# Photon radiation effects in kinematic reconstruction of top quarks

D. Dobur  J. Knolle  G. Mestdach  and K. Skovpen11footnotetext: Corresponding
author.

###### Abstract

Kinematic reconstruction of top quarks allows to define a set of kinematic
observables relevant to various physics processes that involve top quarks and
provides an additional handle for the suppression of background events.
Radiation of photons in association with the top quarks alters the kinematics
and the topology of the event, leading to visible systematic effects in
measurable observables. The present study introduces an improved
reconstruction of the top quark kinematics in the presence of photon
radiation. The results are presented for processes with top quark pair
production, as well as for singly-produced top quarks.

##  1 Introduction

The measurement of the top quark production cross sections, as well as the
study of the properties of top quarks, remain a foreground direction in a
large number of experimental studies across several experiments at the Large
Hadron Collider (LHC) at CERN. Top quarks are copiously produced at the LHC,
allowing to achieve an unprecedented precision in the measurement of the
inclusive production cross sections of top quark pairs ($\mathrm{t\bar{t}}$)
down to the level of $\simeq$ 2% [1]. The production cross section of a single
top quark ($\mathrm{t(\bar{t})}$) in the predominant $t$ channel has been
measured with the precision of $\simeq$ 15% [2]. In addition to the
measurement of the inclusive cross sections, the amount of recorded data at
the LHC allows to perform measurements of the differential production cross
sections as a function of various kinematic observables.

The electroweak couplings of the top quark can be directly probed in processes
involving the associated production of top quarks with vector bosons. The
production of top quarks in association with a photon
($\mathrm{t\bar{t}\gamma}$) provides direct access to the study of the
electromagnetic couplings of the top quark at hadron colliders [3, 4, 5, 6, 7,
8]. With respect to $\mathrm{t\bar{t}}$ production, the top quark charge
asymmetry is particularly enhanced to the level of $\simeq$ 10% in the
$\mathrm{q\bar{q}}$-initiated production channel of the
$\mathrm{t\bar{t}\gamma}$ process [9], which is significantly larger than in
$\mathrm{t\bar{t}}$. Potential new physics effects can be induced as anomalous
electric dipole moments, modifying the standard model (SM) predictions for
various kinematic observables for this process [10, 11]. Within the effective
field theory (EFT) approach, the potential modifications of the structure of
the $\mathrm{t\bar{t}\gamma}$ interaction vertex are parametrized with the
respective dimension-six operators [12].

The $\mathrm{t\bar{t}\gamma}$ process was experimentally studied at CDF [13],
ATLAS [14, 15, 16, 17] and CMS [18, 19]. The measured cross sections in
semileptonic and dilepton channels show good agreement with the SM
predictions. The differential cross section is measured as a function of
multiple kinematic variables involving leptons and radiated photons. Several
of these variables, such as the angular separation between the two leptons,
which can be reconstructed in the dilepton channel, are particularly sensitive
to $\mathrm{t\bar{t}}$ spin correlation effects. The charge asymmetry has not
yet been studied experimentally, as it requires a good handle to separate the
$\mathrm{gg}$\- and $\mathrm{q\bar{q}}$-initiated $\mathrm{t\bar{t}\gamma}$
production processes [9]. It was shown that the photon rapidity can
potentially allow to distinguish between these two processes in the measured
differential distributions. The measurement of the $\mathrm{t\bar{t}}$ charge
asymmetry in $\mathrm{t\bar{t}\gamma}$ events however requires a full
reconstruction of the $\mathrm{t\bar{t}\gamma}$ final state, which has not yet
been established in experimental studies.

In addition to the $\mathrm{t\bar{t}}$ process, the photons can also be
radiated in processes involving the production of single top quarks,
$\mathrm{t(\bar{t})\gamma}$ [20, 21]. This process has been studied by the CMS
experiment leading to the observed evidence of 4.4 standard deviations [22].
The production mechanism of $\mathrm{t(\bar{t})\gamma}$ is dominated by the
electroweak $t$ channel process, where the light-flavour quark in the hard-
scattering process recoils against the top quark to produce an energetic jet
in the forward region of the detector. As in $\mathrm{t\bar{t}\gamma}$
production, the $\mathrm{t(\bar{t})\gamma}$ process is sensitive to the
electromagnetic dipole moments of the top quark and potential new physics
effects described within an EFT approach.

##  2 Photon radiation in processes with top quarks

The performed study aims at reconstructing top quarks in the presence of
photon radiation in several event topologies including single-top and
$\mathrm{t\bar{t}}$ production channels. The photon can be emitted from any
charged particle that is involved in the process, from the products of
subsequent decays of unstable particles, as well as in the parton shower
process. The proposed algorithm of the kinematic reconstruction targets at
properly assigning the origin of the emitted photon. The study primarily
focuses on the processes with the production of top quarks, where a photon is
radiated at the matrix-element (ME) level. The photon can be radiated from the
initial state quarks, the intermediate top quarks and W bosons, as well as
from the final-state quarks and leptons. The kinematic effects that are
induced by the photon radiation in the $\mathrm{t\bar{t}}$ process were
previously discussed in Ref. [5], indicating a significant fraction of events
with photon emission from top quark decays, especially in the low photon
$\mathrm{p_{T}}$ region. The inclusion of radiated photons in the
reconstruction of events with top quarks is therefore crucial in order to
properly define the top quark-related kinematic observables at the
reconstruction level in the measurement of differential cross sections, as
well as in studies of the $\mathrm{t\bar{t}}$ charge asymmetry and spin
correlation effects.

Leptonic decays of W bosons originating from top quark decays lead to the
presence of a neutrino (or an anti-neutrino) in events, which can only be
partially reconstructed at hadron colliders. The longitudinal component of the
neutrino’s momentum ($\mathrm{p_{z}^{\nu}}$) remains unconstrained. However,
it can be inferred by imposing a set of kinematic constraints on the topology
of the reconstructed events that describe the top quark decay kinematics. The
$\mathrm{p_{z}^{\nu}}$ can be derived by resolving a quadratic equation
involving constraints on the reconstructed masses of the W boson and the top
quark. The W boson mass is reconstructed from a lepton and a neutrino
($\mathrm{W^{-}\to\ell^{-}\bar{\nu}}$, $\mathrm{W^{+}\to\ell^{+}\nu}$), while
the reconstruction of the top quark mass additionally involves the hadronic
jet that is associated with the decay of a heavy hadron, a b jet
($\mathrm{t\to\ell^{+}\nu}b$, $\mathrm{\bar{t}\to\ell^{-}\bar{\nu}}\bar{b}$).
The missing transverse energy, ($\mathrm{E_{T}^{miss}}$) which is defined as
the negative vectorial sum of all reconstructed objects in the event in the
transverse plane of the colliding beams, provides crucial information about
the transverse component of the neutrino’s momentum. In the case of the fully
hadronic decays of the top quarks, the reconstruction of the top quark mass
involves three jets, one of which is identified as a b jet. The dominant
contribution to the measured experimental resolution in the reconstructed
spectra of the W boson and the top quark masses is therefore predominantly
described by the jet energy scale and resolution effects. The production of
single top quarks leads to the presence of either a leptonic or a hadronic W
boson decay, with an additional b quark arising from the top quark decay.

The top quarks that are produced in pairs lead to two distinctive event
topologies. The semileptonic $\mathrm{t\bar{t}}$ events contain one leptonic
decay of a W boson, with the other W boson decaying hadronically. The dilepton
final states arise from leptonic decays of two W bosons, subsequently
producing two neutrinos in the final state. The kinematic properties of the
described event topologies can be fully established, if the corresponding
leptons, jets and $\mathrm{E_{T}^{miss}}$ are well reconstructed in the event.

The kinematic reconstruction of top quarks is performed in
$\mathrm{t\bar{t}\gamma}$ semileptonic and dilepton events, as well as in
events with an associative production of single top quarks and a photon with
leptonic W boson decays. Events are simulated with the
$\mathrm{MadGraph5\\_aMC@NLO}$ v2.8.2 [23] generator at leading order,
interfaced with the Pythia v8.1 [24] program for the simulation of
hadronization and fragmentation processes. At ME level, the event generation
corresponds to 2 $\to$ 7 and 2 $\to$ 5 production processes for
$\mathrm{t\bar{t}\gamma}$ and $\mathrm{t(\bar{t})\gamma}$, respectively, where
a photon can be radiated from any charged particle involved in the process.
Event generation involves on-shell top quarks, and it accounts for
interference effects in the relevant production diagrams. The photon origin is
determined by looking at its ancestors in the generated event record. Angular
separation between a photon with a minimum $\mathrm{p_{T}}$ of 5 GeV and any
other final-state particle is required to be $\mathrm{\Delta R}$ =
$\mathrm{\sqrt{(\Delta\phi)^{2}+(\Delta\eta)^{2}}}$ $>$ 0.3. The generated
events are passed through a simplified detector simulation that is realized
within the Delphes v.3.4.2 [25] package that models a realistic detector
response and performs the event reconstruction. Reconstructed events that
correspond to at least one top quark decaying via a leptonically decaying W
boson are required to have at least one lepton (electron or muon) and one
photon with $\mathrm{p_{T}}$ $>$ 20 GeV and an absolute pseudorapidity,
|$\eta$|, of less than 2.4. Jets are reconstructed using the
anti-$\mathrm{k_{T}}$ jet algorithm [26] with R = 0.4 and are selected with
$\mathrm{p_{T}}$ $>$ 30 GeV and |$\eta$| $<$ 2.4. It is additionally required
that jets do not have a nearby lepton that is reconstructed within
$\mathrm{\Delta R}$ = 0.4. The photon must be separated from any lepton or jet
object by $\mathrm{\Delta R}$ > 0.4. The event selection applied in the
dilepton channel requires the presence of at least two leptons in the final
state. The $\mathrm{E_{T}^{miss}}$ is reconstructed from tracks and particle-
flow calorimeter deposits. The reconstructed leptons, jets and the photon, are
geometrically matched within $\mathrm{\Delta R}$ = 0.4 to the corresponding
generated particles that are associated with the parton-level production and
decay processes. Selected events where all generated particles are properly
matched to the corresponding reconstructed objects are used to perform the
study of the kinematic reconstruction.

##  3 Kinematic event reconstruction

Events that satisfy the described selection criteria are used to perform a
kinematic reconstruction of the $\mathrm{t\bar{t}\gamma}$ and
$\mathrm{t(\bar{t})\gamma}$ processes, and are classified into event
categories where the photon is radiated either from the production part of the
parton-level process (“production”), or from the decay products of top quarks
(“decay”). The number of reconstructed objects used as input to the kinematic
fit corresponds to the number of generated particles at the ME level. The
fraction of the events where a photon is emitted in the decay, and the
distributions representing an angular separation between the photon and the
closest parton-level final state particle, are presented in Fig. 1. The
radiation of photons with high momentum is kinematically enhanced in the
production case, while the emitted photons in the top quark decay are mainly
radiated at small angles and generally have a softer $\mathrm{p_{T}}$
spectrum. The observed difference in the measured event fractions between the
semileptonic and the dilepton channels is due to the selection criteria
applied on the $\mathrm{\Delta R}$ separation between a reconstructed photon
and other final-state objects.

Figure 1:  Left: Relative fraction of events with a photon that is radiated
from the decay products of top quarks. Right: Minimal $\mathrm{\Delta R}$
separation between the photon and any of the parton-level final state
particles.

The reconstruction of the neutrino’s longitudinal momentum in the context of
$\mathrm{t\bar{t}}$ events, covering both the semileptonic and the dilepton
final states, is discussed in detail in Refs. [27, 28, 29, 30, 31, 32, 33, 34,
35], with the analytic solutions for $\mathrm{p_{z}^{\nu}}$ derived in Refs.
[36, 37, 38]. The methodology of the presented study does not directly use the
proposed analytic solutions, but rather attempts at resolving the system of
the relevant unknowns by performing a likelihood fit based on the initial set
of equations involving $\mathrm{p_{z}^{\nu}}$. A suitable solution for
$\mathrm{p_{z}^{\nu}}$ is determined in a log-likelihood fit that is
implemented in a dedicated TopPhit package [39], which makes use of the ROOT
toolkit libraries [40]. The fit is based on the comparison of the
reconstructed top quark and the W boson masses with the corresponding truth-
level values. The general likelihood function that is used to perform a fit is
defined as:

$\mathrm{\mathcal{L}=-2ln\bigg{[}\prod_{i}P_{i}(rec|gen)\times
P_{neg}\bigg{]}},$ (3.1)

where the $\mathrm{P_{i}}$ denote the probabilities of the reconstructed
masses of a top quark and a W boson to correspond to their predicted values
from generator, following the Breit-Wigner distribution.

The likelihood function contains four main terms that correspond to the top
quark, the top antiquark, and two W bosons in the kinematic reconstruction of
$\mathrm{t\bar{t}\gamma}$ events. There is a single neutrino produced in
semileptonic $\mathrm{t\bar{t}\gamma}$ events, and therefore the
$\mathrm{p_{z}^{\nu}}$ remains the only unknown. As a consequence of resolving
a quadratic equation, there are two possible $\mathrm{p_{z}^{\nu}}$ solutions.
The ambiguity is resolved by imposing a constraint on the reconstructed top
quark mass value, in addition to the W boson mass requirement. The hadronic
decay of the top quark in $\mathrm{t\bar{t}\gamma}$ semileptonic events is
reconstructed using the corresponding W boson and top quark mass requirements,
leading to four constraints, together with the reconstruction of the leptonic
top quark decay. There are also four main likelihood terms included in the
kinematic fit of dileptonic $\mathrm{t\bar{t}\gamma}$ events. However, in this
case there are two neutrinos with four unknowns in the reconstruction. With
four terms corresponding to the W boson and top quark masses included in the
likelihood fit, the minimized function has zero degrees of freedom in the fit.
There are two likelihood terms that are included in the
$\mathrm{t(\bar{t})\gamma}$ case, similar to the reconstruction of the
leptonic decay of the top quark in the $\mathrm{t\bar{t}\gamma}$ semileptonic
system. The last term ($\mathrm{P_{neg}}$) in the likelihood definition refers
to the additional penalty term against the nonphysical solutions associated
with imaginary values that can appear in the derivation of the neutrino’s
longitudinal momentum. This penalty term is defined as the sum of absolute
values of square roots giving imaginary solutions in event, guiding the
minimization procedure towards the correct minima.

Figure 2:  Some examples of transfer functions used in the kinematic
reconstruction that are measured for various reconstructed objects.

The likelihood function is evaluated for each possible assignment of
reconstructed leptons and jets to the hard-process particles. The likelihood
minimization is performed in each permutation of selected leptons, jets and
photons in event. The permutations include the photon’s origin assignment to
various particles involved in the hard process. In order to account for
possible resolution effects in the reconstruction process, a set of the so-
called transfer functions (TFs) is used that establishes the correspondence
between the generated particles and their reconstructed counterparts. A TF is
defined as the relative difference between the truth-level and the
reconstructed quantities, measured in each considered category of the
reconstructed objects, including jets, $\mathrm{E_{T}^{miss}}$, leptons and
photons, as presented in Fig. 2. The use of TFs maximizes the probability of
finding a viable solution for $\mathrm{p_{z}^{\nu}}$. The TFs are used as
probability density functions to perform the generation of pseudo-experiments
in each event to define the four-momenta of reconstructed objects, and in each
of these variations the corresponding likelihood value is computed. Typically,
about 100 iterations are needed to find the correct minimum in events
containing one neutrino. The kinematic fit in dilepton
$\mathrm{t\bar{t}\gamma}$ events uses the same minimization algorithm
involving TFs with an additional minimization step performed in MINUIT [41].
This is done in order to improve the convergence of the minimization process
when dealing with the more complex two-neutrino case of dilepton events. The
system of equations used to derive the solution for $\mathrm{p_{z}^{\nu}}$ can
be resolved in all relevant event topologies with an efficiency close to 100%,
with some dependence on the number of pseudo-experiments. Permutation that
gives the minimum value of the log-likelihood function is selected to
correspond to the best assignment of reconstructed leptons, jets and photons,
to particles generated at parton level. The fitted values of the likelihood
are shown in Fig. 3. As described above, the minimum value of the likelihood
is close to zero in $\simeq$ 99% of selected events in the dilepton case,
because the performed fit has no degrees of freedom. The corresponding results
in $\mathrm{t\bar{t}\gamma}$ semileptonic events tend to diverge from zero
because the relevant system of equations is overconstrained in the fit.

Figure 3:  Minimum value of the log-likelihood function used in the kinematic
fit in $\mathrm{t\bar{t}\gamma}$ semileptonic (left),
$\mathrm{t\bar{t}\gamma}$ dilepton (middle) and $\mathrm{t(\bar{t})\gamma}$
(right) events.

##  4 Results

The performance of the proposed method is studied by measuring the efficiency
of the correct assignment of reconstructed objects to generated leptons,
quarks and photons. In order to avoid accounting for any inefficiencies due to
event reconstruction effects, the selected events must have the parton-level
particles matched within $\mathrm{\Delta R}$ = 0.4 to the corresponding
reconstructed objects. The measured efficiencies are presented in Fig. 4 and
correspond to the correct matching between the truth-level generated particles
from the decays of top quarks and the reconstructed objects (“top-match”), as
well as when all generated parton-level final state particles (leptons, quarks
and photons) are correctly matched (“all-match”).

The reconstructed photon in $\mathrm{t\bar{t}}$ events can be assigned to
either the top quark or a W boson decay, or to any other particle not involved
in the top quark decay process. Since there are two top quarks and two W
bosons produced in $\mathrm{t\bar{t}}$ events, there are four categories in
total corresponding to the photon origin in top quark decay chain. The fifth
category represents the photon radiation from any charged particle involved in
the process, excluding the top quark decay products. A photon is radiated in
“decay”, if it is assigned to a top quark or a W boson decay. It is considered
as radiation in “production”, otherwise.

The kinematic event reconstruction represents the main handle on the
identification of the photon origin in the photon $\mathrm{p_{T}}$ range below
$\simeq$ 200 GeV. At higher energies, the photon is predominantly emitted in
production, consistent with the results obtained from the kinematic fit.

When a photon is radiated in production, the top-match efficiency reaches the
values of $\simeq$ 90% and $\simeq$ 83% in the semileptonic and dilepton
$\mathrm{t\bar{t}\gamma}$ production channels, respectively, and is rather
stable with respect to the photon $\mathrm{p_{T}}$. In the case of
$\mathrm{t(\bar{t})\gamma}$ process, the light-flavour quark-jet is included
in the jet-parton permutations when assigning the b-quark jet to the
corresponding generator b quark. There is no kinematic requirement that is
used in the fit for the recoiling jet in the $\mathrm{t(\bar{t})\gamma}$
process, which leads to a lower b-quark matching efficiency. In the
$\mathrm{t\bar{t}\gamma}$ semileptonic events the light-flavour quark-jets are
used in the calculation of the top quark mass in hadronic W decays, therefore
constraining the allowed parameter phase space of the b-quark jet kinematics.
When additionally requiring the photon to be correctly assigned to the
corresponding hard-process particle, the overall matching efficiency is found
to be $\simeq$ 65% in the region of the low photon $\mathrm{p_{T}}$ in
$\mathrm{t\bar{t}\gamma}$ semileptonic and $\mathrm{t(\bar{t})\gamma}$ events,
while it reaches $\simeq$ 50% in the $\mathrm{t\bar{t}\gamma}$ dilepton
channel. The kinematic reconstruction in the presence of two neutrinos is
associated with larger systematic effects arising from $\mathrm{E_{T}^{miss}}$
and jet reconstruction, with respect to the final states involving a single
neutrino. Therefore, the measured matching efficiencies for the reconstructed
photon are generally smaller in the $\mathrm{t\bar{t}\gamma}$ dilepton channel
than in other considered event topologies. At higher values of the photon
$\mathrm{p_{T}}$, the matching efficiency reaches a plateau around 100 GeV,
because the photon emission from production becomes dominant, with only a
small contribution from the photon arising from the top quark decay.

In the case of photon radiation from the top quark decay, the measured top-
match and the all-match efficiencies increase with the photon
$\mathrm{p_{T}}$. The effect of including a radiated photon in the kinematic
reconstruction becomes increasingly pronounced at higher values of the photon
$\mathrm{p_{T}}$, where the experimental energy resolution effects in the
object reconstruction become less important. The probability to select a
permutation that corresponds to the proper matching of all hard-process
particles is $\simeq$ 45% in $\mathrm{t\bar{t}\gamma}$ semileptonic events,
while it reaches $\simeq$ 30% and $\simeq$ 40% in $\mathrm{t\bar{t}\gamma}$
dilepton and $\mathrm{t(\bar{t})\gamma}$ events, respectively. In case of the
hadronic decay of a W boson, the reconstructed jets are allowed to be matched
to either of the two quarks from the W boson decay, but not to the same one.

Figure 4:  Efficiency of correct assignment between parton- and reco-level
objects in top quark events with photon emission (top), as well as in events
where a photon is radiated either in the production process (bottom left) or
in a decay of a top quark (bottom right). The efficiencies are shown at
central values of bins defined in the photon $\mathrm{p_{T}}$ and are
presented for the correct matching of the decay products of the produced top
quarks (“top-match”) and when, in addition, the photon is required to be
correctly identified (“all-match”). Colored bands represent the statistical
uncertainty.

A correct assignment of reconstructed objects to the hard-process particles
allows to define kinematic properties of produced top quarks. The comparison
between the reconstructed and the generated top quark $\mathrm{p_{T}}$ in
$\mathrm{t\bar{t}\gamma}$ semileptonic events is presented in Fig. 5. A
similar comparison for an hadronically decaying top quark is shown in Fig. 6.
The results from the application of kinematic reconstruction to the
$\mathrm{t\bar{t}\gamma}$ dilepton and $\mathrm{t(\bar{t})\gamma}$ events are
presented in Figs. 7 and 8, respectively. The comparisons are shown for the
case, where the photon is omitted in the kinematic event reconstruction, as
well as for the case where it is included in the fit. When the photon is not
accounted for in the reconstruction, the correlation between the reconstructed
and generated top quark $\mathrm{p_{T}}$ appears to be clearly biased and
correlated to the minimum photon $\mathrm{p_{T}}$ requirement that is applied
in selected events, while the inclusion of the photon leads to a significantly
improved resolution in derived kinematic variables. The results are also
presented as the mean values and the corresponding variances in the measured
top quark $\mathrm{p_{T}}$ in Fig. 9.

Figure 5:  Transverse momentum of the top quark that corresponds to a W boson
leptonic decay as obtained in semileptonic $\mathrm{t\bar{t}\gamma}$ events
with a radiated photon of $\mathrm{p_{T}}$ > 50 GeV. A correlation pattern is
shown between the generated and the reconstructed values, when excluding
(left) or including (right) the reconstructed photon in the kinematic fit.

Figure 6:  Invariant mass of two top quarks in semileptonic
$\mathrm{t\bar{t}\gamma}$ events with a radiated photon of $\mathrm{p_{T}}$ >
50 GeV. A correlation pattern is shown between the generated and the
reconstructed values, when excluding (left) or including (right) the
reconstructed photon in the kinematic fit.

Figure 7:  Transverse momentum of top quarks in dilepton
$\mathrm{t\bar{t}\gamma}$ events with a radiated photon of $\mathrm{p_{T}}$ >
50 GeV. A correlation pattern is shown between the generated and the
reconstructed values, when excluding (left) or including (right) the
reconstructed photon in the kinematic fit.

Figure 8:  Transverse momentum of top quarks in $\mathrm{t(\bar{t})\gamma}$
events with a radiated photon of $\mathrm{p_{T}}$ > 20 GeV. A correlation
pattern is shown between the generated and the reconstructed values, when
excluding (left) or including (right) the reconstructed photon in the
kinematic fit.

Figure 9:  The measured mean values and the corresponding variances for the
relative difference in the transverse momentum of reconstructed and generated
top quarks in semileptonic $\mathrm{t\bar{t}\gamma}$, dilepton
$\mathrm{t\bar{t}\gamma}$ and $\mathrm{t(\bar{t})\gamma}$ events. The
comparison is presented for two scenarios: when a radiated photon of
$\mathrm{p_{T}}$ > 50 (20) GeV in $\mathrm{t\bar{t}\gamma}$
($\mathrm{t(\bar{t})\gamma}$) events is either excluded or included in the
kinematic fit.

##  5 Summary

A method for the reconstruction of the top quark event kinematics in the
presence of photon radiation is presented. The kinematic reconstruction is
applied to events with the production of top quark pairs in association with a
photon, and to events with an associated production of single top quarks with
a photon. The inclusion of a radiated photon in a kinematic fit allows to
significantly improve the precision of reconstructed top quark kinematic
observables, when compared to the event generator truth-level information. The
proposed method can be used in experimental studies of the processes with top
quarks with an additional radiation of photons. It aims at improving the
precision of the differential cross section measurements, especially in the
low photon $\mathrm{p_{T}}$ region, as well as at providing an additional
handle for the top quark charge asymmetry measurement. The presented algorithm
of kinematic reconstruction only relies on the knowledge of the top quark and
the W boson masses and therefore can be applied to other processes with
similar decay topologies where photon radiation effects are of importance.

## Acknowledgments

We would like to warmly thank Dennis Schwarz, Francisco Yumiceva, Nadjieh
Jafari and Daniel Noonan for carefully reading the manuscript and for
providing an invaluable set of comments on the presented study. We also thank
Robert Schöfbeck and Lukas Lechner for numerous discussions on the subject of
an experimental study of the process with the production of top quark pairs in
association with photons over the past years.

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