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| CMS-TOP-19-007 ; CERN-EP-2019-189 | ||
| Running of the top quark mass from proton-proton collisions at ${\sqrt{s}} = $ 13 TeV | ||
| CMS Collaboration | ||
| 19 September 2019 | ||
| Phys. Lett. B 803 (2020) 135263 | ||
| Abstract: The running of the top quark mass is experimentally investigated for the first time. The mass of the top quark in the modified minimal subtraction (${\mathrm{\overline{MS}}} $) renormalization scheme is extracted from a comparison of the differential top quark-antiquark ($\mathrm{t\bar{t}}$) cross section as a function of the invariant mass of the $\mathrm{t\bar{t}}$ system to next-to-leading-order theoretical predictions. The differential cross section is determined at the parton level by means of a maximum-likelihood fit to distributions of final-state observables. The analysis is performed using $\mathrm{t\bar{t}}$ candidate events in the $\mathrm{e}^{\pm}\mu^{\mp}$ channel in proton-proton collision data at a centre-of-mass energy of 13 TeV recorded by the CMS detector at the CERN LHC in 2016, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The extracted running is found to be compatible with the scale dependence predicted by the corresponding renormalization group equation. In this analysis, the running is probed up to a scale of the order of 1 TeV. | ||
| Links: e-print arXiv:1909.09193 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
Distribution of $ {m_{\mathrm{t} {}\mathrm{\bar{t}}} ^{\text {reco}}}$ after the fit to the data, with the same binning as used in the fit. The hatched band corresponds to the total uncertainty in the predicted yields and includes all correlations. The ${\mathrm{t} {}\mathrm{\bar{t}}}$ MC sample is split into four subsamples, denoted with "Signal $({\mu _k})$'', corresponding to bins of ${m_{\mathrm{t} {}\mathrm{\bar{t}}}}$ at the parton level. The first and last bins contain all events with $ {m_{\mathrm{t} {}\mathrm{\bar{t}}} ^{\text {reco}}} < $ 420 GeV and $ {m_{\mathrm{t} {}\mathrm{\bar{t}}} ^{\text {reco}}} > $ 810 GeV, respectively. |
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Figure 2:
Measured values of ${\sigma _{\mathrm{t} {}\mathrm{\bar{t}}} ^{(\mu _k)}}$ (markers) and their uncertainties (vertical error bars) compared to NLO predictions in the ${\mathrm {\overline {MS}}}$ scheme obtained with different values of ${{m_{\mathrm{t}}} ({m_{\mathrm{t}}})}$ (horizontal lines of different styles). The values of ${\sigma _{\mathrm{t} {}\mathrm{\bar{t}}} ^{(\mu _k)}}$ are shown at the representative scale of the process ${\mu _k}$, defined as the centre-of-gravity of the ${m_{\mathrm{t} {}\mathrm{\bar{t}}}}$ spectrum of each bin. The first and last bins contain all events with $ {m_{\mathrm{t} {}\mathrm{\bar{t}}}} < $ 420 GeV and $ {m_{\mathrm{t} {}\mathrm{\bar{t}}}} > $ 810 GeV, respectively. |
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Figure 3:
Extracted running of the top quark mass $ {{m_{\mathrm{t}}} (\mu)} / {{m_{\mathrm{t}}} ({\mu _\text {ref}})} $ compared to the RGE prediction at one-loop precision ($ {n_f} = $ 5) evolved from the initial scale $\mu _0 = {\mu _\text {ref}} = $ 476 GeV (left). The result is compared to the value of $ {{m_{\mathrm{t}}} ^\text {incl}({m_{\mathrm{t}}})} / {{m_{\mathrm{t}}} ({\mu _\text {ref}})} $, where ${{m_{\mathrm{t}}} ^\text {incl}({m_{\mathrm{t}}})}$ is the value of ${{m_{\mathrm{t}}} ({m_{\mathrm{t}}})}$ extracted from the inclusive cross section measured in Ref. [14], which is based on the same data set. The uncertainty in ${{m_{\mathrm{t}}} ^\text {incl}({m_{\mathrm{t}}})}$ is evolved from the initial scale $\mu _0 = {m_{\mathrm{t}}} = $ 163 GeV using the same RGE prediction (right). |
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Figure 3-a:
Extracted running of the top quark mass $ {{m_{\mathrm{t}}} (\mu)} / {{m_{\mathrm{t}}} ({\mu _\text {ref}})} $ compared to the RGE prediction at one-loop precision ($ {n_f} = $ 5) evolved from the initial scale $\mu _0 = {\mu _\text {ref}} = $ 476 GeV. The result is compared to the value of $ {{m_{\mathrm{t}}} ^\text {incl}({m_{\mathrm{t}}})} / {{m_{\mathrm{t}}} ({\mu _\text {ref}})} $, where ${{m_{\mathrm{t}}} ^\text {incl}({m_{\mathrm{t}}})}$ is the value of ${{m_{\mathrm{t}}} ({m_{\mathrm{t}}})}$ extracted from the inclusive cross section measured in Ref. [14], which is based on the same data set. |
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Figure 3-b:
The uncertainty in ${{m_{\mathrm{t}}} ^\text {incl}({m_{\mathrm{t}}})}$ is evolved from the initial scale $\mu _0 = {m_{\mathrm{t}}} = $ 163 GeV using the same RGE prediction. |
| Tables | |
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Table 1:
Bins of ${m_{\mathrm{t} {}\mathrm{\bar{t}}}}$, the corresponding fraction of events in the {powheg} simulation, and the representative scale ${\mu _k}$. |
| Summary |
|
In this Letter, the first experimental investigation of the running of the top quark mass, ${m_{\mathrm{t}} }$, is presented. The running is extracted from a measurement of the differential top quark-antiquark ($\mathrm{t\bar{t}}$) cross section as a function of the invariant mass of the $\mathrm{t\bar{t}}$ system, $ {m_\mathrm{t\bar{t}}} $. The differential $\mathrm{t\bar{t}}$ cross section, ${{\mathrm{d}}{\sigma_\mathrm{t\bar{t}}} /{\mathrm{d}{m_\mathrm{t\bar{t}}}}} $, is determined at the parton level using a maximum-likelihood fit to distributions of final-state observables, using $\mathrm{t\bar{t}}$ candidate events in the $\mathrm{e}^{\pm}\mu^{\mp}$ channel. This technique allows the nuisance parameters to be constrained simultaneously with the differential cross section in the visible phase space and therefore provides results with significantly improved precision compared to conventional procedures in which the unfolding is performed as a separate step. The analysis is performed using proton-proton collision data at a centre-of-mass energy of 13 TeV recorded by the CMS detector at the CERN LHC in 2016, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The running mass ${m_{\mathrm{t}} (\mu)} $, as defined in the modified minimal subtraction ($ {\mathrm{\overline{MS}}} $) renormalization scheme, is extracted at next-to-leading order (NLO) as a function of $ {m_\mathrm{t\bar{t}}} $ by comparing fixed-order theoretical predictions at NLO to the measured ${{\mathrm{d}}{\sigma_\mathrm{t\bar{t}}} /{\mathrm{d}}{m_\mathrm{t\bar{t}}}} $. The extracted running of ${m_{\mathrm{t}} }$ is found to be in agreement with the prediction of the corresponding renormalization group equation, within {1.1} standard deviations, and the no-running hypothesis is excluded at above 95% confidence level. The running of ${m_{\mathrm{t}} }$ is probed up to a scale of the order of 1 TeV. |
| Additional Figures | |
png pdf |
Additional Figure 1:
Extracted running of the top quark mass $m_{\mathrm{t}}(\mu_{m})/m_{\mathrm{t}}(\mu_{\text{ref}})$ (dots) compared to the one-loop solution of the corresponding renormalization group equation (RGE, line), assuming five active quark flavours ($n_{f} = $ 5), calculated from the initial scale $\mu_{0} = \mu_{\text{ref}} = $ 238 GeV (hollow dot). In the calculation, the scale $\mu_{m}$ is set to $ \mu_{k} $/2, where $\mu_{k}$ is the centre-of-gravity of the $m_{\mathrm{t\bar{t}}}$ distribution in bin $k$, as defined in Phys. Lett. B 803 (2020) 135263. In this way, $\mu_{m}$ is set independently in each bin of $m_{\mathrm{t\bar{t}}}$ and the value of $m_{\mathrm{t}}(\mu_{k}/2)$ is extracted directly. The values of $\mu_{\text{r}}$ and $\mu_{\text{f}}$ are both set to $m_{\mathrm{t}}(\mu_{m})$. The best-fit value of the parameter $x$ in Eq. 3 of Phys. Lett. B 803 (2020) 135263 is found to be $\hat{x} = $ 1.57 $\pm$ 0.57 (fit) $^{+0.28}_{-0.53}$ (PDF + $\alpha_{\text{S}}$) $^{+0.21}_{-0.46}$ (extr), in good agreement with the RGE prediction, which corresponds to $x =$ 1. The no-running hypothesis, corresponding to $ x =$ 0, is excluded at 96.2% confidence level. The extracted running is compared to the result presented in Phys. Lett. B 803 (2020) 135263, but with the choice of $\mu_{m}$ described above (hollow squares). |
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Compact Muon Solenoid LHC, CERN |
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