CMSTOP22007 ; CERNEP2024085  
Searches for violation of Lorentz invariance in $ \mathrm{t} \overline{\mathrm{t}} $ production using dilepton events in protonproton collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
23 May 2024  
Submitted to Phys. Lett. B  
Abstract: A search for violation of Lorentz invariance in the production of top quark pairs ($ \mathrm{t} \overline{\mathrm{t}} $) is presented. The measured normalized differential $ \mathrm{t} \overline{\mathrm{t}} $ production cross section, as function of the sidereal time, is examined for potential modulations induced by Lorentzinvariance breaking operators in an effective field theory extension of the standard model (SM). The cross section is measured from collision events collected by the CMS detector at a centerofmassenergy of 13 TeV, corresponding to an integrated luminosity of 77.8 fb$ ^{1} $, and containing one electron and one muon. The results are found to be compatible with zero, in agreement with the SM, and are used to bound the Lorentzviolating couplings to be in ranges of 18 $ \times $ 10$^{3} $ at 68% confidence level. This is the first precision test of the isotropy in special relativity with top quarks at the LHC, restricting further the bounds on such couplings by up two orders of magnitude with respect to previous searches conducted at the Tevatron.  
Links: eprint arXiv:2405.14757 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures  
png pdf 
Figure 1:
Distribution of the number of b jets in data and simulation, after the event selection, (left) in 2016 and (right) in 2017 samples. The hatched band includes statistical and systematic uncertainties in the predictions. The vertical bars associated with the data points represent their statistical uncertainty. The lower panels show the ratio of the observed data event yields to those expected from simulation. 
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Figure 1a:
Distribution of the number of b jets in data and simulation, after the event selection, (left) in 2016 and (right) in 2017 samples. The hatched band includes statistical and systematic uncertainties in the predictions. The vertical bars associated with the data points represent their statistical uncertainty. The lower panels show the ratio of the observed data event yields to those expected from simulation. 
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Figure 1b:
Distribution of the number of b jets in data and simulation, after the event selection, (left) in 2016 and (right) in 2017 samples. The hatched band includes statistical and systematic uncertainties in the predictions. The vertical bars associated with the data points represent their statistical uncertainty. The lower panels show the ratio of the observed data event yields to those expected from simulation. 
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Figure 2:
Prefit (upper) and postfit (lower) distributions of the number of b jets in sidereal hour bins, in 2016 and 2017 data. The gray band reflects the statistical and systematic uncertainty predicted in each bin, including correlations across bins. The vertical bars associated with the data points represent their statistical uncertainty. The lower panels show the ratio of the observed data event yields to those expected from simulation. 
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Figure 2a:
Prefit (upper) and postfit (lower) distributions of the number of b jets in sidereal hour bins, in 2016 and 2017 data. The gray band reflects the statistical and systematic uncertainty predicted in each bin, including correlations across bins. The vertical bars associated with the data points represent their statistical uncertainty. The lower panels show the ratio of the observed data event yields to those expected from simulation. 
png pdf 
Figure 2b:
Prefit (upper) and postfit (lower) distributions of the number of b jets in sidereal hour bins, in 2016 and 2017 data. The gray band reflects the statistical and systematic uncertainty predicted in each bin, including correlations across bins. The vertical bars associated with the data points represent their statistical uncertainty. The lower panels show the ratio of the observed data event yields to those expected from simulation. 
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Figure 3:
The normalized differential cross section for $ \mathrm{t} \overline{\mathrm{t}} $ as a function of sidereal time, using combined 20162017 data. The error bars show statistical, as well as statistical and systematic uncertainties, including correlations across bins. 
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Figure 3a:
The normalized differential cross section for $ \mathrm{t} \overline{\mathrm{t}} $ as a function of sidereal time, using combined 20162017 data. The error bars show statistical, as well as statistical and systematic uncertainties, including correlations across bins. 
png pdf 
Figure 3b:
The normalized differential cross section for $ \mathrm{t} \overline{\mathrm{t}} $ as a function of sidereal time, using combined 20162017 data. The error bars show statistical, as well as statistical and systematic uncertainties, including correlations across bins. 
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Figure 4:
Comparison of systematic and statistical uncertainties, where the former are grouped according to the treatment of time dependence:\ uniform (flat luminosity component, background normalization, theory), correlated (trigger, luminosity stability and linearity, pileup, and MC statistical uncertainty), or uncorrelated (other experimental uncertainties) across sidereal time bins. 
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Figure 4a:
Comparison of systematic and statistical uncertainties, where the former are grouped according to the treatment of time dependence:\ uniform (flat luminosity component, background normalization, theory), correlated (trigger, luminosity stability and linearity, pileup, and MC statistical uncertainty), or uncorrelated (other experimental uncertainties) across sidereal time bins. 
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Figure 4b:
Comparison of systematic and statistical uncertainties, where the former are grouped according to the treatment of time dependence:\ uniform (flat luminosity component, background normalization, theory), correlated (trigger, luminosity stability and linearity, pileup, and MC statistical uncertainty), or uncorrelated (other experimental uncertainties) across sidereal time bins. 
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Figure 5:
Number of $ \mathrm{t} \overline{\mathrm{t}} $ events reconstructed in the SME hypothesis divided by the number of events in the SM hypothesis, as a function of the number of b jets and sidereal time, for the four directions of the $ c_L $ coefficients. The uncertainty band represents the MC statistical uncertainty in the sample used to compute the SME hypothesis. The sinusoidal variation is arising from the $ f(t) $ dependence on sidereal time, while smaller structures reflect the number of b jets in each sidereal time bin. 
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Figure 6:
Fitted SME coefficients and their 68 and 95% CL, measured in fits of single coefficients while the coefficients corresponding to the three other directions are left floating, within the $ c_L $, $ c_R $, $ c $, and $ d $ families. The error bar includes statistical and systematic uncertainties. Fitting a single coefficient, with the others fixed to the SM value, leads to negligible changes in the results. 
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Figure 7:
Uncertainty breakdown for SME fits of single coefficients while the coefficients corresponding to the three other directions are left floating, by splitting according to the treatment of time dependence: flat across sidereal time (flat luminosity component, background normalization, theory), correlated in sidereal time bins (trigger, luminosity stability and linearity, pileup, MC statistical uncertainty, single top quark decay in the SME), systematics uncorrelated in sidereal time bins (other experimental uncertainties), and statistical uncertainty. 
Tables  
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Table 1:
Event yields in data and MC simulation in 20162017, after selection. The uncertainties include statistical and systematic sources, with correlations. 
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Table 2:
Summary of the systematic uncertainties and their correlation scheme between 2016 and 2017 data sets, and between sidereal time bins. Sources marked with an asterisk are only included in the SME fits. Sources marked with a dagger are uniform and correlated in sidereal time. 
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Table 3:
Expected and observed 68% confidence level interval measured for the SME fits of single coefficients while the others are fixed to their SM value, and while coefficients for the three other directions are floating. 
Summary 
A search for violation of Lorentz invariance has been performed using top quark pairs ($ \mathrm{t} \overline{\mathrm{t}} $), requiring the presence of one muon and one electron in the events. Data collected in 20162017 with the CMS detector corresponding to an integrated luminosity of 77.8 fb$ ^{1} $ are used. A measurement of the $ \mathrm{t} \overline{\mathrm{t}} $ normalized differential cross section as a function of sidereal time is performed. The Lorentz invariance assumption is tested by measuring 16 sets of Wilson coefficients within the standard model extension, an effective field theory predicting a modulation of the $ \mathrm{t} \overline{\mathrm{t}} $ cross section with sidereal time. Measurements of the Lorentzviolating couplings are found to be compatible with the standard model hypothesis. The precision of the results ranges from less than 1 $ \times $ 10$^{3} $ to 8 $ \times $ 10$^{3} $ for the measured coefficients. This constitutes the most precise test of the isotropy in special relativity using top quarks at a hadron collider. 
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