CMS-PAS-TOP-19-007 | ||

First measurement of the running of the top quark mass | ||

CMS Collaboration | ||

August 2019 | ||

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Abstract:
The first measurement of the running of the top quark mass is presented. The mass of the top quark in the modified minimal subtraction renormalization scheme is extracted from the differential $\mathrm{t\bar{t}}$ cross section as a function of the invariant mass of the $\mathrm{t\bar{t}}$ system via a $\chi^2$ fit to next-to-leading-order differential theory predictions. The differential cross section is measured at the parton level by means of a maximum-likelihood fit to multidifferential distributions of final state observables. The analysis is performed using $\mathrm{t\bar{t}}$ candidate events in the $\mathrm{e}^\pm \mu^\mp$ final state, using data recorded by the CMS experiment at the CERN LHC in 2016 corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The observed running is found to be compatible with the scale dependence predicted by the renormalization group equation.
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Links:
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These preliminary results are superseded in this paper, PLB 803 (2020) 135263.The superseded preliminary plots can be found here. |

Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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Figures | |

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Figure 1:
Measured values of ${\sigma _{\mathrm{t} \mathrm{\bar{t}}} ^{(\mu _k)}}$ (dots) and their uncertainties (vertical error bars) compared to NLO predictions in the ${\mathrm {\overline {MS}}}$ scheme obtained with different values of ${{m_\mathrm {\mathrm{t}}} ({m_\mathrm {\mathrm{t}}})}$ (lines of different colours). The values of ${\sigma _{\mathrm{t} \mathrm{\bar{t}}} ^{(\mu _k)}}$ are shown at the central scale of the process $\mu _k$, defined as the centre-of-gravity of the ${m_{\mathrm{t} \mathrm{\bar{t}}}}$ spectrum of each bin. |

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Figure 2:
Left: measured running of the top quark mass ${{m_\mathrm {\mathrm{t}}} (\mu)}$/$ {m_\mathrm {\mathrm{t}}} (\mu _\text {ref})$ compared to the prediction from RGE solved with one-loop precision assuming five active flavours. The reference scale $\mu _\text {ref}$ corresponds to 476.2 GeV. Right: comparison of the result with the value of ${{m_\mathrm {\mathrm{t}}} ^\text {incl}({m_\mathrm {\mathrm{t}}})} $/$ {m_\mathrm {\mathrm{t}}} (\mu _\text {ref})$, where ${{m_\mathrm {\mathrm{t}}} ^\text {incl}({m_\mathrm {\mathrm{t}}})} $ is extracted from the inclusive ${\mathrm{t} \mathrm{\bar{t}}}$ cross section measurement of Ref. [7] at NLO. The uncertainty in ${{m_\mathrm {\mathrm{t}}} ^\text {incl}({m_\mathrm {\mathrm{t}}})} $ includes experimental, extrapolation and PDF uncertainties. The measurement of the inclusive ${\sigma _{\mathrm{t} \mathrm{\bar{t}}}}$ uses the same data as this analysis. |

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Figure 2-a:
Left: measured running of the top quark mass ${{m_\mathrm {\mathrm{t}}} (\mu)}$/$ {m_\mathrm {\mathrm{t}}} (\mu _\text {ref})$ compared to the prediction from RGE solved with one-loop precision assuming five active flavours. The reference scale $\mu _\text {ref}$ corresponds to 476.2 GeV. Right: comparison of the result with the value of ${{m_\mathrm {\mathrm{t}}} ^\text {incl}({m_\mathrm {\mathrm{t}}})} $/$ {m_\mathrm {\mathrm{t}}} (\mu _\text {ref})$, where ${{m_\mathrm {\mathrm{t}}} ^\text {incl}({m_\mathrm {\mathrm{t}}})} $ is extracted from the inclusive ${\mathrm{t} \mathrm{\bar{t}}}$ cross section measurement of Ref. [7] at NLO. The uncertainty in ${{m_\mathrm {\mathrm{t}}} ^\text {incl}({m_\mathrm {\mathrm{t}}})} $ includes experimental, extrapolation and PDF uncertainties. The measurement of the inclusive ${\sigma _{\mathrm{t} \mathrm{\bar{t}}}}$ uses the same data as this analysis. |

png pdf |
Figure 2-b:
Left: measured running of the top quark mass ${{m_\mathrm {\mathrm{t}}} (\mu)}$/$ {m_\mathrm {\mathrm{t}}} (\mu _\text {ref})$ compared to the prediction from RGE solved with one-loop precision assuming five active flavours. The reference scale $\mu _\text {ref}$ corresponds to 476.2 GeV. Right: comparison of the result with the value of ${{m_\mathrm {\mathrm{t}}} ^\text {incl}({m_\mathrm {\mathrm{t}}})} $/$ {m_\mathrm {\mathrm{t}}} (\mu _\text {ref})$, where ${{m_\mathrm {\mathrm{t}}} ^\text {incl}({m_\mathrm {\mathrm{t}}})} $ is extracted from the inclusive ${\mathrm{t} \mathrm{\bar{t}}}$ cross section measurement of Ref. [7] at NLO. The uncertainty in ${{m_\mathrm {\mathrm{t}}} ^\text {incl}({m_\mathrm {\mathrm{t}}})} $ includes experimental, extrapolation and PDF uncertainties. The measurement of the inclusive ${\sigma _{\mathrm{t} \mathrm{\bar{t}}}}$ uses the same data as this analysis. |

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 note, the first measurement of the running of the top quark mass is presented. The running of $ {m_{\mathrm{t}} (\mu)} $ is extracted at next-to-leading order as a function of the invariant mass of the $\mathrm{t\bar{t}}$ system, $ {m_{\mathrm{t\bar{t}}}} $, from a measurement of the differential $\mathrm{t\bar{t}}$ cross section obtained using proton-proton collision data recorded by the CMS experiment at the centre-of-mass energy of 13 TeV. The measurement is performed using $\mathrm{t\bar{t}}$ candidate events in the final state with an electron and a muon of opposite charge. The differential $\mathrm{t\bar{t}}$ cross section is measured at the parton level as a function of $ {m_{\mathrm{t\bar{t}}}} $ using a maximum-likelihood fit to multidifferential distributions of final state observables. This technique, known as maximum-likelihood unfolding, allows constraining the nuisance parameters simultaneously with the differential cross section and therefore provides results with significantly improved precision compared to conventional procedures in which the unfolding is performed as a separate step. The ${\mathrm{\overline{MS}}}$ mass of the top quark $m_{\mathrm{t}} (m_{\mathrm{t}} )$ is determined independently in each $ {m_{\mathrm{t\bar{t}}}} $ bin via a ${\chi^2}$ fit to theory predictions at next-to-leading order. The extracted masses are then evolved to the representative scale of the process in each bin. The observed evolution of $ {m_{\mathrm{t}} (\mu)} $ is found to be in agreement with the prediction from the renormalization group equation at one-loop precision, within {1.3} standard deviations, and the significance of the observed running is found to be 2.6 standard deviations with respect to the no-running hypothesis. |

Additional Figures | |

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Additional Figure 1:
Distribution of the reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system after the fit to the data, with the same binning as used in the fit. The hatched band corresponds to the total systematic uncertainty including all correlations, while the solid gray band represents the contribution of the statistical uncertainty in the MC simulation. The $ \mathrm{t\bar{t}} $ MC sample is split into four subsamples, denoted with "Signal ($\mu_k$)'', corresponding to the bins in invariant mass of the $ \mathrm{t\bar{t}} $ system at the parton level. |

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Additional Figure 2:
Post-fit distribution of fit input in the category with less than two jets and zero or more than two b-tagged jets. |

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Additional Figure 3:
Post-fit distribution of fit input in the category with zero or more than two b-tagged jets and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system below 420 GeV. |

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Additional Figure 4:
Post-fit distribution of fit input in the category with zero or more than two b-tagged jets and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system between 420 and 550 GeV. |

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Additional Figure 5:
Post-fit distribution of fit input in the category with zero or more than two b-tagged jets and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system between 550 and 810 GeV. |

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Additional Figure 6:
Post-fit distribution of fit input in the category with zero or more than two b-tagged jets and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system above 810 GeV. |

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Additional Figure 7:
Post-fit distribution of fit input in the category with less than two jets and one b-tagged jet. |

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Additional Figure 8:
Post-fit distribution of fit input in the category with one b-tagged jet and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system below 420 GeV. |

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Additional Figure 9:
Post-fit distribution of fit input in the category with one b-tagged jet and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system between 420 and 550 GeV. |

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Additional Figure 10:
Post-fit distribution of fit input in the category with one b-tagged jet and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system between 550 and 810 GeV. |

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Additional Figure 11:
Post-fit distribution of fit input in the category with one b-tagged jet and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system above 810 GeV. |

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Additional Figure 12:
Post-fit distribution of fit input in the category with two b-tagged jet and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system below 420 GeV. |

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Additional Figure 13:
Post-fit distribution of fit input in the category with two b-tagged jet and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system between 420 and 550 GeV. |

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Additional Figure 14:
Post-fit distribution of fit input in the category with two b-tagged jet and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system between 550 and 810 GeV. |

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Additional Figure 15:
Post-fit distribution of fit input in the category with two b-tagged jet and reconstructed invariant mass of the $ \mathrm{t\bar{t}} $ system above 810 GeV. |

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