CMS-CR-2024-003

Inclusive and differential cross section measurements of
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ production in the
lepton+jets channel at $\sqrt{s}=$13\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}$$

Emanuel Pfeffer111Contact<EMAIL_ADDRESS>
on behalf of the CMS Collaboration

Institute for Experimental Particle Physics
Karlsruhe Institute of Technology, Germany

> Differential cross section measurements of the associated production of top
> quark and b quark pairs,
> $\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$, are presented. The
> results are based on data from proton-proton collisions collected by the CMS
> detector at the LHC at a centre-of-mass energy of
> $\sqrt{s}=$13\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}$$, corresponding to an
> integrated luminosity of $138\text{\,}\mathrm{f}\mathrm{b}^{-1}$. Four
> fiducial phase space regions are defined targeting distinct aspects of the
> $\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ process. Kinematic
> variables are defined at the stable particle level and distributions are
> unfolded to the particle level through maximum likelihood fits. The cross
> sections are measured in the lepton+jets decay channel of the top quark
> pair, using events with exactly one isolated electron or muon and at least
> five jets. The results are compared with predictions from several event
> generators. The differential measurements have relative uncertainties in the
> range of $2\\!-\\!50\%$, depending on the phase space and the observable.

> PRESENTED AT
>
>
>
>
> $16^{\mathrm{th}}$ International Workshop on Top Quark Physics
> (Top2023), 24–29 September, 2023

##  1 Introduction

The two widely separated energy scales of the top and the bottom quark, each
with a very different, non-negligible mass, result in particular complexity
when it comes to modeling processes in which both quark flavours occur
simultaneously as pairs [1, 2]. These processes arise in proton-proton
collisions at the CERN LHC as associated production of top and bottom quark-
antiquark pairs, $\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$. Due
to the different emerging energy scales, the measurement of these processes is
a major test of perturbative quantum chromodynamics (QCD) calculations. In
addition, a precise knowledge of
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ production is crucial
in order to be able to understand other important processes for which
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ forms the leading
irreducible background. Among these processes and searches are the measurement
of the associated production of top quark pairs with Higgs bosons with the
Higgs boson decaying into a pair of b quarks
(t$\overline{\text{t}}\text{H}(\text{b}{\overline{\text{b}}})$) [3, 4], and
measurements of the simultaneous production of four top quarks
($\text{t}\overline{\text{t}}\text{t}\overline{\text{t}}$) [5, 6]. Both
processes directly access a key parameter of the Standard Model (SM), the top
quark Yukawa coupling.

##  2 The CMS detector

The Compact Muon Solenoid (CMS) detector is an experiment at the CERN LHC with
a superconducting solenoid reaching a high magnetic field of
$3.8\text{\,}\mathrm{T}$. An all-silicon pixel and strip tracker is positioned
as close as possible to the beam axis. The trackers are surrounded by a lead-
tungstate scintillating-crystals electromagnetic calorimeter, and followed by
a brass-scintillator sampling hadron calorimeter. All these components are
located inside the solenoid. Outside the magnet the iron yoke of the flux-
return is combined with muon detectors. This onion-like construction allows
almost every spatial angle to be covered so that as much of the collision as
possible may be reconstructed and recorded. A two-staged trigger system is
employed for the recording in order to be able to handle the resulting data
volume of over 40 million collisions per second. Only after the calculation by
a processor farm of the second tier it is possible to store the collected data
[7].

##  3 Modelling approaches

In the analysis, six different modelling approaches for
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ production are
compared with the measurements. These approaches differ in the Monte Carlo
(MC) event generators used, the processes simulated at the matrix-element (ME)
level, the applied parton showering (PS) models, the scales used and
additional parameters which can be found in [8]. The main difference between
the simulations, apart from the settings mentioned before, is the simulated
process at ME level. Most importantly, a distinction can be made between
models using a $\text{t}\overline{\text{t}}$ simulation at the ME level at
next-to-leading order (NLO) accuracy in QCD and models using
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ at the ME level at
NLO. Two of the tested models describe $\text{t}\overline{\text{t}}$ at the ME
level, three others test
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ at ME level and one
simulation describes $\text{t}\overline{\text{t}}{+}\textrm{jets}$ with up to
two additional jets at ME level. All the simulation approaches are summarized
in Table 1.

Table 1: Generator settings for all considered modeling approaches of
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ production. The top
quark mass value is set to $m_{\mathrm{t}}=172.5\,\text{GeV}$, and in cases
where a massive b quark is defined, the mass is set to
$m_{\mathrm{b}}=4.75\,\text{GeV}$. The transverse mass is defined as
$\smash{m_{\mathrm{T},i}=\sqrt{m_{i}^{2}+p_{\mathrm{T},i}^{2}}}$ and used to
calculate the scalar sum
${H_{\mathrm{T}}}=\sum_{i=\mathrm{t},\mathrm{\overline{t}},\mathrm{b},\mathrm{\overline{b}},\mathrm{g}}m_{\mathrm{T},i}$.
The Powheg specific $\mathrm{\textit{h}}_{\mathrm{damp}}$ value is given for
the first three generator setups, all others do not use this parameter and are
therefore marked with (N/A) [8].

Generator setup Process/ Generator/ Tune PDF set
$\mathrm{\textit{h}}_{\mathrm{damp}}$ Scales ME order Shower Powheg+p8
$\text{t}\overline{\text{t}}$/ Powheg v2/ CP5 5FS NNPDF3.1
1.379$m_{\mathrm{t}}$
$\mu_{\mathrm{F}}=\mu_{\mathrm{R}}=m_{\mathrm{T},\mathrm{t}}$
$\text{t}\overline{\text{t}}$ 5fs NLO pythia 8.240 NNLO Powheg+h7
$\text{t}\overline{\text{t}}$/ Powheg v2/ CH3 5FS NNPDF3.1
1.379$m_{\mathrm{t}}$
$\mu_{\mathrm{F}}=\mu_{\mathrm{R}}=m_{\mathrm{T},\mathrm{t}}$
$\text{t}\overline{\text{t}}$ 5fs NLO herwig 7.13 NNLO Powheg+ol+p8
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$/ Powheg-box-res/ CP5
4FS NNPDF3.1 1.379$m_{\mathrm{t}}$
$\smash{\mu_{\mathrm{R}}=\frac{1}{2}\prod_{i=\mathrm{t},\mathrm{\overline{t}},\mathrm{b},\mathrm{\overline{b}}}m_{\mathrm{T},i}^{1/4}}$,
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ 4fs NLO pythia 8.240
NNLO as 0118 $\mu_{\mathrm{F}}={H_{\mathrm{T}}}/4$ sherpa+ol
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$/ sherpa 2.2.4 sherpa
4FS NNPDF3.0 N/A
$\mu_{\mathrm{R}}=\prod_{i=\mathrm{t},\mathrm{\overline{t}},\mathrm{b},\mathrm{\overline{b}}}m_{\mathrm{T},i}^{1/4}$,
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ 4fs NLO NNLO as 0118
$\mu_{\mathrm{F}}={H_{\mathrm{T}}}/2$ mg5_amc+p8
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$/ MadGraph5_amc@nlo
CP5 4FS NNPDF3.1 N/A $\mu_{\mathrm{F}}=\mu_{\mathrm{R}}=\sum m_{\mathrm{T}}$
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ 4fs NLO v2.4.2/pythia
8.230 NNLO as 0118 mg5_amc+p8 $\text{t}\overline{\text{t}}{+}\textrm{jets}$
FxFx/ MadGraph5_amc@nlo CP5 5FS NNPDF3.1 N/A
$\mu_{\mathrm{F}}=\mu_{\mathrm{R}}=\sum m_{\mathrm{T}}$,
$\text{t}\overline{\text{t}}{+}\textrm{jets}$ FxFx 5fs NLO [$\leq$2 jets]
v2.6.1/pythia 8.240 NNLO $\textrm{qCut}=40\,\text{GeV}$,
$\textrm{qCutME}=20\,\text{GeV}$

##  4 Phase space regions and observables

Four different phase space regions are defined, which specifically examine
different facets of $\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$
production. These are partially overlapping and therefore not orthogonal. The
first region requires at least five jets with at least three of them being b
jets (“${\geq}5$ jets: ${\geq}3$b”). This is the most inclusive of all the
regions considered and takes into account that one of the expected jets may be
located outside the acceptance region. A second region, labeled as “${\geq}6$
jets: ${\geq}4$b”, targets fully resolved
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ events and requires
at least six jets of which at least four must be b jets. Two additional
regions focus on the additional radiation of further light-flavour (i.e. non
b) jets, these demand at least six (seven) jets, at least three (four) b jets
and at least three light-flavour jets and are labeled as “${\geq}6$ jets:
${\geq}3$b, ${\geq}3$ light” (“${\geq}7$ jets: ${\geq}4$b, ${\geq}3$ light”).
Each of these four fiducial phase space regions additionally requires exactly
one electron or muon. Jets considered must meet
$p_{\mathrm{T}}>$30\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}$$ and
$\left|\eta\right|<2.4$ thresholds. All detailed specifications for object and
event reconstruction, particle level definitions as well as event selection
can be found in [8]. Together with the inclusive cross section for all four
regions previously described, a total of 37 different observables are defined.
Four of these normalized differential cross section distributions are
discussed in Section 5.

##  5 Normalized differential cross sections

Two of the observables in the “${\geq}6$ jets: ${\geq}4$b” region discussed
below are based on the definition of the pair of b jets which have the
smallest spatial separation in the $\left(\eta,\phi\right)$-plane. For this,
every possible b jet combination is calculated according to

$\Delta
R_{\mathrm{b}\mathrm{b}}=\sqrt{(\Delta\eta_{\mathrm{b}\mathrm{b}})^{2}+(\Delta\phi_{\mathrm{b}\mathrm{b}})^{2}}\qquad.$
(1)

The b jet pair with the smallest spatial distance $\Delta
R_{\mathrm{b}\mathrm{b}}$ is then labeled as
$\mathrm{b}\mathrm{b}^{\text{extra}}$ in the following. With this methodology,
the b jets determined in this manner are the two additional b jets that do not
originate from the top quark decay in 49% of the events in the phase space
under scrutiny [8]. In this way, observables with properties expected to be
sensitive to the modeling of the gluon splittings to $\mathrm{b}\mathrm{b}$
are considered. The two observables defined on this basis are the spatial
distance ($\Delta R({\mathrm{b}\mathrm{b}^{\text{extra}}})$) and the invariant
mass of the $\mathrm{b}\mathrm{b}$ pair
($m({\mathrm{b}\mathrm{b}^{\text{extra}}})$). The distributions of these
observables are shown in Figure 1. It can be seen that the distribution of the
spatial distance $\Delta R({\mathrm{b}\mathrm{b}^{\text{extra}}})$ for the
simulations Powheg+ol+p8
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ 4fs and sherpa+ol
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ 4fs agree quite well
with data in this observable. In contrast, the modeling approach Powheg+p8
$\text{t}\overline{\text{t}}$ 5fs shows distances $\Delta R$ that are too
large. This cannot simply be attributed to the different calculation at ME
level, as the Powheg+h7 $\text{t}\overline{\text{t}}$ 5fs model also shows a
deviation, but with an opposite trend towards too small distances $\Delta
R({\mathrm{b}\mathrm{b}^{\text{extra}}})$. This observable is mainly driven by
the PS, which is different in both $\text{t}\overline{\text{t}}$ modeling
approaches. This indicates that the different PS configurations are not
optimally tuned in this observable. The deviating behavior of the event
simulation in this crucial observable can also be seen in the
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ modeling performed in
the context of the LHC Higgs Working Group [9]. The behavior of the
distribution of the invariant mass of the
$\mathrm{b}\mathrm{b}^{\text{extra}}$ pair is similar to the distance $\Delta
R({\mathrm{b}\mathrm{b}^{\text{extra}}})$. Here, the simulations Powheg+ol+p8
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ 4fs and sherpa+ol
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ 4fs describe the
invariant mass quite well compared to the measured data, while the modeling
approach Powheg+h7 $\text{t}\overline{\text{t}}$ 5fs tends to predict
invariant masses that are too small.

---
Figure 1: Predicted and observed normalized differential cross sections in the
${\geq}6$ jets: ${\geq}4$b fiducial phase space, for the $\Delta R$ (upper
left), invariant mass (upper right) of the extra b-jet pair
($\mathrm{b}\mathrm{b}^{\text{extra}}$), average $\Delta
R_{\mathrm{b}\mathrm{b}}^{\text{avg}}$ of all b jets in an event (lower left),
and the scalar $p_{\mathrm{T}}$ sum of all light jets
$H^{\text{light}}_{\mathrm{T}}$ in the ${\geq}6$ jets: ${\geq}3$b, ${\geq}3$
light phase space. Data represented by points. Inner (outer) vertical bars as
well as blue (grey) bands are indicating the systematic (total) uncertainties.
The predictions include their statistical uncertainties due to limited number
of simulated events [8].

Another interesting observable is the average spatial distance $\Delta R$ of
all b jets in an event, $\Delta R_{\mathrm{b}\mathrm{b}}^{\text{avg}}$. Such
an observable is used, for example, in
t$\overline{\text{t}}\text{H}(\text{b}{\overline{\text{b}}})$ analyses as an
helpful input feature for artificial neural networks in the separation of
signal and backgrounds [4]. In Figure 1 (lower left) it can be seen that all
modeling approaches examined tend to deliver on average $\Delta
R_{\mathrm{b}\mathrm{b}}^{\text{avg}}$ values that are too large compared to
data. However, it should be noted that the uncertainties of the measurement
are still large, such that the trend is not (yet) very significant and mainly
statistically limited.

An observable that probes the additional light-flavour jet radiation is the
scalar $p_{\mathrm{T}}$ sum of all light-flavour jets in the ${\geq}6$ jets:
${\geq}3$b, ${\geq}3$ light phase space. The normalized differential cross
section is shown in Figure 1 (lower right). This observable reveals that the
prediction of $H^{\text{light}}_{\mathrm{T}}$ in the Powheg+ol+p8
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ 4fs modeling approach
is mis-modeled compared to the measured data since the $p_{\mathrm{T}}$ of the
light jets tends to be predicted too large. On the other hand, in the
Powheg+h7 $\text{t}\overline{\text{t}}$ 5fs modeling approach the
$p_{\mathrm{T}}$ of the light-flavour jets is rather soft. All other event
simulations examined show a tendency to describe this observable more
accurately.

Important parameters for
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ simulations at the ME
level are the renormalization and factorization scales $\mu_{\mathrm{R}}$ and
$\mu_{\mathrm{F}}$. Various nominal models are used by the ATLAS and CMS
Collaborations and are compared in [9]. Therefore, it is important to check
variations of $\mu_{\mathrm{R}},\mu_{\mathrm{F}}$ and their effect on
distributions depending on the choice of both scales. These scales are
independently varied by a factor of 2 and 0.5 and the corresponding re-
weighted distributions of the Powheg+ol+p8
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ 4fs modeling approach
are examined. This is shown for the $H^{\text{light}}_{\mathrm{T}}$ observable
in the ${\geq}6$ jets: ${\geq}3$b, ${\geq}3$ light phase space in Figure 2.

Figure 2: Powheg+ol+p8
$\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ 4fs modeling approach
with varied $\mu_{\mathrm{R}}$ and $\mu_{\mathrm{F}}$ scale settings as a
ratio of normalized differential cross section predictions to the measured
normalized differential cross sections for $H^{\text{light}}_{\mathrm{T}}$ in
the ${\geq}6$ jets: ${\geq}3$b, ${\geq}3$ light phase space. The systematic
(total) uncertainties of the measurement are represented as blue (grey) bands.
Variations of the $\mu_{\mathrm{R}}$ ($\mu_{\mathrm{F}}$) scale relative to
the nominal scale setting are shown in orange (purple) [8].

In the ratio of the predictions with varied scale settings to the measured
data it can be observed that a larger choice of both scales would be preferred
by the data in this particular observable. This suggests the prediction of
light-flavor jets with preferably large transverse momenta may not necessarily
be a problem of the generator, instead it could be necessary to optimize the
choice of scales being applied. Similar trends are observed for other
observables, as discussed in [8].

##  6 Summary

Normalized differential cross section measurements of the associated
production of top quark-antiquark and bottom quark-antiquark pairs for events
with precisely one electron or muon have been presented. These measurements
are based on recorded data from proton-proton collisions by the CMS experiment
at $\sqrt{s}=$13\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}$$ and a corresponding
to an integrated luminosity of $138\text{\,}\mathrm{f}\mathrm{b}^{-1}$ [8].
Multiple observables are defined targeting b jets as well as additional light
jet radiation produced in association with top quark pairs. The relative
uncertainties range from $2\\!-\\!50\%$ depending on the phase space and the
observable. None of the modeling approaches examined simultaneously describe
all measured differential distributions in all phase space regions. Thus,
depending on the phase space and observable, mis-modeling is still evident and
optimization is necessary for a more accurate description of the observed
processes. A Rivet routine is available for tuning new modeling approaches
[10].

ACKNOWLEDGEMENTS

This research was supported by the German Federal Ministry of Education and
Research (BMBF) under grant 05H21VKCCB. I would like to express my gratitude
for BMBF’s financial support.

## References

  * [1] F. Buccioni et al.  NLO QCD predictions for $\text{t}\overline{\text{t}}\text{b}\overline{\text{b}}$ production in association with a light jet at the LHC.  JHEP, 12:015, 2019.  https://doi.org/10.1007/JHEP12(2019)015.
  * [2] T. Ježo et al.  New NLOPS predictions for $\text{t}\overline{\text{t}}$+b-jet production at the LHC.  Eur. Phys. J. C, 78:502, 2018.  https://doi.org/10.1140/epjc/s10052-018-5956-0.
  * [3] ATLAS Collaboration.  Measurement of Higgs boson decay into b-quarks in associated production with a top-quark pair in pp collisions at $\sqrt{s}={13\,\text{TeV}}$ with the ATLAS detector.  JHEP, 06:97, 2022.  http://dx.doi.org/10.1007/JHEP06(2022)097.
  * [4] CMS Collaboration.  Measurement of the cross section for $\text{t}\overline{\text{t}}$ production with additional jets and b jets in $pp$ collisions at $\sqrt{s}={13\,\text{TeV}}$.  JHEP, 07:125, 2020.  https://doi.org/10.1007/JHEP07(2020)125.
  * [5] ATLAS Collaboration.  Observation of four-top-quark production in the multilepton final state with the ATLAS detector.  Eur. Phys. J. C, 83:496, 2023.  https://doi.org/10.1140/epjc/s10052-023-11573-0.
  * [6] CMS Collaboration.  Observation of four top quark production in proton-proton collisions at $\sqrt{s}={13\,\text{TeV}}$.  Physics Letters B, 847:138290, 2023.  https://doi.org/10.1016/j.physletb.2023.138290.
  * [7] CMS Collaboration.  The CMS experiment at the CERN LHC.  Journal of Instrumentation, Aug 2008.  https://doi.org/10.1088/1748-0221/3/08/S08004.
  * [8] CMS Collaboration.  Inclusive and differential cross section measurements of $\mathrm{t\overline{t}b\overline{b}}$ production in the lepton+jets channel at $\sqrt{s}={13\,\text{TeV}}$.  https://arxiv.org/abs/2309.14442, 2023.  Submitted to JHEP.
  * [9] L. Ferencz et al.  Study of ttbb and ttW background modelling for ttH analyses.  https://arxiv.org/abs/2301.11670, 2023.
  * [10] CMS Collaboration.  Inclusive and differential cross section measurements of $\mathrm{t\overline{t}b\overline{b}}$ production in the lepton+jets channel at $\sqrt{s}$ = 13 TeV (Version 1).  HEPData (collection), 2023.  https://doi.org/10.17182/hepdata.138416.v1.