TOP-20-005

TOP-20-005

# Search for CP violation using events in the lepton+jets channel in $\Pp\Pp$
collisions at $\sqrt{s}=13\TeV$

###### Abstract

Results are presented on a search for CP violation in the production and decay
of top quark-antiquark pairs in the lepton+jets channel. The search is based
on data from proton-proton collisions at $\sqrt{s}=13\TeV$, collected with the
CMS detector, corresponding to an integrated luminosity of 138. Possible CP
violation effects are evaluated by measuring uncorrected asymmetries in
observables constructed from linearly independent four-momentum vectors of the
final-state particles. The dimensionless chromoelectric dipole moment of the
top quark obtained from the observed asymmetries is measured to be $0.04\pm
0.10\stat\pm 0.07\syst$, and the asymmetries exhibit no evidence for CP-
violating effects, consistent with expectations from the standard model.

##  0.1 Introduction

The standard model (SM) of particle physics predicts the violation of the
combined charge conjugation and parity (CP) symmetry that originates from a
complex phase in the Cabibbo–Kobayashi–Maskawa matrix [1]. Measurements of CP
violation (CPV) in the strange (), bottom (), and charm () quark sectors
conducted over the past few decades [2, 3, 4] have been found to be consistent
with the SM expectations. However, the level of CPV in the SM is insufficient
to accommodate the observed matter-antimatter asymmetry in the universe [5],
motivating searches for sources of CPV beyond the SM (BSM). In contrast to the
, , and quark sectors, CPV in the top () quark sector is relatively
unexplored. In the SM, the CPV effects in top quark pair () decays are
expected to be small due to the large mass of the top quark in comparison with
the other quarks, leading to the Glashow–Iliopoulos–Maiani cancellation [6].
Thus, any observed CP-violating asymmetry would indicate the presence of BSM
phenomena [7]. For example, a nonzero chromoelectric dipole moment (CEDM) of
the top quark [8, 9, 10, 11] can generate sizable CPV in the production of .
Previous studies performed by CMS in data from $\Pp\Pp$ collisions at
$\sqrt{s}=8\TeV$ [12] found the CP-violating asymmetries ($A_{\text{CP}}$) in
the lepton+jets channel to be consistent with the SM prediction.

This paper presents the results of new searches by the CMS Collaboration for
CP-violating asymmetries in events using the lepton+jets channel from $\Pp\Pp$
collisions produced at the LHC. A possible source of CPV at the top quark
production and decay vertices arises from BSM interactions through the CEDM of
the top quark. In a model with contributions from a CEDM [9], the magnetic and
electric couplings between top quarks and gluons () are conventionally written
as

$\mathcal{L}=\frac{g_{s}}{2}\PAQt
T^{a}\sigma^{\mu\nu}(a_{\PQt}^{\Pg}+i\gamma_{5}d_{\PQt}^{\Pg})\PQt
G_{\mu\nu}^{a},$ (1)

where $g_{s}$ and $G_{\mu\nu}^{a}$ are the strong coupling constant and the
gluon field strength tensor, respectively; and are the wavefunctions of the
top quark and antiquark; $T^{a}$ are $SU(3)$ generators; $\sigma^{\mu\nu}$ is
defined by the operator $\frac{i}{2}[\gamma^{\mu},\gamma^{\nu}]$;
$a_{\PQt}^{\Pg}$ refers to the parameter of the chromomagnetic dipole moment;
and $d_{\PQt}^{\Pg}$ is the CP-odd CEDM. From Ref. [9], $d_{\PQt}^{\Pg}$ can
be converted into a dimensionless CEDM parameter $d_{\PQt\mathrm{G}}$ as

$d_{\PQt}^{\Pg}=\frac{\sqrt{2}v}{\Lambda^{2}}\text{Im}(d_{\PQt\mathrm{G}}),$
(2)

where $\Lambda$ is a high-mass scale of the BSM phenomena and $v$ is the
vacuum expectation value for the Higgs boson field ($v\approx 246\GeV$).
Higher $d_{\PQt\mathrm{G}}$ values are expected to yield larger
$A_{\text{CP}}$ contributions.

In the lepton+jets channel, one of the top quarks is presumed to decay into a
bottom quark and a boson that subsequently decays into quark pairs (). The
other top quark is required to decay into a bottom quark and a boson that
decays leptonically into an electron or muon and its associated neutrino. We
will refer to this as the leptonically decaying top quark. The analysis
exploits four T-odd observables, where T is the time-reversal operator, as
proposed in Ref. [9]. The CP observables are chosen to come from
reconstructable final-state objects that can be well measured. For example,
some observables have been discarded because they need the momentum of the
leptonically decaying top quark, which is not experimentally measured. The CP
observables take the form $\vec{v_{1}}\cdot(\vec{v_{2}}\times\vec{v_{3}})$,
where $\vec{v_{i}}$ are spin or momentum vectors and $i=1\text{--}3$ [8, 9,
10]. These triple-product observables are odd under CP transformation if CPT
is conserved. The four CP observables measured in this analysis are defined as

$\displaystyle O_{3}$
$\displaystyle=Q_{\Pell}\epsilon(p_{\PQb},\,p_{\PAQb},\,p_{\Pell},\,p_{j_{1}})\propto
Q_{\Pell}\vec{p}_{\PQb}^{\ast}\cdot(\vec{p}_{\Pell}^{\ast}\times\vec{p}_{j_{1}}^{\ast}),$
(3) $\displaystyle O_{6}$
$\displaystyle=Q_{\Pell}\epsilon(P,\,p_{\PQb}-p_{\PAQb},\,p_{\Pell},\,p_{j_{1}})\propto
Q_{\Pell}(\vec{p}_{\PQb}-\vec{p}_{\PAQb})\cdot(\vec{p}_{\Pell}\times\vec{p}_{j_{1}}),$
$\displaystyle O_{12}$
$\displaystyle=q\cdot(p_{\PQb}-p_{\PAQb})\epsilon(P,\,q,\,p_{\PQb},\,p_{\PAQb})\propto(\vec{p}_{\PQb}-\vec{p}_{\PAQb})_{z}\cdot(\vec{p}_{\PQb}\times\vec{p}_{\PAQb})_{z},$
$\displaystyle O_{14}$
$\displaystyle=\epsilon(P,\,p_{\PQb}+p_{\PAQb},\,p_{\Pell},\,p_{j_{1}})\propto(\vec{p}_{\PQb}+\vec{p}_{\PAQb})\cdot(\vec{p}_{\Pell}\times\vec{p}_{j_{1}}).$

The symbol $\propto$ indicates that the CP observable is proportional to the
triple product; the asterisk symbol represents the quantity measured in the
center-of-mass frame of the $\bbbar$ pair, where indicates the antiquark;
$\epsilon(a,b,c,d)\equiv\epsilon_{\mu\nu\alpha\beta}a^{\mu}b^{\nu}c^{\alpha}d^{\beta}$,
where $\epsilon_{\mu\nu\alpha\beta}$ is the Levi–Civita tensor; $P$ and $q$
are the sum and difference of the four-momenta of the protons in the $\Pp\Pp$
collision, respectively; $p_{\PQb}$ and $p_{\PAQb}$ refer to the two jet
momenta, where the jet definition will be given below; $p_{\Pell}$ is the
momentum of the lepton () that originates from the boson decay; $p_{j_{1}}$
refers to the momentum of the highest transverse momentum () jet from the
hadronically decaying boson; $Q_{\Pell}$ is the charge of the lepton; and the
$z$ subscript indicates a projection along the beam axis in the CMS coordinate
system.

The tabulated results are provided in the HEPData record for this analysis
[13]. The paper is organized as follows. Section 0.2 introduces the basic
features of the CMS detector. Sections 0.3 and 0.4 provide information on the
data, simulations, and selection criteria. Sections 0.5 and 0.6 describe the
fitting procedures, the instrumental effects, and the resulting systematic
uncertainties. The final results are presented in Section 0.7, with a brief
summary given in Section 0.8.

##  0.2 The CMS detector

The central feature of the CMS apparatus is a superconducting solenoid of 6m
internal diameter, providing a magnetic field of 3.8T. Within the solenoid
volume are a silicon pixel and strip tracker, a lead tungstate crystal
electromagnetic calorimeter (ECAL), and a brass and scintillator hadron
calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward
calorimeters extend the pseudorapidity ($\eta$) coverage provided by the
barrel and endcap detectors. Muons are detected in gas-ionization chambers
embedded in the steel flux-return yoke outside the solenoid.

Events of interest are selected using a two-tiered trigger system [14]. The
first level is composed of specialized hardware processors using information
from the calorimeters and muon detectors to select events at a rate of around
100kHz. The second level, known as the high-level trigger, consists of a farm
of processors running a version of the full event reconstruction software
optimized for fast processing, which reduces the event rate to around 1kHz
before data storage [15].

A more detailed description of the CMS detector, together with a definition of
the coordinate system and kinematic variables, can be found in Ref. [16].

##  0.3 Data and simulated samples

This study involves data from $\Pp\Pp$ collisions at $\sqrt{s}=13\TeV$
collected with the CMS detector in 2016–2018, corresponding to an integrated
luminosity of 138with an overall luminosity uncertainty of 1.6% [17, 18, 19].

The production events are simulated using Monte Carlo (MC) programs. The is
simulated using quantum chromodynamics (QCD) at next-to-leading-order (NLO)
precision through the matrix element (ME) in the 2.0 event generator [20, 21,
22, 23]. The value of the top quark mass ($m_{\PQt}$) is set to 172.5. The
output is combined with the parton shower (PS) simulation of 8.205 [24], with
the underlying-event (UE) tune CP5 [25]. The parton distribution functions
(PDFs) NNPDF 3.1 [26] at next-to-NLO order (NNLO) are used to model the data.
The samples with different values of CEDM are simulated with the generator
[27] at leading-order (LO) precision interfaced with . Those samples are used
as a cross-check of the model dependency of each CP observable.

Several backgrounds are considered with single top quark production being the
leading contribution. This is simulated at NLO using 2.4.2 with the FxFx
matching scheme [28] for $s$-channel production and for $t$-channel and
$\PQt\PW$ production. All samples are interfaced with through the UE tune
CUETP8M1 [29] for $t$-channel production for the 2016 data and CP5 for the
rest. Diboson ($\PV\PV$), $\PW\text{+jets}$, Drell–Yan (DY), and QCD multijet
productions are simulated at LO using the 2.4.4 generator. They are then
interfaced with using the MLM matching scheme [30]. Events coming from the
decay of into either dilepton+jets or hadronic multijets can be incorrectly
included in the signal event sample due to particle misidentification. They
are considered as a background. The background from boson events with heavy-
flavor quarks ($\PW\text{+HF}$), which is not a large background, is important
during the estimation of the systematic uncertainties, and will be discussed
in detail in Section 0.6.

The simulation of the experimental apparatus is based on [31]. To model the
effect of additional $\Pp\Pp$ interactions within the same or nearby bunch
crossings (pileup), simulated minimum-bias interactions are included in the
simulated samples [32]. The number of pileup interactions in the simulation is
reweighted to match the distribution in data.

##  0.4 Physical objects and event selection

The event selection criteria are based on the lepton+jets channel signature of
the process. The signal events are required to contain one reconstructed
lepton, and at least four reconstructed jets, including two -tagged jets
(defined below) originating from decays. The events are further categorized
into two channels based on the lepton flavor: either electron or muon. Events
are selected at the trigger level using single-lepton triggers, which require
the presence of an isolated lepton with a threshold in the range 24–35,
depending on the year, and $\abs{\eta}<2.4$. The same trigger selection is
applied to data and to the simulated samples. All physics objects are
reconstructed offline using a particle-flow (PF) algorithm [33]. The aim of
the algorithm is to reconstruct all final-state particles (photons, charged
and neutral hadrons, muons, and electrons) in the event, using combined
information from the CMS detector. The reconstructed vertex with the largest
sum of object $\PT^{2}$ is taken to be the primary $\Pp\Pp$ interaction
vertex.

Electron candidates are identified using the combination of the silicon
tracker and the corresponding ECAL cluster information [34]. Electron energies
are determined using the momenta derived from the electron track in the
tracker system, the energy of the spatially compatible ECAL cluster, and the
sum of all compatible bremsstrahlung photon energies. In order to reject
events with misidentified electron candidates and candidates originating from
photon conversions, additional electron identification requirements are
applied. A PF-based combined relative isolation, $I_{\text{rel}}$, is defined
as the sum of all neutral hadron, charged hadron, and photon candidates within
a cone of size $\DR=\sqrt{\smash[b]{(\Delta\eta)^{2}+(\Delta\phi)^{2}}}<0.4$
(where $\phi$ is the azimuthal angle in radians) around the lepton direction,
divided by the lepton , with a correction to suppress the residual effect of
pileup [35]. The isolated electron candidate is required to have $\PT>38\GeV$,
$\abs{\eta}<2.4$, and $I_{\text{rel}}<0.0287+0.506/\PT$ ($0.0445+0.963/\PT$)
in the barrel (endcaps), with in . Due to reduced reconstruction efficiency,
the gap ($1.44<\abs{\eta}<1.57$) between the barrel and endcap parts of the
ECAL is excluded. Events with additional electrons satisfying a looser set of
selection criteria with a lower-threshold and a looser isolation requirement
are rejected to reduce the background contribution (, from DY production).

Muon candidates are reconstructed using information obtained in the tracker,
combined with the muon system [36]. Identification methods are applied to
reject muon candidates that are misidentified or muons that originated from
decay-in-flight. The isolated muon candidate is required to have $\PT>30\GeV$,
$\abs{\eta}<2.4$, and $I_{\text{rel}}<0.15$. Events with additional muons
satisfying a looser set of selection criteria are rejected as well.

Jets are clustered using the anti-algorithm with a distance parameter of 0.4
[37, 38]. The jet is defined as the vectorial sum of the momenta of all PF
candidates in the jet cone. Pileup can contribute additional tracks and
calorimetric energy depositions to the jet momentum. To mitigate this effect,
tracks identified as originating from pileup vertices are discarded, and an
offset correction is applied to correct for remaining contributions from
neutral particles from pileup [33]. Corrections to the jet energy are applied
as a function of jet and $\eta$ by studying discrepancies between simulation
and data. At least four jets are required with $\PT>30\GeV$, $\abs{\eta}<2.4$,
and angular separation relative to the selected lepton of $\DR>0.4$. Jets are
identified as arising from the hadronization of quarks, denoted as either
-tagged jets or jets, using the deep-learned combined secondary-vertex
algorithm (DeepCSV). This combines the information for a given jet from track
impact parameters and secondary vertices into a model optimized through a deep
neural network. The selected working point has a signal identification
efficiency of 68%, with a probability to misidentify quark, and light-flavor
quark and gluon jets as jets of approximately 12 and 1.1% in events,
respectively [39].

The top quark and antiquark candidates associated with bosons decaying to are
reconstructed using one of the -tagged jets and two non--tagged jets in the
event through a $\chi^{2}$ algorithm that uses the top quark and boson masses
as constraints [40]. Those candidates are chosen from the combination having
the lowest $\chi^{2}$ value, with the $\chi^{2}$ defined as

$\chi^{2}=\left(\frac{m_{\mathrm{jj}\PQb}-m_{\PQt}}{\sigma_{\PQt}}\right)^{2}+\left(\frac{m_{\mathrm{jj}}-m_{\PW}}{\sigma_{\PW}}\right)^{2},$
(4)

where $m_{\mathrm{jj}\PQb}$ is the invariant mass of the two non--tagged jets
and the associated -tagged jet; $m_{\PQt}$ and $\sigma_{\PQt}$ are the default
top quark mass and average top quark invariant mass resolution of 172.5 and
16.3, respectively; $m_{\mathrm{jj}}$ is the invariant mass of the two non--
tagged jets; and $m_{\PW}$ and $\sigma_{\PW}$ are the default boson mass and
average boson invariant mass resolution of 82.9 and 9.5, respectively [41].

The other -tagged jet associated with the leptonically decaying boson
candidate is assigned as being from the hadronization of a bottom quark or
antiquark based on the charge sign of the lepton. The jets are correctly
assigned in 60% of events. However, from simulation it is found that when the
invariant mass of the combined isolated lepton and associated -tagged jet
($m_{\Pell\PQb}$) is greater than 150, the events have a large fraction of
incorrect jet assignments. Therefore, from studies of the simulated sample,
further requirements of $\chi^{2}<20$ and $m_{\Pell\PQb}<150\GeV$ are imposed.
This improves the fraction of correctly assigned jets to $\approx$74%, while
keeping $\approx$65% of the events. After these selection criteria, the purity
of the events is 95%, with single top quark production contributing a
background of 3%. The upper panels in Figs. 1 and 2 show the distributions of
the CP observables for the electron and muon channels, respectively. The
middle panels display the ratio of the data to the simulated distributions,
which show reasonable agreement within the one-standard-deviation band. The
bottom panels present the ratio of the CEDM to the SM predictions for
$d_{\PQt\mathrm{G}}=\pm 3$. In these figures, the values of the CP observables
are divided by $m_{\PQt}^{3}$ to convert the units to . The systematic
uncertainties shown in Figs. 1 and 2, as well as in later figures and tables,
include all the systematic uncertainties, except for that coming from changing
the background templates. This uncertainty contributes only to the final
$A_{\text{CP}}$ measurements instead of the number of signal events and will
be discussed in detail in Section 0.6. Table 0.4 shows the predicted signal
and background contributions to the signal events from simulation for the
electron and muon channels. The QCD and multijet events are highly suppressed
by the selection requirements and provide negligible contributions of around
0.2% and 0.05%, respectively, to the signal events. The estimation of the
number of misidentified signal events coming from decays to dilepton+jets is
discussed in Section 0.5.

Figure 1:  Distributions of the CP observables $O_{3}$ (upper left), $O_{6}$
(upper right), $O_{12}$ (lower left), and $O_{14}$ (lower right), normalized
with respect to $m_{\PQt}^{3}$, from data (points) and from the various
sources in simulation (colored histograms) for electron events in the signal
region. The solid-blue line shows the CEDM simulated signal normalized to the
data with the CP-odd parameter $d_{\PQt\mathrm{G}}=+3$. The vertical bars on
the data points indicate the statistical uncertainties in the data, and the
hatched bands show the quadrature sum of the statistical and systematic
uncertainties in the simulation. The lower two panels display the ratio of the
data to the sum of the MC predictions and the ratio of the CEDM to the SM
predictions for $d_{\PQt\mathrm{G}}=+3$ (red lines) and $-3$ (dark-blue
lines).

Figure 2:  Distributions of the CP observables $O_{3}$ (upper left), $O_{6}$
(upper right), $O_{12}$ (lower left), and $O_{14}$ (lower right), normalized
with respect to $m_{\PQt}^{3}$, from data (points) and from the various
sources in simulation (colored histograms) for muon events in the signal
region. The solid-blue line shows the CEDM simulated signal normalized to the
data with the CP-odd parameter $d_{\PQt\mathrm{G}}=+3$. The vertical bars on
the data points indicate the statistical uncertainties in the data, and the
hatched bands show the quadrature sum of the statistical and systematic
uncertainties in the simulation. The lower two panels display the ratio of the
data to the sum of the MC predictions and the ratio of the CEDM to the SM
predictions for $d_{\PQt\mathrm{G}}=+3$ (red lines) and $-3$ (dark-blue
lines).

The predicted signal and background contributions to the signal events from
simulation for the electron and muon channels.  Process Electron channel (%)
Muon channel (%) in lepton+jets 89.9 89.5 in dilepton+jets 5.5 5.5 multijet
0.1 0.1 Single  2.9 2.9 $\PW\text{+jets}$ 1.0 1.1 DY+jets 0.4 0.2 QCD multijet
0.2 0.6 $\PZ\PZ$ / $\PW\PW$ / $\PW\PZ$ 0.1 0.1

Background events can induce spurious measurements of the asymmetries, so a
sample of background-enriched data events is used to check for such effects.
In order to enhance the fraction of background events and minimize the
contribution from , events are required to have no -tagged jets. The jet veto
is defined using a weakly restrictive working point of DeepCSV, corresponding
to an 84% efficiency in identifying jets and an 11% misidentification rate for
light-flavor quark and gluon jets [39]. The isolation requirement in the
looser set of selection criteria for leptons is relaxed, so events with
additional leptons produced through the decay of a bottom quark can be more
highly rejected. The rest of the selection criteria are the same as used for
the signal events. The misidentified jet from the hadronically decaying top
quark is determined through the $\chi^{2}$ algorithm, and the other
misidentified jet is assigned to the jet closest to the isolated lepton. The
background-enriched events are expected to be dominated by non-processes
($\approx$90%), including a major contribution from $\PW\text{+jets}$.

##  0.5 Fitting procedure and extraction of asymmetries

###  0.5.1 Fitting procedure

The presence of CPV can manifest itself through a nonzero value of the
asymmetry defined as

$A_{\text{CP}}(O_{i})=\frac{N_{\text{events}}(O_{i}>0)-N_{\text{events}}(O_{i}<0)}{N_{\text{events}}(O_{i}>0)+N_{\text{events}}(O_{i}<0)},\quad
i=3,\,6,\,12,\,14.$ (5)

The CP-violating asymmetries $A_{\text{CP}}(O_{i})$ are expected to vanish in
the SM. However, nonzero CP-violating couplings of the top quark from BSM
phenomena can lead to sizable asymmetries. An anomalous CEDM contribution [9]
can be as large as 8 and 0.4% for $A_{\text{CP}}(O_{3})$ and
$A_{\text{CP}}(O_{12})$, respectively.

Experimental factors, such as the misreconstruction of the physical objects,
can affect the measurements of the asymmetries [9]. For example, misidentified
signal events coming from in the dilepton+jets channel can cause spurious
asymmetry measurements. We denote $A_{\text{CP}}$ as the asymmetry that would
be measured with an ideal detector and $A^{\prime}_{\text{CP}}$ as the
measured effective asymmetry, including experimental factors. An estimate of
$A_{\text{CP}}$ can be obtained after correcting the measured asymmetry for
instrumental effects. Given that the SM predicts negligible $A_{\text{CP}}$ in
the top quark sector, a nonzero effective $A^{\prime}_{\text{CP}}$ would be a
strong hint of BSM phenomena. For this reason, measurements of
$A^{\prime}_{\text{CP}}$ can be computed using events and are the primary
results presented in this paper.

Because multijet events are highly suppressed by the signal-event
requirements, only the to lepton+jets and dilepton+jets channels are
considered in the contribution, with the latter assumed to be background. The
signal and background yields are determined through an extended maximum
likelihood fit to the $m_{\Pell\PQb}$ distributions in data using simulated-
event templates. The template is obtained from simulation, and the background
template from the background-enriched events in data. For each CP observable,
the templates are classified according to the sign of the CP observable. The
extended likelihood function is defined as

$\displaystyle L_{\text{ext}}$
$\displaystyle=\frac{\re^{-(n_{s}^{+}+r_{b}n_{b})}}{N^{+}!}\prod^{N^{+}}_{i=1}n_{s}^{+}f_{s}^{+}(m_{\Pell\PQb}^{i})+r_{b}n_{b}f_{b}^{+}(m_{\Pell\PQb}^{i})$
(6)
$\displaystyle+\frac{\re^{-(n_{s}^{-}+(1-r_{b})n_{b})}}{N^{-}!}\prod^{N^{-}}_{i=1}n_{s}^{-}f_{s}^{-}(m_{\Pell\PQb}^{i})+(1-r_{b})n_{b}f_{b}^{-}(m_{\Pell\PQb}^{i}),$

where $n_{b}$, $n_{s}^{+}$, and $n_{s}^{-}$ are the parameters of interest and
refer to the yields of background, and events with positive and negative CP
observable values, respectively; $r_{b}$ refers to the fraction of background
events with positive CP observable values obtained from the background
template; $f_{s}^{+}(m_{\Pell\PQb})$, $f_{s}^{-}(m_{\Pell\PQb})$,
$f_{b}^{+}(m_{\Pell\PQb})$, and $f_{b}^{-}(m_{\Pell\PQb})$ refer to the
probability density functions (pdf) of $m_{\Pell\PQb}$ obtained from the and
background templates according to the sign of the CP observable, respectively;
and $N^{+}$ and $N^{-}$ are the number of events according to the sign of the
CP observable. To improve the fit results, the upper bound on $m_{\Pell\PQb}$
is relaxed to 500in the fit in order to include more sideband events. However,
to be consistent with the signal-event requirements, events with
$m_{\Pell\PQb}>150\GeV$ are excluded after the fit in determining the final
event yields for each CP observable.

Figure 3 displays the normalized $m_{\Pell\PQb}$ distributions from the signal
and background-enriched events for the electron (left) and muon (right)
channels. The upper plots compare the distribution for the background-enriched
data events to that from the MC prediction. Good agreement is observed between
the two distributions, showing that the background-enriched events are
consistent with being entirely background. The lower plots display the
distributions for the background-enriched events in data and the predicted MC
background in the signal-event sample. The $m_{\Pell\PQb}$ distribution of
background-enriched events in data is slightly wider than the predicted MC
background in signal events. This difference is taken as one of the systematic
uncertainties, as discussed in Section 0.6.

Figure 3:  The normalized $m_{\Pell\PQb}$ distributions for the electron
(left) and muon (right) channels. The upper two plots compare the background-
enriched distributions from data (solid line) to the MC predictions (dotted-
red line). The lower two plots give the background-enriched distributions from
data (solid line) and the MC predictions for the distributions from the
background in the signal events.

The $m_{\Pell\PQb}$ distributions in data are shown in Fig. 4, along with the
results of the fit. The measured numbers of signal and background events in
the electron and muon channels from the fits, and the corresponding purities,
are presented in Table 0.5.1. The final $A^{\prime}_{\text{CP}}$ measurements
can then be computed using the event-counting method of Eq. (5).

Figure 4:  The $m_{\Pell\PQb}$ invariant mass distributions in the electron
(left) and muon (right) channels from data (points). The results of the fit to
the and background templates are shown by the red and green histograms,
respectively. The vertical bars on the data points in the upper panels
indicate the statistical uncertainties in the data and the hatched bands show
the combined statistical and systematic uncertainties in the simulation. The
lower panels give the ratio of the data to the sum of the fitted MC
predictions. The blue bands represent the systematic uncertainties in the
expected yield in the simulation for all sources of systematic uncertainty
(Section 0.6).

The fitted number of signal and background events (fitted ) and other
background events (fitted background) in the electron and muon channels, along
with the purities. Although the fit is performed for $m_{\Pell\PQb}<500\GeV$,
the event yields are given for $m_{\Pell\PQb}<150\GeV$. The uncertainties
shown are statistical only.  Electron channel Muon channel Fitted
$604\,700\pm 1200$ $1\,062\,600\pm 1500$ Fitted background $34\,030\pm 480$
$58\,490\pm 820$ Fitted fraction of (%) $94.7\pm 0.1$ $94.8\pm 0.1$

###  0.5.2 Experimental sensitivity

The sensitivity of the asymmetry measurement can be diluted due to detector
and reconstruction effects, which can be parametrized through a dilution
factor ($D$). The $A^{\prime}_{\text{CP}}$ and $A_{\text{CP}}$ values are
related through $D$, applied as a multiplicative correction
$A^{\prime}_{\text{CP}}=DA_{\text{CP}}$ [9]. The dilution factor can be
defined as

$D=\epsilon_{c}-\epsilon_{w},$ (7)

where $\epsilon_{c}$ is the fraction of events where the measured CP
observable has the correct sign, and $\epsilon_{w}$ is the fraction with the
wrong sign. Events are classified into the correct-sign (wrong-sign) type when
the sign of the CP observable at the reconstruction level agrees with (differs
from) that at the generator level.

The value of $D$ depends on the final-state objects used to form each CP
observable. In contrast to $O_{12}$ and $O_{14}$, it is necessary for $O_{3}$
and $O_{6}$ to distinguish the charges of the quarks by using the sign of the
lepton charge, and therefore they tend to have a lower fraction of correct-
sign events and smaller values of $D$. The value of $D$ can also be affected
by possible contributions of BSM processes, because the CP observables are
reconstructed using kinematic features of the final-state objects. The values
of $D$ determined from the SM simulations are given in Table 0.5.2, along with
their systematic uncertainties described in Section 0.6.

The dilution factor $D$ determined from simulation and its systematic
uncertainty for each CP observable. The statistical uncertainty is negligible
compared to the systematic uncertainty.  CP observable Dilution factor $D$
$O_{3}$ $0.46\,^{+0.01}_{-0.02}$ $O_{6}$ $0.44\,^{+0.01}_{-0.02}$ $O_{12}$
$0.74\,^{+0.01}_{-0.02}$ $O_{14}$ $0.60\,^{+0.01}_{-0.01}$

In order to better understand the measured $D$ values, the lepton+jets and
dilepton+jets events in the simulated samples are reweighted at the generator
level to produce various pseudo-asymmetry values. As shown in Fig. 5, the CP-
violating asymmetries $A_{\text{CP}}$ (diamond points) are then obtained by
dividing the effective asymmetries $A^{\prime}_{\text{CP}}$ (circular points)
by the corresponding dilution factor determined from simulation. Fitting the
$A^{\prime}_{\text{CP}}$ and $A_{\text{CP}}$ values to linear functions of the
generator-level pseudo-asymmetry values results in the red-dotted and blue-
solid lines shown in Fig. 5, respectively. All the fits have good $\chi^{2}$
values, and the slopes and $y$ intercepts of the fitted lines to
$A_{\text{CP}}$ are consistent with 1.0 and 0.0, respectively.

Figure 5:  The measured CP-violating asymmetries in simulation as a function
of the generator-level pseudo-asymmetry for the CP observables $O_{3}$ (upper
left), $O_{6}$ (upper right), $O_{12}$ (lower left), and $O_{14}$ (lower
right). The red circles and blue diamonds give the $A^{\prime}_{\text{CP}}$
and $A_{\text{CP}}$ values, respectively, with the red-dotted and blue-solid
lines showing the results of linear fits to those corresponding values. The
$A_{\text{CP}}$ value is obtained by dividing the $A^{\prime}_{\text{CP}}$
value by the dilution factor determined from simulation for that CP
observable. The statistical uncertainties in the $A^{\prime}_{\text{CP}}$
values are smaller than the markers.

##  0.6 Systematic uncertainties

The sources of systematic uncertainty considered in this paper are presented
below in the following order: intrinsic detector bias, other experimental
uncertainties, and theoretical uncertainties. The systematic effects are
expected to contribute similarly to the positive and negative regions of each
CP observable, thereby largely canceling in the ratio shown in Eq. (5), used
to measure the CP asymmetries.

###  0.6.1 Detector and reconstruction effects

The CP-violating asymmetries can arise due to both couplings from BSM
processes and detector and reconstruction effects. The precision of the
resulting CP-violating asymmetries from detector and reconstruction effects
can be improved using signal events, and therefore an event-mixing method is
used to evaluate the possible bias resulting in a nonzero value of
$A^{\prime}_{\text{CP}}$. The event-mixing method is performed by mixing the
four-momentum information of the -tagged jet from the hadronically decaying
top quark and the highest light-flavor jet among the events. A total of 1000
mixed data sets are produced by applying the event-mixing method to the data
in the signal events to eliminate possible effects from any BSM coupling. For
the $i^{\text{th}}$ mixed data set, the corresponding four-momentum
information of the $j^{\text{th}}$ event is passed circularly to the
$(j+i)^{\text{th}}$ event. The resulting sets of asymmetries are independent
of the physical processes involved in the signal and background events and
represent only the bias from the detector and reconstruction effects. Separate
measurements are performed for each CP observable, year of data taking, and
lepton flavor. The resulting mean values of $A^{\prime}_{\text{CP}}$ are
presented in Table 0.6.1 and show no statistically significant detector or
reconstruction bias for either lepton flavor.

The $A^{\prime}_{\text{CP}}$ values and their statistical uncertainties in
percent for each CP observable from the electron and muon event-mixing samples
and their combination, used to search for detector or reconstruction bias.
$A^{\prime}_{\text{CP}}$ from event-mixing samples (%) CP observable
$\Pe\text{+jets}$ $\PGm\text{+jets}$ Combined $O_{3}$ $-0.004\pm 0.004$
$+0.005\pm 0.003$ $+0.003\pm 0.003$ $O_{6}$ $-0.006\pm 0.005$ $+0.003\pm
0.003$ $+0.003\pm 0.003$ $O_{12}$ $+0.005\pm 0.005$ $-0.001\pm 0.003$
$+0.001\pm 0.002$ $O_{14}$ $-0.008\pm 0.004$ $-0.001\pm 0.003$ $-0.005\pm
0.002$

###  0.6.2 Other experimental and theoretical systematic uncertainties

In order to avoid bias from a single estimation of a systematic uncertainty,
pseudo-experiments are employed instead. For each systematic change, a
reference histogram is created using a nominal signal template. Four thousand
sets of pseudo-data are sampled from the reference histogram and fitted with
the nominal (varied) signal and background templates to get the nominal
(varied) fitted signal yields. The $A^{\prime}_{\text{CP}}$ can then be
measured using the signal yields in the positive and negative regions of each
CP observable. The 4000 $A^{\prime}_{\text{CP}}$ values for each CP observable
are fit to a Gaussian function to obtain a mean and standard deviation. The
larger of the absolute value of the mean and the standard deviation is then
used to estimate the systematic uncertainty from this source. The results are
summarized in Table 0.6.2 and described in the following subsections.

The sources and values of the systematic uncertainties in
$A^{\prime}_{\text{CP}}$ for each of the CP observables in percent, averaged
over the two lepton-flavor channels. The experimental sources are listed first
and then the theoretical ones.  Systematic sources $A^{\prime}_{\text{CP}}$
(%) $O_{3}$ $O_{6}$ $O_{12}$ $O_{14}$ Pileup $-0.0008$ $+0.0010$ $-0.0003$
$+0.0007$ $+0.0023$ $-0.0017$ $+0.0040$ $-0.0044$ tagging scale factor (and
quarks) $+0.0002$ $-0.0002$ $+0.0001$ $-0.0003$ ${<}0.0001$ ${<}0.0001$
${<}0.0001$ $-0.0002$ tagging scale factor (light-flavor quarks and gluons)
$-0.0003$ $+0.0004$ $-0.0003$ ${<}0.0001$ $-0.0009$ $+0.0007$ $-0.0007$
$+0.0005$ Lepton efficiencies $-0.0002$ $+0.0002$ $-0.0001$ $-0.0001$
$-0.0001$ ${<}0.0001$ $-0.0004$ $+0.0001$ Jet energy resolution $-0.0028$
$-0.0029$ $-0.0069$ $+0.0032$ $-0.0024$ $-0.0021$ $-0.0070$ $+0.0026$ Jet
energy scale $-0.0051$ $-0.0018$ $-0.0046$ $+0.0065$ $-0.0046$ $+0.0011$
$-0.0062$ $+0.0041$ Background template $+0.0061$ $+0.0050$ $+0.0139$
$+0.0016$ PDF $+0.0008$ $-0.0008$ $-0.0008$ $+0.0006$ $+0.0003$ $-0.0004$
$+0.0003$ $-0.0006$ QCD renormalization and factorization $+0.0008$ $+0.0012$
$+0.0008$ $-0.0002$ $+0.0013$ $-0.0033$ $+0.0007$ $-0.0004$ Initial-state QCD
radiation $+0.0006$ $-0.0004$ $-0.0005$ $+0.0004$ $+0.0017$ $-0.0015$
$+0.0024$ $-0.0021$ Final-state QCD radiation $-0.0001$ $-0.0008$ $-0.0215$
$+0.0122$ $+0.0053$ $-0.0017$ $-0.0129$ $+0.0060$ Color reconnection $-0.0162$
${<}0.0001$ $+0.0186$ $-0.0206$ $+0.0091$ $-0.0464$ $+0.0384$ $+0.0304$ ME-PS
matching $-0.0235$ $+0.0399$ $-0.0043$ $+0.0177$ $-0.0185$ $+0.0139$ $+0.0352$
$+0.0376$ Underlying event $-0.0515$ $-0.0099$ $-0.0576$ $+0.0355$ $-0.0082$
$+0.0218$ $+0.0116$ $+0.0424$ Flavor response $-0.0017$ $-0.0024$ $-0.0007$
$+0.0024$ $-0.0033$ $-0.0004$ $-0.0105$ $+0.0070$ Top quark mass variation
$+0.0049$ $-0.0179$ $+0.0152$ $-0.0118$ $+0.0119$ $-0.0097$ $+0.0082$
$-0.0046$ Per-event resolution $-0.0027$ $-0.0004$ $-0.0022$ $+0.0040$
$+0.0023$ $+0.0014$ $-0.0005$ $+0.0048$ $\PW\text{+HF}$ fraction $-0.0174$
$-0.0132$ $-0.0102$ $-0.0098$ No top quark  reweighting $-0.0008$ $-0.0005$
${<}0.0001$ ${<}0.0001$

#### Other experimental systematic uncertainties

The systematic uncertainty due to the modeling of pileup is estimated by
shifting the total inelastic cross section up and down by 4.6% [32]. The
contribution to the overall uncertainty in $A^{\prime}_{\text{CP}}$ is less
than 0.005%.

To assess the uncertainty coming from the tagging scale factors, the factors
are varied according to their uncertainties. The effect of changing the heavy-
flavor quark (and ), and light-flavor quark and gluon (, , , and ) scale
factors, are calculated separately. The two variations are combined in
quadrature to give the total tagging uncertainty, which contributes $<$0.001%
to the final $A^{\prime}_{\text{CP}}$ measurements.

The uncertainties from lepton identification, isolation, and trigger
efficiencies are determined by changing the corresponding scale factors
according to their uncertainties. Among the sources of experimental
uncertainty, those associated with these sources have the smallest values,
with a contribution of $<$0.0005% to the total systematic uncertainty.

The jet energy scale (JES) and jet energy resolution are changed according to
their - and $\eta$-dependent uncertainties [42]. Both impact the
$m_{\Pell\PQb}$ distribution and contribute $<$0.007% uncertainties to the
final results.

In this paper, a background template derived from the background-enriched
events in data is used. However, this template is not identical to the
predicted MC background in signal events. The difference is considered as one
of our systematic uncertainties, obtained by replacing the nominal template by
the simulated one. The resulting $\approx$0.01% uncertainty in
$A^{\prime}_{\text{CP}}$ is the largest experimental uncertainty.

#### Theoretical systematic uncertainties

The uncertainty from the PDF used in the simulation of the process is
estimated by reweighting the corresponding variations in the NNPDF 3.1 sets
[43]. This results in one of the smallest contributions among all the sources
of theoretical uncertainty with a value of $<$0.001% in the final
$A^{\prime}_{\text{CP}}$ measurements.

The impact of the QCD renormalization and factorization scales on the
simulation is obtained by changing them independently during the production of
the simulated samples by a factor of 0.5, 1, or 2. The two contributions where
one scale is moved up while the other is changed down are excluded. The total
uncertainty is estimated by taking the maximum deviation from the nominal
result. The resulting uncertainties are $<$0.003% to the final results.

The uncertainty from the modeling of the PS is obtained by changing the
renormalization scale for initial- and final-state QCD radiation (ISR and FSR)
up and down by a factor of 2 (for ISR) and $\sqrt{2}$ (for FSR). The resulting
uncertainties are around 0.002 and 0.02% for ISR and FSR, respectively.

The default MC simulation uses the multiple-parton interaction (MPI) scheme
for color reconnection (CR) with early-resonance decays switched off in the
package. The uncertainty from this method is estimated using two other CR
models within , a gluon-move scheme and a QCD-inspired scheme [44, 45]. The
resulting systematic uncertainty associated with CR is $<$0.05%.

The uncertainty in the matching scale between the ME and PS is derived by
varying a damping parameter in . Its nominal value in simulation of
$1.379m_{\PQt}$ is changed to $2.305m_{\PQt}$ and $0.8738m_{\PQt}$ [25]. The
resulting estimation of the systematic uncertainty in $A^{\prime}_{\text{CP}}$
is $<$0.04%.

The uncertainty from modeling of the UE is estimated by varying the CP5 tune
in the MC samples [25]. Among the theoretical uncertainties, this has the
largest value of $\approx$0.05% in the $A^{\prime}_{\text{CP}}$ measurement.

The uncertainty coming from the jet response to gluons and , , and light
quarks is estimated by varying separately the JES responses for each of the
four jet flavors within their uncertainties. A systematic uncertainty of about
0.002% in $A^{\prime}_{\text{CP}}$ was found.

The top quark mass value in the simulation is varied by $\pm 1\GeV$ to
estimate the uncertainty due to this parameter, leading to a value of
$\approx$0.01%.

An average mass resolution for the reconstructed top quark and boson invariant
masses is used in the $\chi^{2}$ calculation. The actual event-by-event
resolutions depend on the detector response within different $\eta$ and $\phi$
regions. With different detector responses, the measured mass resolutions of
the reconstructed top quark and boson masses change accordingly. However, the
overall effects have a negligible impact compared to using the average
resolution. To estimate the worst-case scenario, the top quark and boson mass
resolutions are scaled up and down by 10% per event. The resulting uncertainty
is $<$0.005% in the final $A^{\prime}_{\text{CP}}$ measurements.

The fraction of $\PW\text{+HF}$ events might be different in the background-
enriched events than in the signal events because of the requirement of not
having a -tagged jet. This would cause a misestimation of the background in
the signal region. To estimate the effect of this possible bias, the
$\PW\text{+HF}$ events in the signal region are reweighted in the simulation
by a factor of 10 in the signal region to raise the corresponding fraction.
The systematic uncertainties are estimated by replacing the original
$\PW\text{+jets}$ samples, which leads to an estimated systematic uncertainty
of about 0.01%.

The measured spectrum of top quarks in data is considerably softer than
predicted by the MC simulations. This feature has been seen by both the ATLAS
and CMS experiments in previous measurements [46, 47, 48, 49]. To correct for
this, the simulated spectrum in the nominal samples is reweighted to match the
measured distribution in data. To estimate the uncertainty in the
$A^{\prime}_{\text{CP}}$ measurement from this effect, the reweighting is
removed. A resulting uncertainty of $<$0.001% is determined.

From Table 0.6.2, we see that the dominant sources of systematic uncertainty
are from the ME-PS matching, the UE simulation, and the correction for the
$\PW\text{+HF}$ content.

##  0.7 Results

###  0.7.1 Asymmetry measurements

The effective asymmetries $A^{\prime}_{\text{CP}}$ are obtained after
implementing the fitting procedure described in Section 0.5. The final results
for $A^{\prime}_{\text{CP}}$ in each lepton-flavor channel are displayed in
Fig. 6 and the values given in Table 0.7.1. The results from the previous CMS
search at $\sqrt{s}=8\TeV$ [12] are shown for comparison in Fig. 6. There is
no statistically significant evidence for CPV from the present analysis in
either lepton-flavor channel for any of the CP observables. The measured
$A^{\prime}_{\text{CP}}$ values are in agreement with the SM expectations and
have uncertainties roughly a factor of 3 smaller than the previous CMS result.

Figure 6:  The measured effective asymmetries $A^{\prime}_{\text{CP}}$ for
each CP observable from the electron, muon, and combined lepton+jets channels.
The results from the previous CMS measurement at $\sqrt{s}=8\TeV$ [12] are
shown by the green circles. The inner vertical bars on the symbols represent
the statistical uncertainty, and the outer bars the statistical and systematic
uncertainties added in quadrature.

The measured effective asymmetries $A^{\prime}_{\text{CP}}$ in percent for
each of the CP observables for the electron, muon, and combined data samples.
The first uncertainty is statistical and the second is systematic. The
statistical uncertainties are the same for each lepton type because the
numbers of signal events are the same.  $A^{\prime}_{\text{CP}}$ (%)
$\Pe\text{+jets}$ $\PGm\text{+jets}$ Combined $O_{3}$ $-0.07\pm
0.15\,^{+0.09}_{-0.06}$ $-0.04\pm 0.12\,^{+0.02}_{-0.09}$ $-0.05\pm
0.09\,^{+0.04}_{-0.07}$ $O_{6}$ $-0.17\pm 0.15\,^{+0.08}_{-0.04}$ $-0.11\pm
0.12\,^{+0.04}_{-0.09}$ $-0.13\pm 0.09\,^{+0.05}_{-0.07}$ $O_{12}$ $-0.04\pm
0.15\,^{+0.06}_{-0.09}$ $+0.16\pm 0.12\,^{+0.04}_{-0.07}$ $+0.09\pm
0.09\,^{+0.03}_{-0.05}$ $O_{14}$ $-0.19\pm 0.15\,^{+0.08}_{-0.07}$ $-0.16\pm
0.12\,^{+0.12}_{-0.03}$ $-0.17\pm 0.09\,^{+0.09}_{-0.02}$

###  0.7.2 Constraint on the dimensionless CEDM

Each of the measured $A^{\prime}_{\text{CP}}$ values from the combined
lepton+jets channel is divided by the dilution factor for that CP observable
to obtain the corrected asymmetry $A_{\text{CP}}$. These values are
independent of any detector or reconstruction bias and can therefore be used
to search for CPV in the top quark sector. The constraints on the
dimensionless CEDM $d_{\PQt\mathrm{G}}$ are determined based on the
$A_{\text{CP}}$ value of each CP observable, and are then combined using the
best linear unbiased estimator method [50], taking into account the
correlation of the $d_{\PQt\mathrm{G}}$ measurements among the CP observables.
Since there is no statistically significant evidence of CPV for any CP
observable, the expected dilution factor $D$ from the SM simulation given in
Table 0.5.2 is used to convert the measured $A^{\prime}_{\text{CP}}$ for each
CP observable to the corresponding $A_{\text{CP}}$ value. Since the unbiased
estimator method only uses symmetric uncertainties, the larger of the plus and
minus uncertainties in $A^{\prime}_{\text{CP}}$ is taken in each case.

Dedicated CP-violating samples using the modified top quark production vertex
described by Eq. (1) are simulated with different $d_{\PQt\mathrm{G}}$ values
at the generator level with to determine the relationship between
$A_{\text{CP}}$ and $d_{\PQt\mathrm{G}}$. This relationship is parametrized by
the function [9]

$A_{\text{CP}}=\frac{d_{\PQt\mathrm{G}}+a}{bd_{\PQt\mathrm{G}}^{2}+cd_{\PQt\mathrm{G}}+d},$
(8)

where the parameters $a$, $b$, $c$, and $d$ are taken from a $\chi^{2}$ fit to
the $A_{\text{CP}}$ and $d_{\PQt\mathrm{G}}$ values obtained from the
different CP-violating samples.

From this relation, the dimensionless CEDM parameter $d_{\PQt\mathrm{G}}$ is
obtained from the measured $A_{\text{CP}}$ value, and the uncertainty in
$d_{\PQt\mathrm{G}}$ is calculated using the full covariance matrix from the
fit:

$\Delta^{2}_{d_{\PQt\mathrm{G}}}=\begin{pmatrix}\frac{\partial
d_{\PQt\mathrm{G}}}{\partial A_{\text{CP}}}\\\\[5.0pt] \frac{\partial
d_{\PQt\mathrm{G}}}{\partial a}\\\\[5.0pt] \frac{\partial
d_{\PQt\mathrm{G}}}{\partial b}\\\\[5.0pt] \frac{\partial
d_{\PQt\mathrm{G}}}{\partial c}\\\\[5.0pt] \frac{\partial
d_{\PQt\mathrm{G}}}{\partial
d}\end{pmatrix}^{T}\begin{pmatrix}\Delta^{2}_{A_{\text{CP}}}&0&0&0&0\\\
0&\Delta^{2}_{a}&\cov(a,b)&\cov(a,c)&\cov(a,d)\\\
0&\cov(b,a)&\Delta^{2}_{b}&\cov(b,c)&\cov(b,d)\\\
0&\cov(c,a)&\cov(c,b)&\Delta^{2}_{c}&\cov(c,d)\\\
0&\cov(d,a)&\cov(d,b)&\cov(d,c)&\Delta^{2}_{d}\\\
\end{pmatrix}\begin{pmatrix}\frac{\partial d_{\PQt\mathrm{G}}}{\partial
A_{\text{CP}}}\\\\[5.0pt] \frac{\partial d_{\PQt\mathrm{G}}}{\partial
a}\\\\[5.0pt] \frac{\partial d_{\PQt\mathrm{G}}}{\partial b}\\\\[5.0pt]
\frac{\partial d_{\PQt\mathrm{G}}}{\partial c}\\\\[5.0pt] \frac{\partial
d_{\PQt\mathrm{G}}}{\partial d}\end{pmatrix},$ (9)

where $\Delta^{2}_{d_{\PQt\mathrm{G}}}$, $\Delta^{2}_{A_{\text{CP}}}$,
$\Delta^{2}_{a}$, $\Delta^{2}_{b}$, $\Delta^{2}_{c}$, and $\Delta^{2}_{d}$ are
the uncertainties in $d_{\PQt\mathrm{G}}$, $A_{\text{CP}}$, $a$, $b$, $c$, and
$d$, respectively.

The resulting CP-violating asymmetry $A_{\text{CP}}$ and the dimensionless
CEDM $d_{\PQt\mathrm{G}}$, with their statistical and systematic
uncertainties, are shown in Table 0.7.2 for each of the CP observables. The
final systematic uncertainties are taken as the larger value of the total
systematic uncertainties between the up and down directions. The resulting
constraints on $d_{\PQt\mathrm{G}}$ are displayed in Fig. 7. Combining the
results from the four asymmetries, leads to an overall value of
$d_{\PQt\mathrm{G}}=0.04\pm 0.10\stat\pm 0.07\syst$. This corresponds to a
limit of $\abs{d_{\PQt\mathrm{G}}}<0.25$ at the 95% confidence level (). The
final results are in agreement with the SM expectation.

The measured $A_{\text{CP}}$ and corresponding $d_{\PQt\mathrm{G}}$ values for
each of the CP observables using the SM simulation predictions for the
dilution factor $D$ in the combined lepton+jets channel. The first uncertainty
is statistical and the second is systematic.  CP observable $A_{\text{CP}}$
(%) $d_{\PQt\mathrm{G}}$ $O_{3}$ $-0.10\pm 0.20\pm 0.14$ $+0.04\pm 0.11\pm
0.07$ $O_{6}$ $-0.30\pm 0.21\pm 0.16$ $+0.25\pm 0.20\pm 0.15$ $O_{12}$
$+0.12\pm 0.13\pm 0.07$ $+0.45\pm 0.47\pm 0.27$ $O_{14}$ $-0.29\pm 0.16\pm
0.14$ $-0.81\pm 0.48\pm 0.44$

Figure 7:  The measured dimensionless CEDM $d_{\PQt\mathrm{G}}$ for each CP
observable (blue squares) in the lepton+jets channel and the combined result
(red point). The inner horizontal bars on the points represent the statistical
uncertainty and the outer bar the combined statistical and systematic
uncertainties added in quadrature.

Constraints on the CEDM of the top quark have also been set by CMS from
measurements of the spin correlations [51] in dilepton events using
$\hat{d}_{\PQt}$, which is the dimensionless parameter of CEDM in the
convention of Ref. [52]. The relation between $\hat{d}_{\PQt}$ and
$d_{\PQt}^{\Pg}$ can be expressed as $\hat{d}_{\PQt}=m_{\PQt}d_{\PQt}^{\Pg}$
[53]. From Eq. (2), with the BSM scale $\Lambda$ at 1, the combined
$d_{\PQt\mathrm{G}}$ values from this analysis can be converted into a 95%
limit of $\abs{\hat{d}_{\PQt}}<0.015$. This is competitive with the 95% limits
obtained by the spin-correlation measurement [51] of
$-0.020<\hat{d}_{\PQt}<0.012$.

##  0.8 Summary

The results of a search have been presented for the combined charge conjugate
and parity (CP) violation effects in top quark-antiquark events performed in
the electron+jets and muon+jets final states. The top quark and antiquark are
each assumed to decay into a bottom quark and a boson, with one boson decaying
hadronically and the other leptonically into an electron or muon and
accompanying neutrino. This study uses data collected by the CMS experiment at
the LHC from proton-proton collisions at $\sqrt{s}=13\TeV$, corresponding to
an integrated luminosity of 138. The CP-violating asymmetries are obtained
with four different triple-product T-odd observables, where T is the time-
reversal operator, constructed using linearly independent four-momentum
vectors associated with the final-state particles. The uncorrected asymmetries
are computed using the fitted signal. There are no statistically significant
indications of CP violation, with all the CP asymmetries being consistent with
the standard model expectations. The resulting combined measurement of the
dimensionless chromoelectric dipole moment gives $d_{\PQt\mathrm{G}}=0.04\pm
0.10\stat\pm 0.07\syst$ and exhibits no evidence for CP-violating effects,
consistent with expectations from the standard model. These results are
compatible with a previous study performed by CMS in data from $\Pp\Pp$
collisions at $\sqrt{s}=8\TeV$ [12] with uncertainties improved by roughly a
factor of 3.

## References

  * [1] A. Hoecker and Z. Ligeti, “CP violation and the CKM matrix”,  Ann. Rev. Nucl. Part. Sci. 56 (2006) 501, 10.1146/annurev.nucl.56.080805.140456, arXiv:hep-ph/0605217.
  * [2] NA48 Collaboration, “A new measurement of direct CP violation in two pion decays of the neutral kaon”,  Phys. Lett. B 465 (1999) 335, 10.1016/S0370-2693(99)01030-8, arXiv:hep-ex/9909022.
  * [3] BaBar and Belle Collaborations, “The physics of the factories”,  Eur. Phys. J. C 74 (2014) 3026, 10.1140/epjc/s10052-014-3026-9, arXiv:1406.6311.
  * [4] LHCb Collaboration, “CP violation in charm at LHCb”,  Nuovo Cim. C 42 (2020) 250, 10.1393/ncc/i2019-19250-3.
  * [5] Particle Data Group, P. A. Zyla et al., “Review of particle physics”,  Prog. Theor. Exp. Phys. 2020 (2020) 083C01, 10.1093/ptep/ptaa104.
  * [6] S. L. Glashow, J. Iliopoulos, and L. Maiani, “Weak interactions with lepton-hadron symmetry”,  Phys. Rev. D 2 (1970) 1285, 10.1103/PhysRevD.2.1285.
  * [7] D. Atwood, S. Bar-Shalom, G. Eilam, and A. Soni, “CP violation in top physics”,  Phys. Rept. 347 (2001) 1, 10.1016/S0370-1573(00)00112-5, arXiv:hep-ph/0006032.
  * [8] S. K. Gupta, A. S. Mete, and G. Valencia, “CP-violating anomalous top-quark couplings at the LHC”,  Phys. Rev. D 80 (2009) 034013, 10.1103/PhysRevD.80.034013, arXiv:0905.1074.
  * [9] A. Hayreter and G. Valencia, “T-odd correlations from top-quark CEDM in lepton plus jets top-pair events”,  Phys. Rev. D 93 (2016) 014020, 10.1103/PhysRevD.93.014020, arXiv:1511.01464.
  * [10] S. K. Gupta and G. Valencia, “CP-odd correlations using jet momenta from events at the Tevatron”,  Phys. Rev. D 81 (2010) 034013, 10.1103/PhysRevD.81.034013, arXiv:0912.0707.
  * [11] G. Valencia, “CP violation in top-quark physics”,  Nuovo Cim. C 033 (2010) 263, 10.1393/ncc/i2010-10673-2, arXiv:1007.4765.
  * [12] CMS Collaboration, “Search for CP violation in production and decay in proton-proton collisions at $\sqrt{s}={8\TeV}$”,  JHEP 03 (2017) 101, 10.1007/JHEP03(2017)101, arXiv:1611.08931.
  * [13] HEPData record for this analysis, 2022.  10.17182/hepdata.114781.
  * [14] CMS Collaboration, “The CMS trigger system”,  JINST 12 (2017) P01020, 10.1088/1748-0221/12/01/P01020, arXiv:1609.02366.
  * [15] CMS Collaboration, “Commissioning of the CMS high-level trigger with cosmic rays”,  JINST 5 (2010) T03005, 10.1088/1748-0221/5/03/T03005, arXiv:0911.4889.
  * [16] CMS Collaboration, “The CMS experiment at the CERN LHC”,  JINST 3 (2008) S08004, 10.1088/1748-0221/3/08/S08004.
  * [17] CMS Collaboration, “Precision luminosity measurement in proton-proton collisions at $\sqrt{s}={13\TeV}$ in 2015 and 2016 at CMS”,  Eur. Phys. J. C 81 (2021) 800, 10.1140/epjc/s10052-021-09538-2, arXiv:2104.01927.
  * [18] CMS Collaboration, “CMS luminosity measurement for the 2017 data-taking period at $\sqrt{s}={13\TeV}$”, CMS Physics Analysis Summary CMS-PAS-LUM-17-004, 2018\.
  * [19] CMS Collaboration, “CMS luminosity measurement for the 2018 data-taking period at $\sqrt{s}={13\TeV}$”, CMS Physics Analysis Summary CMS-PAS-LUM-18-002, 2019\.
  * [20] P. Nason, “A new method for combining NLO QCD with shower Monte Carlo algorithms”,  JHEP 11 (2004) 040, 10.1088/1126-6708/2004/11/040, arXiv:hep-ph/0409146.
  * [21] S. Frixione, P. Nason, and C. Oleari, “Matching NLO QCD computations with parton shower simulations: the method”,  JHEP 11 (2007) 070, 10.1088/1126-6708/2007/11/070, arXiv:0709.2092.
  * [22] S. Alioli, P. Nason, C. Oleari, and E. Re, “A general framework for implementing NLO calculations in shower Monte Carlo programs: the box”,  JHEP 06 (2010) 043, 10.1007/JHEP06(2010)043, arXiv:1002.2581.
  * [23] J. M. Campbell, R. K. Ellis, P. Nason, and E. Re, “Top-pair production and decay at NLO matched with parton showers”,  JHEP 04 (2015) 114, 10.1007/JHEP04(2015)114, arXiv:1412.1828.
  * [24] T. Sjöstrand et al., “An introduction to 8.2”,  Comput. Phys. Commun. 191 (2015) 159, 10.1016/j.cpc.2015.01.024, arXiv:1410.3012.
  * [25] CMS Collaboration, “Extraction and validation of a new set of CMS 8 tunes from underlying-event measurements”,  Eur. Phys. J. C 80 (2020) 4, 10.1140/epjc/s10052-019-7499-4, arXiv:1903.12179.
  * [26] NNPDF Collaboration, “Parton distributions from high-precision collider data”,  Eur. Phys. J. C 77 (2017) 663, 10.1140/epjc/s10052-017-5199-5, arXiv:1706.00428.
  * [27] J. Alwall et al., “The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations”,  JHEP 07 (2014) 079, 10.1007/JHEP07(2014)079, arXiv:1405.0301.
  * [28] R. Frederix and S. Frixione, “Merging meets matching in ”,  JHEP 12 (2012) 061, 10.1007/JHEP12(2012)061, arXiv:1209.6215.
  * [29] CMS Collaboration, “Event generator tunes obtained from underlying event and multiparton scattering measurements”,  Eur. Phys. J. C 76 (2016) 155, 10.1140/epjc/s10052-016-3988-x, arXiv:1512.00815.
  * [30] J. Alwall et al., “Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions”,  Eur. Phys. J. C 53 (2008) 473, 10.1140/epjc/s10052-007-0490-5, arXiv:0706.2569.
  * [31] GEANT4 Collaboration, “—a simulation toolkit”,  Nucl. Instrum. Meth. A 506 (2003) 250, 10.1016/S0168-9002(03)01368-8.
  * [32] CMS Collaboration, “Measurement of the inelastic proton-proton cross section at $\sqrt{s}={13\TeV}$”,  JHEP 07 (2018) 161, 10.1007/JHEP07(2018)161, arXiv:1802.02613.
  * [33] CMS Collaboration, “Particle-flow reconstruction and global event description with the CMS detector”,  JINST 12 (2017) P10003, 10.1088/1748-0221/12/10/P10003, arXiv:1706.04965.
  * [34] CMS Collaboration, “Performance of electron reconstruction and selection with the CMS detector in proton-proton collisions at $\sqrt{s}={8\TeV}$”,  JINST 10 (2015) P06005, 10.1088/1748-0221/10/06/P06005, arXiv:1502.02701.
  * [35] CMS Collaboration, “Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC”,  JINST 16 (2021) P05014, 10.1088/1748-0221/16/05/P05014, arXiv:2012.06888.
  * [36] CMS Collaboration, “Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $\sqrt{s}={13\TeV}$”,  JINST 13 (2018) P06015, 10.1088/1748-0221/13/06/P06015, arXiv:1804.04528.
  * [37] M. Cacciari, G. P. Salam, and G. Soyez, “ user manual”,  Eur. Phys. J. C 72 (2012) 1896, 10.1140/epjc/s10052-012-1896-2, arXiv:1111.6097.
  * [38] M. Cacciari, G. P. Salam, and G. Soyez, “The anti-jet clustering algorithm”,  JHEP 04 (2008) 063, 10.1088/1126-6708/2008/04/063, arXiv:0802.1189.
  * [39] CMS Collaboration, “Identification of heavy-flavour jets with the CMS detector in $\Pp\Pp$ collisions at 13”,  JINST 13 (2018) P05011, 10.1088/1748-0221/13/05/P05011, arXiv:1712.07158.
  * [40] CMS Collaboration, “Measurements of the production cross section in lepton+jets final states in $\Pp\Pp$ collisions at 8 and ratio of 8 to 7 cross sections”,  Eur. Phys. J. C 77 (2017) 15, 10.1140/epjc/s10052-016-4504-z, arXiv:1602.09024.
  * [41] CMS Collaboration, “Identification of -quark jets with the CMS experiment”,  JINST 8 (2013) P04013, 10.1088/1748-0221/8/04/P04013, arXiv:1211.4462.
  * [42] CMS Collaboration, “Jet energy scale and resolution in the CMS experiment in $\Pp\Pp$ collisions at 8”,  JINST 12 (2017) P02014, 10.1088/1748-0221/12/02/P02014, arXiv:1607.03663.
  * [43] A. Buckley et al., “LHAPDF6: parton density access in the LHC precision era”,  Eur. Phys. J. C 75 (2015) 132, 10.1140/epjc/s10052-015-3318-8, arXiv:1412.7420.
  * [44] J. R. Christiansen and P. Z. Skands, “String formation beyond leading colour”,  JHEP 08 (2015) 003, 10.1007/JHEP08(2015)003, arXiv:1505.01681.
  * [45] S. Argyropoulos and T. Sjöstrand, “Effects of color reconnection on final states at the LHC”,  JHEP 11 (2014) 043, 10.1007/JHEP11(2014)043, arXiv:1407.6653.
  * [46] N. Kidonakis, “NNLL threshold resummation for top-pair and single-top production”,  Phys. Part. Nucl. 45 (2014) 714, 10.1134/S1063779614040091, arXiv:1210.7813.
  * [47] M. Czakon, D. Heymes, and A. Mitov, “High-precision differential predictions for top-quark pairs at the LHC”,  Phys. Rev. Lett. 116 (2016) 082003, 10.1103/PhysRevLett.116.082003, arXiv:1511.00549.
  * [48] M. Czakon et al., “Top-pair production at the LHC through NNLO QCD and NLO EW”,  JHEP 10 (2017) 186, 10.1007/JHEP10(2017)186, arXiv:1705.04105.
  * [49] S. Catani et al., “Top-quark pair production at the LHC: fully differential QCD predictions at NNLO”,  JHEP 07 (2019) 100, 10.1007/JHEP07(2019)100, arXiv:1906.06535.
  * [50] L. Lyons, D. Gibaut, and P. Clifford, “How to combine correlated estimates of a single physical quantity”,  Nucl. Instrum. Meth. A 270 (1988) 110, 10.1016/0168-9002(88)90018-6.
  * [51] CMS Collaboration, “Measurement of the top quark polarization and spin correlations using dilepton final states in proton-proton collisions at $\sqrt{s}={13\TeV}$”,  Phys. Rev. D 100 (2019) 072002, 10.1103/PhysRevD.100.072002, arXiv:1907.03729.
  * [52] W. Bernreuther and Z.-G. Si, “Top quark spin correlations and polarization at the LHC: standard model predictions and effects of anomalous top chromo moments”,  Phys. Lett. B 725 (2013) 115, 10.1016/j.physletb.2013.06.051, arXiv:1305.2066.
  * [53] W. Bernreuther, D. Heisler, and Z.-G. Si, “A set of top quark spin correlation and polarization observables for the LHC: standard model predictions and new physics contributions”,  JHEP 12 (2015) 026, 10.1007/JHEP12(2015)026, arXiv:1508.05271.