Top Quark Decay Width

In the past years, measurements of the top quark decay width were performed at the Tevatron and the LHC. Such measurements are either direct or indirect. The latter term refers to the fact that indirect measurements rely on certain SM assumptions as it will be explained in more detail in the following. This section presents those recent measurements ofΓ_t to allow for a comparison with the result obtained in this analysis.

The latest direct measurement at the Tevatron was published by the CDF collaboration[14]. This analysis uses the full Tevatron Run II dataset ofp

s=1.96 TeV proton-antiproton collision data and concentrates on decays in the lepton+jets decay channel oft¯t pairs. The dataset recorded by the CDF II detector corresponds to an integrated luminosity of 8.7 fb⁻¹. The mass of the top quark and of the hadronically decayingWboson are reconstructed for all events and compared with distributions from Monte Carlo signal and background samples to evaluateΓ_t. The reconstructed top quark mass distribution measured in data is compared to templates from generatedt¯t signal samples based on decay width values in the range from 0.1 to 30 GeV, assuming a fixed top quark mass of 172.5 GeV, in order to distinguish between differentΓt values in this measurement. Furthermore, a set of samples is generated where the jet energy scale (JES), as one of the dominant systematic uncertainties, is varied independently. The jet energies are modified in data by a factor of 1+∆JES to take the energy scale uncertainty of the measurement into account while in the simulated samples∆JES is varied from−3σc to+3σc. The latter factor denotes the CDF fractional uncertainty of the JES.

The main analysis steps are thus the following: After the event selection according to the require-ments of the lepton+jets decay channel, the top quark mass m_t and the hadronically decaying W boson massm_{j j} are reconstructed for all events. The former is the observable sensitive to the decay widthΓt whereas the latter is used for the in-situ calibration of the JES. This analysis step is followed by a template likelihood fit of bothm_t andm_{j j} using simulated signal and background events. Example templates for these two mass observables are shown in Fig. 2.11.

The result of the template fit is utilised to extract 68% confidence level (CL) limits ofΓt based on

(a) (b)

Figure 2.11:(a)m_ttemplates for three different values ofΓtwith the nominal setting∆JES= 0 and (b)m_{j j} templates for three values of∆JESbased onΓt=1.5GeV as used in the direct decay width measurement performed by CDF [14].

a likelihood ratio ordering. A central value of Γ_t =1.63 GeV is retrieved from data leading to a two-sided limit of 1.10 <Γ_t < 4.05 GeV at the 68% CL for a fixed top quark mass of 172.5 GeV.

This measured range is equivalent to a lifetime of 1.6·10⁻²⁵< τt<6.0·10⁻²⁵s.

A direct measurement was also performed by the CMS Collaboration recently using 12.9 fb⁻¹ of proton-proton collision data collected atp

s=13 TeV[15]. To obtain this preliminary result, the measurement is realised in the dilepton channel oft¯tdecays, i.e. events are selected that contain at least two charged leptons (electrons or muons) and at least two jets with at least one jet identified as abjet. Signal samples includet¯tevents and also the single topW tcontribution. The utilised signal MC samples have next-to-leading order precision in production but only leading order accuracy in decay. As a consequence, this measurement is assumed to be sensitive to missing orders in the MC precision.

The observable used for the decay width measurement is the invariant mass of the lepton and the b-tagged jet,m_{`b</sub>. As two masses can be reconstructed per event,m<sub>`b}is derived from a pairing of the two leading-p_Tcharged leptons with two leading-p_T b-tagged jets. The resulting distribution is compared to simulated expectations corresponding to different underlying decay width values employing a likelihood technique. Likelihood ratios obtained from pairs of shape hypotheses are analysed to test different hypotheses of alternative values ofΓ_t. The null hypothesis corresponds to the SM prediction of Γt. Using ratios of relativistic Breit-Wigner distributions, the alternative hypotheses are created by reweighting the parton level top quark mass distributions. For the validation of this reweighting method, a sample based on a width of four times the SM value is employed. The hypotheses tests yield a result of 0.6 <Γt <2.5 GeV at the 95% CL assuming a top quark mass of 172.5 GeV. The evolution of the corresponding CL_S curve used to evaluate theΓt

range is shown in Fig. 2.12.

2 . 3 T O P Q U A R K D E C AY W I D T H

Figure 2.12:Evolution of CL_Sas a function ofΓt used to compute 95% confidence level limits.

Pre- and post-fit model expectations as well as the measured curve are shown. µdenotes the signal strength [15].

The top quark decay width was also measured indirectly, i.e. these measurements are based on certain Standard Model assumptions as outlined in the following and thus not as sensitive to BSM physics as direct measurements are.

A very recent indirect measurement ofΓt was conducted by the CMS experiment using t¯t decays in the dilepton channel collected in proton-proton collision data recorded atp

s=8 TeV with an integrated luminosity of 19.7 fb⁻¹ [173]. This measurement is based on the extraction of the ratio of branching fractionsR=B(t→W b)/B(t→W q). The value ofR is obtained from a fit using the observed b-tagged jet distributions with a parametric model which relies on the measured cross-section and corrects for the fraction of jets in the events that cannot be associated with a single top quark decay (t→W q). The resulting value ofR from the fit is combined with a CMS measurement of the single top t-channel cross-section[174]to obtain the indirect estimate ofΓt. Using the assumption thatP

q=B(t→W q) =1, the ratio reduces toR=B(t→W b)and the decay width can be determined via:

Γt= σt−channel

B(t→W b)·Γ(t→W b)

σ^theory_t−channel =R⁻¹·σt−channel

σ^theory_t−channelΓ(t→W b).

The termΓ(t →W b) denotes the partial decay width of the top quark to decay into aW boson and a bquark,σ_t−channel andσ^theory_t−channel are the measured and the theoreticalt-channel single top quark cross-sections, respectively. The value for the measured single top cross-section is taken from [174] where the theoretical calculation originates from [94]. The partial decay width is computed for a top quark mass ofm_t =172.5 GeV and amounts toΓ(t→W b) =1.329 GeV[28] with a theoretical uncertainty of less than 1%. The only quantity remaining isR and, hence, the

decay width Γt is extracted using a maximum-likelihood fit similar to the determination of the value ofR[173]leavingΓ_t as a free parameter. The uncertainties on the predicted and measured cross-sections are considered via additional nuisance parameters in the fit. The result is found to be Γt =1.36±0.02(stat.)⁺_−0.11^0.14 (syst.)GeV, which is in good agreement with the SM expectation.

The dominant source of systematic uncertainty is due to the value of the measured t-channel cross-section.

Another indirect measurement ofΓt using the same analysis strategy was performed by the DØ ex-periment at the Tevatron collider atp

s=1.96 TeV and yieldedΓt=2.00⁺₋^0.47_0.43[175].