Model independent top quark width measurement using a combination of resonant and non resonant cross sections

Though top quark was discovered more than twenty years ago, measurement of its width is still challenging task. Most measurements either have rather low precision or they are done in assumption of the SM top quark interactions. We consider model independent parametrization of the top quark width and provide estimations on achievable accuracy using a combination of fiducial cross sections in double, single and non-resonant regions.


I. INTRODUCTION
The top quark is the heaviest known elementary particle. This fact makes it along with the Higgs In this paper we discuss another method of setting model independent limits on the top quark width in a complete gauge invariant way by fitting fiducial cross sections of W + bW −b production in certain phase space regions called double-resonant, single-resonant, and non-resonant. Similar method for the case of e + e − collisions has been discussed in [8]. The idea of the method was illustrated on a simple 2 → 3 example for the process gg → tW −b in [9]. This work is a generalization of that study.
The idea of the width measurement from the comparison of rates in on-and off-shell regions was previously proposed for the Higgs boson [10,11]. In corresponding measurements the Higgs boson width is extracted from pp → ZZ production above the threshold and from pp → H → ZZ * production below the threshold in the ZZ * mass region close the Higgs boson mass. This approach can not be directly applied to the top quark. The Higgs boson is much more narrow resonance than the top quark. This fact allows to calculate separately amplitudes for pp → ZZ and pp → H → ZZ * processes in a gauge invariant way. In case of the off-shell top quark production with its subsequent decay to W b one can not make calculations of diagrams involving the top quark pair and the single top separately in a gauge invariant way. Therefore we perform the computation of the complete gauge invariant set of diagrams and investigate a sensitivity of fiducial cross sections to deviations from the SM caused by the top quark width and related Wtb coupling. This approach enables to 3 put model independent and fully gauge invariant constrains on the top quark width.
A. Study of the process pp → W + W − bb We consider complete tree-level set of Feynman diagrams for the process pp → W + W − bb, in which both top quarks are off-shell. As well known, the main contribution comes from the gluon fusion subprocess [12], however, we take into account the contributions from all partonic subprocesses. The CompHEP generator [13] with MSTW2008 PDF [14] is used for the calculation.
The computations are performed for a certain value of the top quark mass, for a definiteness it was taken to be m t = 172.5 GeV, and for various values of the top quark width with the corresponding rescaling of the Wtb coupling.
Hadronization and fragmentation effects, as well as backgrounds impact are postponed to the next more realistic analysis, not to distract from the main idea of this research. Realistic estimations of this effects will be included in systematic uncertainty estimations.
The NLO QCD corrections for the process pp → W + W − bb were computed [15] showing an impact on various kinematic distributions and making results more stable with respect to the QCD scale variation. The NLO corrections to the complete 2 → 6 process involving off-shell W bosons were calculated [16] and the k-factor for 13 TeV LHC energy was found to be 1. 16. At this stage of our analysis, which aims to show the main effect caused by the width change, the complete leading order contributions have been taken into account, and the impact of the NLO corrections has been included in the assumed systematic uncertainties, as will be explained below.
The boundaries of fiducial double-resonant, single-resonant and non-resonant regions are expressed in terms of the SM value of the top quark width in the following way.
Here M W + b and M W −b are the invariant masses, n and k are integer numbers with obvious requirement n ≤ k to have no overlapping regions.
One can parametrize the total top quark width as follows reflecting that the top quark width may differ from its SM value either by a modification of the Wtb coupling (e.g. see [17]) or by a presence of additional non-SM decay modes (e.g. see [18,19]). In Eq. 2 the parameter ξ simultaneously changes the top quark width and rescales the W tb coupling.
The parameter ∆ affects the only top quark width. One should note the production cross section times branching ratio remains unchanged with variation of the parameter ξ in case of ∆ = 0. It is useful to parametrize the deviation ∆ also in terms of the SM top quark width as ∆ = δ · Γ SM t . The parameters ξ and δ have different origin, affect the matrix element in a different way, and therefore can not be combined in a single parameter.
In the SM ξ = 1 and δ = 0. In order to study deviations of the top quark width from its SM value it is more convenient to have two parameters equal to zero in the SM and introduce the parameter instead of ξ as follows.
= ξ 2 − 1. ( Current experimental data [2-6] indicate that deviations from the SM for the top quark width should be small. Not to contradict with this we will study dependencies of fiducial cross sections from two small parameters and δ. As demonstrated in [9], it is reasonable to select integer parameters n and k in the interval from 10 to 20 for boundaries between resonant and non-resonant Precision measurements of the fiducial cross sections of the top quark production play a crucial role. Experimental analysis precision is limited by systematic uncertainties of jet energy scale, b-tagging and luminosity [21]. Statistical uncertainties are below percent level today and will decrease further with high luminosity updates [22]. We assume feasible accuracy of 10%, 8% and 5% for 14, 28 and 100 TeV collision energies including theoretical uncertainties at NLO, NNLO and, possibly, higher level by the time when new high energy machines will be realized. Using the standard χ 2 method ( χ 2 (σ) = σ SM −σ Model independent constrains on the top quark width are estimated to be from 23% to 12% for the energies from 14 to 100 TeV with assumed experimental accuracy of fiducial cross section measurements from 10% to 5%.

II. RESULTS
Gauge invariant estimation of deviations of the top quark width from its SM value is obtained in different kinematic regions. It is shown that top quark production cross section in the double resonant (DR) region is mostly sensitive to the δ parameter, which modifies only the top quark width. The fiducial cross section in the non-resonant (NR) region has sensitivity to parameter, which modifies top quark width and the Wtb coupling simultaneously. Single resonant (SR) region has comparative sensitivity to both parameters. Significant difference in dependence of fiducial cross sections in DR, SR and NR regions on and δ parameters one of the main observation of this study. This fact allows to put combined limits on δ and parameters simultaneously, and using these limits obtain constrains on the top quark. Achievable constrains in the model independent way on the top quark width are estimated to be from 23% to 12% for corresponding experimental accuracy from 10% to 5%. These results are achieved using simplified approach, all effects such as hadronization and fragmentation, detector response as well as an impact of backgrounds are beyond the scope of current simply study demonstrating the main idea. Study of mentioned effects is postponed to the next more realistic analysis.

III. ACKNOWLEDGMENTS
The work was supported by grant 16-12-10280 of Russian Science Foundation.