Associated production of a topquark pair with vector bosons at NLO in QCD: impact on \( \mathrm{t}\overline{\mathrm{t}}\mathrm{H} \) searches at the LHC
JHE
Associated production of a topquark pair with vector
Fabio Maltoni 0 1 2 3
Davide Pagani 0 1 2 3
Ioannis Tsinikos 0 1 2 3
0 Chemin du Cyclotron , 2, LouvainlaNeuve, B1348 Belgium
1 CP3 Universite catholique de Louvain
2 Centre for Cosmology , Particle Physics and Phenomenology
3 in MadGraph5
We study the production of a topquark pair in association with one and two vector bosons, ttV and ttV V with V = ; Z; W , at the LHC. We provide predictions at nexttoleading order in QCD for total cross sections and topquark charge asymmetries as well as for di erential distributions. A thorough discussion of the residual theoretical uncertainties related to missing higher orders and to parton distribution functions is presented. As an application, we calculate the total cross sections for this class of processes (together with ttH and tttt production) at hadron colliders for energies up to 100 TeV. In addition, by matching the NLO calculation to a parton shower, we determine the contri
QCD Phenomenology; NLO Computations

HJEP02(16)3
bution of ttV and ttV V to
nal state signatures (twophoton and twosamesign,
threeand fourlepton) relevant for ttH analyses at the Run II of the LHC.
1 Introduction 2 Fixedorder corrections at the production level 3
4
1
2.1
ttV processes and ttH production
2.2 ttV V processes
2.3 tttt production 2.4
Total cross sections from 8 to 100 TeV
Analyses of ttH signatures
3.1
3.2
Signature with two photons
Signatures with leptons
Conclusions
Introduction
With the second run of the LHC at 13 TeV of centre of mass energy, the Standard Model
(SM) is being probed at the highest energy scale ever reached in collider experiments. At
these energies, heavy particles and highmultiplicity
nal states are abundantly produced,
o ering the opportunity to scrutinise the dynamics and the strength of the interactions
among the heaviest particles discovered so far: the W and Z bosons, the top quark and
the recently observed scalar boson [1, 2]. The possibility of measuring the couplings of the
top quark with the W and Z bosons and the triple (quadruple) gaugeboson couplings will
further test the consistency of the SM and in case quantify possible deviations. In addition,
the couplings of the Higgs with the W and Z bosons and the top quark, which are also
crucial to fully characterise the scalar sector of the SM, could possibly open a window on
BeyondtheStandardModel (BSM) interactions.
Besides the study of their interactions,
nal states involving the heaviest states of
the SM are an important part of the LHC program, because they naturally lead to
highmultiplicity
nal states (with or without missing transverse momentum). This kind of
signatures are typical in BSM scenarios featuring new heavy states that decay via long
chains involving, e.g., dark matter candidates. Thus, either as signal or as background
processes, predictions for this class of SM processes need to be known at the best possible
accuracy and precision to maximise the sensitivity to deviations from the SM. In other
words, the size of higherorder corrections and the total theoretical uncertainties have to
energies and luminosities, the phenomenological relevance of this kind of processes and
the impact of higherorder corrections on the corresponding theoretical predictions are
expected to become even more relevant [3].
In this work we focus on a speci c class of highmultiplicity production process in the
SM, i.e., the associated production of a topquark pair with either one (ttV ) or two gauge
vector bosons (ttV V ). The former includes the processes ttW
tt , while the latter counts six di erent
nal states, i.e., ttW +W , ttZZ, tt
(ttW + + ttW
), ttZ and
, ttW
ttW
Z and ttZ . In addition, we consider also the associated production of two topquark
pairs (tttt), since it will be relevant for the phenomenological analyses that are presented
in this work.
The aim of our work is twofold. Firstly, we perform a detailed study of the predictions
at xed NLO QCD accuracy for all the ttV and ttV V processes, together with ttH and tttt
production, within the same calculation framework and using the same input parameters.
This approach allows to investigate, for the rst time, whether either common features
or substantial di erences exist among the theoretical predictions for di erent nal states.
More speci cally, we investigate the impact of NLO QCD corrections on total cross sections
and di erential distributions. We systematically study the residual theoretical uncertainties
due to missing higher orders by considering the dependence of key observables on di erent
de nitions of central renormalisation and factorisation scales and on their variations. NLO
QCD corrections are known for ttH in [4{7], for tt in [8, 9], for ttZ in [9{13], for ttW
in [9, 13{15] and for tttt in [16, 17]. NLO electroweak and QCD corrections have also
already been calculated for ttH in [18{20] and for ttW
and ttZ in [20]. Moreover, in
the case of ttH, NLO QCD corrections have been matched to parton showers [21, 22]
and calculated for o shell top (anti)quarks with leptonic decays in [23]. In the case
of tt , NLO QCD corrections have been matched to parton showers in [24].
For the
ttV V processes a detailed study of NLO QCD corrections has been performed only for
tt
[25, 26]. So far, only representative results at the level of total cross sections have
been presented for the remaining ttV V processes [3, 17]. When possible, i.e. for ttV , ttH
and tt
, our results have been checked against those available in the literature in previous
works [9, 13, 14, 17, 20{22, 24, 25], and we have found perfect agreement with them. This
crosscheck can also be interpreted as a further veri cation of the correctness of both the
results in the literature and of the automation of the calculation of NLO QCD corrections
Secondly, we perform a complete analysis, at NLO QCD accuracy including the
matching to parton shower and decays, in a realistic experimental setup, for both signal and
background processes involved in the searches for ttH at the LHC. Speci cally, we
consider the cases where the Higgs boson decays either into two photons (H !
), or into
leptons (via H ! W W , H ! ZZ , H !
the CMS and ATLAS collaborations at the LHC with 7 and 8 TeV [27{29]. In the rst
case, the process tt
ttW +W , ttZZ, ttW
is the main irreducible background. In the second case, the processes
Z are part of the background, although their rates are very small,
as we will see. However, ttW +W
production, e.g, has already been taken into account
at LO in the analyses of the CMS collaboration at 7 and 8 TeV, see for instance [27]. A
contribution of similar size can originate also from tttt production [30], which consequently
+
), which have already been analysed by
{ 2 {
has to be included for a correct estimation of the background.1 Furthermore, depending
on the exact
nal state signature, the ttV processes can give the dominant contribution,
which is typically one order of magnitude larger than in ttV V and tttt production.
In this work, the calculation of the NLO QCD corrections and the corresponding event
generation has been performed in the MadGraph5 aMC@NLO framework [17]. This code
allows the automatic calculation of treelevel amplitudes, subtraction terms and their
integration over phase space [31] as well as of loopamplitudes [9, 32, 33] once the relevant
Feynman rules and UV/R2 counterterms for a given theory are provided [34{36]. Event
generation is obtained by matching shortdistance events to the shower employing the
MC@NLO method [37], which is implemented for Pythia6 [38], Pythia8 [39],
HERWIG6 [40] and HERWIG++ [41]. The reader can nd in the text all the inputs and set
of instructions that are necessary to obtain the results presented here.
The paper is organised as follows. In section 2 we present a detailed study of the
predictions at NLO QCD accuracy for the total cross sections of ttV , ttV V and tttt production.
We study their dependences on the variation of the factorisation and renormalisation scales.
Furthermore, we investigate the di erences among the use of a xed scale and two possible
de nitions of dynamical scales. Inclusive and di erential Kfactors are also shown. As
already mentioned above, these processes are backgrounds to the ttH production with the
Higgs boson decaying into leptons, which is also considered in this work. To this purpose,
we show also the same kind of results for ttH production. In addition, in the case of
ttV and ttH, we provide predictions at NLO in QCD for the corresponding topcharge
asymmetries and in order to investigate the behaviour of the perturbative expansion for
some key observables, we also compute ttV j and ttHj cross sections at NLO in QCD. Such
results appear here for the rst time. In section 2 we also study the dependence of the
total cross sections and of global Kfactors for ttV V and ttV processes as well as for ttH
and tttt production on the total energy of the protonproton system, providing predictions
in the range from 8 to 100 TeV.
In section 3 we present results at NLO accuracy for the background and signal relevant
for ttH production. In subsection 3.1 we consider the signature where the Higgs decays
into photons. In our analysis we implement a selection and a de nition of the signal region
that are very similar to those of the corresponding CMS study [27]. For the signal and
background processes tt
, we compare LO, NLO results and LO predictions rescaled
by a global at Kfactor for production only, as obtained in section 2. We discuss the
range of validity and the limitations of the last approximation, which is typically employed
in the experimental analyses. In subsection 3.2 we present an analysis at NLO in QCD
accuracy for the searches of ttH production with the Higgs boson subsequently decaying
into leptons (via vector bosons), on the same lines of subsection 3.1. In this case, we
consider di erent signal regions and exclusive nal states, which can receive contributions
from tttt production and from all the ttV and ttV V processes involving at least a heavy
vector boson. Also here, we compare LO, NLO results and LO predictions rescaled by a
1Triple topquark production, tttW and tttj, a process mediated by a weak current, is characterised by
Fixedorder corrections at the production level
In this section we describe the e ects of xedorder NLO QCD corrections at the
production level for ttV processes and ttH production (subsection 2.1), for ttV V processes
(subsection 2.2) and then for tttt production (subsection 2.3). All the results are shown for
13 TeV collisions at the LHC. In subsection 2.4 we provide total cross sections and global
Kfactors for protonproton collision energies from 8 to 100 TeV. With the exception of
tt , detailed studies at NLO for ttV V processes are presented here for the
rst time.
The other processes have already been investigated in previous works, whose references
have been listed in introduction. Here, we (re)perform all such calculations within the
same framework, MadGraph5 aMC@NLO, using a consistent set of input parameters and
paying special attention to features that are either universally shared or di er among the
various processes. Moreover, we investigate aspects that have been only partially
studied in previous works, such as the dependence on (the de nition of) the factorisation and
renormalisation scales, both at integrated and di erential level. To this aim we de ne the
variables that will be used as renormalisation and factorisation scales.
Besides a
xed scale, we will in general explore the e ect of dynamical scales that
depend on the transverse masses (mT;i) of the
nalstate particles. Speci cally, we will
employ the arithmetic mean of the mT;i of the nalstate particles ( a) and the geometric
mean ( g), which are de ned as
a =
0
HT :=
N
1
N
Y
i=1;N
X
i=1;N(+1)
11=N
mT;iA
:
mT;i ;
(2.1)
(2.2)
HJEP02(16)3
In these two de nitions N is the number of nalstate particles at LO and with N (+1)
in eq. (2.1) we understand that, for the realemission events contributing at NLO, we
take into account the transverse mass of the emitted parton.2 There are two key aspects
in the de nition of a dynamical scale: the normalisation and the functional form. We
have chosen a \natural" average normalisation in both cases leading to a value close to
mt when the transverse momenta in the Born con guration can be neglected. This is
somewhat conventional in our approach as the information on what could be considered
a good choice (barring the limited evidence that a NLO calculation can give for that in
rst place) can be only gathered a posteriori by explicitly evaluating the scale dependence
2This cannot be done for g; soft real emission would lead to g
0. Conversely, a can also be de ned
of the results. For this reason, in our studies of the total cross section predictions, we
vary scales over a quite extended range, c=8 <
< 8 c. More elaborate choices of
evenbyevent scales, such as a CKKWlike one [42] where factorisation and renormalisation
scales are \local" and evaluated by assigning a partonshower like history to the nal state
con guration, could be also considered. Being ours the rst comprehensive study for this
class of processes and our aim that of gaining a basic understanding of the dynamical
features of these processes, we focus on the simpler de nitions above and leave possible
re nements to speci c applications.
All the NLO and LO results have been produced with the MSTW2008 (68% c.l.)
PDFs [43] respectively at NLO or LO accuracy, in the ve avourscheme (5FS) and with
the associated values of
s
. ttW +W
production, however, has been calculated in the
four avourscheme (4FS) with 4FS PDFs, since the 5FS introduces intermediate topquark
resonances that need to be subtracted and thus unnecessary technical complications.
The mass of the top quark has been set to mt = 173 GeV and the mass of the Higgs
are performed by leaving the top quark and the vector bosons stable. In simulations at
NLO+PS accuracy, they are decayed by employing MadSpin [44, 45] or by Pythia8. If
not stated otherwise photons are required to have a transverse momentum larger than
20 GeV (pT ( ) > 20 GeV) and Frixione isolation [46] is imposed for jets and additional
photons, with the technical cut R0 = 0:4. The ne structure constant
is set equal to its
corresponding value in the G scheme for all the processes.3
2.1
ttV processes and ttH production
lines) and
and (2.2).
As rst step, we show for ttH production and all the ttV processes the dependence of the
NLO total cross sections, at 13 TeV, on the variation of the renormalisation and
factorisation scales r and f . This dependence is shown in
gure 1 by keeping
varying it by a factor eight around the central value
=
= mt (dotted lines). The scales a and g are respectively de ned in eqs. (2.1)
As typically
a is larger than
g and mt, the bulk of the cross sections originates
from phasespace regions where s( a) <
s( g); s(mt). Consequently, such choice gives
systematically smaller cross sections. On the other hand, the dynamical scale choice g
leads to results very close in shape and normalisation to a
xed scale of order mt.
Driven by the necessity of making a choice, in the following of this section and in the
analyses of section 3 we will use
g as reference scale. Also, we will independently vary
f and
r by a factor of two around the central value g, g=2 <
f ; r < 2 g, in order
to estimate the uncertainty of missing higher orders. This generally includes, e.g., almost
the same range of values spanned by varying
=
r =
f by a factor of four around the
central value
=
a, a=4 <
< 4 a (cf. gure 1) and thus it can be seen as a conservative
choice. In any case, while certainly justi ed a priori as well as a posteriori, we stress that
3This scheme choice for
is particularly suitable for processes involving W bosons [47]. Anyway, in our
can be obtained by simply rescaling the numbers listed in this paper.
ttZ
1.23
]bp1.4 LHCμc1=3μTgeV
[
ttH
O
L
N
M
a
_
5
M
2
4
8
ttH
< 8 c for the three di erent choices of the central value
c
:
g, a, mt. The upper plot
refers to tt production, the lower plot to ttW , ttZ and ttH production.
The rst uncertainty is given by the scale variation within
g=2 < f ; r < 2 g, the second one by
PDFs. The relative statistical integration error is equal or smaller than one permille.
the
=
g choice is an operational one, i.e. we do not consider it as our \best guess"
but just use it as reference for making meaningful comparisons with other possible scale
de nitions and among di erent processes.
Using the procedure described before, in table 1 we list, for all the processes, LO
and NLO cross sections together with PDF and scale uncertainties, and Kfactors for the
central values. The dependence of the LO and NLO cross sections on
= r =
f is also
shown in
gure 2 in the range
g=8 <
< 8 g. As expected, for all the processes, the
scale dependence is strongly reduced from LO to NLO predictions both in the standard
interval g=2 <
< 2 g as well as in the full range g=8 <
< 8 g. For tt process (upper
plots in
gures 1 and 2), we nd that in general the dependence of the crosssection scale
variation is not strongly a ected by the minimum pT of the photon, giving similar results
for pT ( ) > 20 GeV and pT ( ) > 50 GeV. As already stated in section 1, with ttW
we
refer to the sum of the ttW + and ttW
contributions.
We now show the impact of NLO QCD corrections on important distributions and we
all the processes we analysed the distribution of the invariant mass of the topquark pair
1/8
with c =
production.
LO

1/4
1/2
1
ttγ
M
0.8
0.6
0.4
0.2
0
1/8

1/4
1/2
1
LO
ttZ
ttW±
ttH
O
L
N
M
a
_
5
h
p
a
r
M
2
4
8
g. The upper plot refers to tt production, the lower plot to ttW , ttZ and ttH
scalar boson. Given the large amount of distributions, we show only representative results.
All the distributions considered and additional ones can be produced via the public code
For each gure, we display together the same type of distributions for the four di erent
processes: tt , ttH, ttW
and ttZ. Most of the plots for each individual process will be
displayed in the format described in the following.
In each plot, the main panel shows the speci c distribution at LO (blue) and NLO
QCD (red) accuracy, with
=
f =
r equal to the reference scale
g. In the rst inset
we display scale and PDF uncertainties normalised to the blue curve, i.e., the LO with
=
g. The mousegrey band indicates the scale variation at LO in the standard range
g=2 <
f ; r < 2 g, while the darkgrey band shows the PDF uncertainty. The black
dashed line is the central value of the grey band, thus it is by de nition equal to one. The
solid black line is the NLO QCD di erential Kfactor at the scale
=
g, the red band
around it indicates the scale variation in the standard range
g=2 <
f ; r < 2 g. The
additional blue borders show the PDF uncertainty. We stress that in the plots, as well as
in the tables, scale uncertainties are always obtained by the independent variation of the
factorisation and renormalisation scales, via the reweighting technique introduced in [48].
The second and third insets show the same content of the rst inset, but with di erent
scales. In the second panel both LO and NLO have been evaluated with
=
a, in the
third panel with
The fourth and the fth panels show a direct comparison of NLO QCD predictions
using the scale
g and, respectively, a and mt. All curves are normalised to the red
curve in the main panel, i.e., the NLO with
=
g. The mousegrey band now indicates
the scale variation dependence of NLO QCD with
=
g. Again the dashed black line,
the central value, is by de nition equal to one and the darkgrey borders represent the
PDF uncertainties. The black solid line in the fourth panel is the ratio of the NLO QCD
predictions at the scale a and g. The red band shows the scale dependence of NLO QCD
predictions at the scale a, again normalised to the central value of NLO QCD at the scale
{ 7 {
b
b
m
m
NLO
LO
O
LN
pahrGd
MadGra
)g1.4 LO unc.
NLO unc.
the plots is described in detail in the text.
g, denoted as R( a). Blue bands indicate the PDF uncertainties. The fth panel, R(mt),
is completely analogous to the fourth panel, but it compares NLO QCD predictions with
g and mt as central scales.
We start with gure 3, which shows the distributions for the invariant mass of the
topquark pair (m(tt)) for the four production processes. From this distribution it is possible to
note some features that are in general true for most of the distributions. As can be seen in
the fourth insets, the use of
= a leads to NLO values compatible with, but systematically
{ 8 {
LO
NLO
Mad
5h_p
Gra
ad
M
smaller than, those obtained with
=
g. Conversely, the using
= mt leads to scale
uncertainties bands that overlap with those obtained with
=
g. By comparing the
rst three insets for the di erent processes, it can be noted that the reduction of the
scale dependence from LO to NLO results is stronger in ttH production than for the ttV
processes. As we said, all these features are not peculiar for the m(tt) distribution, and are
consistent with the total cross section analysis presented before, see gure 1 and table 1.
From
gure 3 one can see that the two dynamical scales g and a yield
atter Kfactors
than those from the xed scale mt, supporting a posteriori such a reference scale. While
this feature is general, there are important exceptions. This is particular evident for the
distributions of the pT of the topquark pair (pT (tt)) in
gure 4, where the di erential
Kfactors strongly depend on the value of pT (tt) for both dynamical and xed scales. The
relative size of QCD corrections grows with the values of pT (tt) and this e ect is especially
large in ttW
Kfactors. and tt production. In the following we investigate the origin of these large
Topquark pairs with a large pT originate at LO from the recoil against a hard vector
or scalar boson. Conversely, at NLO, the largest contribution to this kinetic con guration
emerges from the recoil of the topquark pair against a hard jet and a soft scalar or vector
boson (see the sketches in
gure 5). In particular, the cross section for a topquark pair
with a large pT receives large corrections from (anti)quarkgluon initial state, which appears
for the rst time in the NLO QCD corrections. This e ect is further enhanced in ttW
production for two di erent reasons. First, at LO ttW
production does not originate,
unlike the other production processes, form the gluongluon initial state, which has the
largest partonic luminosity. Thus, the relative corrections induced by (anti)quarkgluon
initial states have a larger impact. Second, the emission of a W collinear to the nalstate
(anti)quark in qg ! ttW
q0 can be approximated as the qg ! ttq process times a q !
q0W
splitting. For the W momentum, the splitting involves a soft and collinear singularity
which is regulated by the W
mass.
Thus, once the W momentum is integrated, the
qg ! ttW
q0 process yields contributions to the pT (tt) distributions that are proportional
to s log2 [pT (tt)=mW ].4 The same e ect has been already observed for the pT distribution
of one vector boson in NLO QCD and EW corrections to W
W ; W
Z and ZZ bosons
hadroproduction [49{51].
The argument above clari es the origin of the enhancement at high pT of the tt pair,
yet it raises the question of the reliability of the NLO predictions for ttV in this region
of the phase space. In particular the giant Kfactors and the large scale dependence call
for better predictions. At rst, one could argue that only a complete NNLO calculation
for ttV would settle this issue. However, since the dominant kinematic con gurations (see
the sketch on the right in
gure 5) feature a hard jet, it is possible to start from the
ttV j
nal state and reduce the problem to the computation of NLO corrections to ttV j.
Such predictions can be automatically obtained within MadGraph5 aMC@NLO. We have
therefore computed results for di erent minimum pT for the extra jet both at NLO and
LO accuracy. In gure 6 we summarise the most important features of the ttW (j) cross
4In ttZ the same argument holds for the q ! qZ splitting in qg ! ttZq. However, the larger mass of
[pT 0.01
0.0001
)g9
μ
( 5
Κ
n
i
LO
MCa
0.1
0.0001
n
i
b
/
d
/
LO
MCa
5_
aph
r
MadG
described in detail in the text.
section as a function of the pT (tt) as obtained from di erent calculations and orders.
Similar results, even though less extreme, hold for ttZ and ttH
nal states and therefore we
do not show them for sake of brevity. In gure 6, the solid blue and red curves correspond
to the predictions of pT (tt) as obtained from ttW
calculation at LO and NLO,
respectively. The dashed light blue, purple and mousegrey curves are obtained by calculating
ttW
j at LO (yet with NLO PDFs and
s and same scale choice in order to consistently
compare them with NLO ttW
results) with a minimum pT cut for the jets of 50, 100,
150 GeV, respectively. The three curves, while having a di erent threshold behaviour, all
HJEP02(16)3
jet takes most of the recoil and the W boson is soft.
n
i
p
[
T
/dσ 0.001
0.0001
)g2
μ
(Κ1
LHC13
± (μg)
ttW
ttW±j (μg)
NLO
LO
NLO pT(j) > 100 GeV
LO pT(j) > 50 GeV
LO pT(j) > 100 GeV
LO pT(j) > 150 GeV
O
L
N
r
G
d
a
M
ttW±j
pT(j) > 100 GeV
(green), for di erent minimum cuts (50, 100, 150 GeV) on the jet pT . The lower inset shows the
di erential Kfactor as well as the residual uncertainties as given by the ttW
j calculation.
tend smoothly to the ttW
prediction at NLO at high pT (tt), clearly illustrating the fact
that the dominant contributions come from kinematic con gurations featuring a hard jet,
such as those depicted on the right of gure 5. Finally, the dashed green line is the pT (tt) as
obtained from ttW
j at NLO in QCD with a minimum pT cut of the jet of 100 GeV. This
prediction for pT (tt) at high pT is stable and reliable, and in particular does not feature any
large Kfactor, as can be seen in the lower inset which displays the di erential Kfactor
for ttW j production with pT cut of the jet of 100 GeV. For large pT (tt), NLO corrections
to ttW j reduce the scale dependence of LO predictions, but do not increase their central
NLO
LO
g of ttV . The (N)LO cross sections are calculated with (N)LO PDFs, the relative statistical
integration error is equal or smaller than one permil.
value. Consequently, as we do not expect large e ects from NNLO corrections in ttW
production at large pT (tt), a simulation of NLO ttV +jets merged sample a la FxFx [52]
should be su cient to provide reliable predictions over the full phase space.
For completeness, we provide in table 2 the total cross sections at LO and NLO
accuracy for ttW
j, as well as ttZj and ttHj production, with a cut pT (j) > 100 GeV. At
variance with what has been done in
gure 6, LO cross sections are calculated with LO
PDFs and the corresponding
s, as done in the rest of the article.
The mechanism discussed in detail in previous paragraphs is also the source of the
giant Kfactors for large pT (tt) in tt production, see gure 4. This process can originate
from the gluongluon initial state at LO, however, the emission of a photon involves soft
and collinear singularities, which are not regulated by physical masses. When the photon
is collinear to the
nalstate (anti)quark, the qg ! tt q process can be approximated
as the qg ! ttq process times a q ! q splitting. Here, soft and collinear divergencies
are regulated by both the cut on the pT of the photon (pcTut) and the Frixione isolation
parameter R0. We checked that, increasing the values of pcTut and/or R0, the size of the
Kfactors is reduced. It is interesting to note also that corrections in the tail are much
larger for
= g than
=
a. This is due to the fact that the softest photons, which give
the largest contributions, sizeably reduce the value of g, whereas
a is by construction
larger than 2pT (tt). This also suggests that g might be an appropriate scale choice for
this process only when the minimum pT cut and the isolation on the photon are harder.5
In gures 7 and 8 we show the pT distributions for the top quark and the vector or
scalar boson, pT (t) and pT (V ), respectively. For these two observables, we nd the general
features which have already been addressed for the m(tt) distributions in gure 3.
In gure 9 we display the distributions for the rapidity of the vector or scalar boson,
y(V ). In the four processes considered here, the vector or scalar boson is radiated in
di erent ways at LO. In ttH production, the Higgs boson is never radiated from the initial
state. In ttZ and tt
production, in the quarkantiquark channel the vector boson can
be emitted from the initial and
nal states, but in the gluongluon channel it can be
radiated only from the nal state. In ttW
production, the W is always emitted from
5Assuming mT (t)
mT (t) and mT ( ) = pcut, the the ratio a= g increases by increasing pT (t) and,
T
when mT (t) > pcTut, decreases by increasing pcTut.
Moreover, under the same assumption,
a =
g at
50 100 150
pT(t) [GeV]250 300 350 400
200
0
LO
Mad
Gdra
n
i
b
/
d
/
pT0.01
n
i
b
/
p
[
)t 1.4
(m 1
Κ0.6
) 1.2
NLO
LO
OL
MadG
arph
MadG
LO unc.
0.01
)g1.4
n
i
b
/
μ
(Κ0.6
)a1.4
described in detail in the text.
the initial state. The initialstate radiation of a vector boson is enhanced in the forward
and backward direction, i.e., when it is collinear to the beampipe axis. Consequently,
the vector boson is more peripherally distributed in ttW
production, which involves only
initial state radiation, than in tt and especially ttZ production. In ttH production, large
values of jy(V )j are not related to any enhancement and indeed the y(V ) distribution is
much more central than in ttV processes. These features can be quanti ed by looking,
e.g., at the ratio r(V ) := ddy (jyj = 0)= ddy (jyj = 3). At LO we nd, r(W )
r(Z)
17:5 and r(H)
40. As can be seen in the rst three insets of the plots of gure 9,
5, r( )
8:5,
n
i
b
/
d
/
σ
p
[pT 0.01
0.001
1
)g1.4 LO unc.
NLO unc.
NLO
Κ0.6
)t 1.2
(m 1
n
i
b
/
T
R 0.8
0.1 ttH (μg), LHC13
50 100 150
the plots is described in detail in the text.
NLO QCD corrections decrease the values of r(V ) for ttW
and tt production, i.e. the
vector bosons are even more peripherally distributed (r(W )
3:5, r( )
5:5). A similar
but milder e ect is observed also in ttZ production (r(Z)
16). On the contrary, NLO
QCD corrections make the distribution of the rapidity of the Higgs boson even more central
(r(H)
53). In
gure 9 one can also notice how the reduction of the scale dependence
from LO to NLO results is much higher in ttH production than in ttV type processes.
Furthermore, for this observable, Kfactors are in general not at also with the use of
LO
O
apr
adMG
LO unc.
NLO unc.
LO
hpar
adMG
LO
aph
r
aMdG
LO unc.
n
i
b
/
d
/
n
i
b
/
b
NLO
LO
LNO
raph
dGa
M
OLN
0.001
)g1.14
μ
(Κ0.6
) 1.4
n
i
y
d
/
(
R 0.8
of the plots is described in detail in the text.
dynamical scales. From a phenomenological point of view, this is particularly important
for ttW
and tt , since the cross section originating from the peripheral region is not
extremely suppressed, as can be seen from the aforementioned values of r(W ) and r( ).
In gure 10 we show distributions for the rapidities of the top quark and antiquark,
y(t) and y(t). In this case we use a slightly di erent format for the plots. In the main panel,
as in the format of the previous plots, we show LO results in blue and NLO results in red.
Solid lines correspond to y(t), while dashed lines refer to y(t). In the rst and second inset
C
r
G
G
d
d
a
a
M
M
HJEP02(16)3
−3
−2
−1
1
2
3
−3
−2
−1
1
2
3
y(t), y(t)
0
y(t), y(t)
NLO t
LO t
NLO t
LO t
NLO t
LO t
NLO t
LO t
d
/
n
i
b
/
0.001
1.2
LO 1
N0.8
n
i
b
/
b
d
/
[yp0.01
we plot the ratio of the y(t) and y(t) distributions respectively at NLO and LO accuracy.
This ratio is helpful to easily identify which distribution is more central(peripheral) and if
there is a central asymmetry for the topquark pair. Also here, although it is not shown in
the plots, Kfactors are not in general at.
In the case of tt production the central asymmetry, or the forwardbackward asymmetry
in protonantiproton collisions, originates from QCD and EW corrections. At NLO, the
asymmetry arises from the interference of initial and nalstate radiation of neutral vector
bosons (gluon in QCD corrections, and photons or Z bosons in EW corrections) [53{58].
Thus, the real radiation contributions involve, at LO, the processes pp ! ttZ and pp ! tt ,
which are studied here both at LO and at NLO accuracy. As can be seen from
gure 10,
tt
production yields an asymmetry already at LO, a feature studied in [
59
]. The ttZ
production central asymmetry is also expected to be non vanishing at LO, but the results
plotted in
gure 10 tell us that the actual value is very small. The asymmetry is instead
analytically zero in ttW
(ttH) production, where the interference of initial and
nalstate W (Higgs) bosons is not possible.6
6In principle, when the couplings of light avour quarks are considered nonvanishing, initialstate
radiation of a Higgs boson is possible and also a very small asymmetry is generated. However, this possibility
is ignored here.
LO
NLO
LO
NLO
= g. The rst uncertainty is given by the scale variation within
second one by PDFs. The assigned error is the absolute statistical integration error.
At NLO, all the ttV processes and the ttH production have an asymmetry, as can be
seen in gure 10 from the ratios of the y(t) and y(t) distributions at NLO. In the case of
ttW
production the asymmetry, which is generated by NLO QCD corrections, has already
been studied in detail in [15]. In all the other cases it is analysed for the rst time here.
NLO and LO results at 13 TeV for Ac de ned as Ac =
(jytj > jytj)
(jytj < jytj)
(jytj > jytj) + (jytj < jytj)
(2.3)
are listed in table 3, which clearly demonstrates that NLO QCD e ects cannot be neglected,
once again, in the predictions of the asymmetries. For ttW
and ttH production, an
asymmetry is actually generated only at NLO. Furthermore, NLO QCD corrections change
sign and increase by a factor
7 the asymmetry in ttZ production and they decrease it
by a factor larger than two in tt
production. Thus, NLO results point to the necessity
of reassessing the phenomenological impact of the tt signature, which is based on a LO
calculation [
59
]. Moreover, we have also checked that for pT ( ) > 50 GeV both the LO and
NLO central values of the asymmetry are very similar (within 5 per cent) to the results in
table 3, where pT ( ) > 20 GeV.
2.2
ttV V processes
We start showing for all the ttV V processes the dependence of the NLO total cross sections,
at 13 TeV, on the variation of the renormalisation and factorisation scales r and f . This
dependence is shown in
gure 11 and it is obtained by varying
=
r =
f by a factor
eight around the central value
=
=
a (dashed lines) and
= mt
(dotted lines).
Again, for all the processes and especially for those with a photon in
the
nal state, we
nd that
a typically leads to larger cross sections than
g and mt.
For this class of processes we also investigated the e ect of the independent variation of
factorisation and renormalisation scales. We found that the condition
r =
f captures
the full dependence in the ( r; f ) plane in the range a=2 <
f ; r < 2 a. On the other
hand, in the full a=8 < f ; r < 8 a region o diagonal values might di er from the values
spanned at f = r.
ttZZ
ttZZ
ttW+W[4f]
ttγγ
5
h
p
a
r
G
d
a
M
O
L
N
5
h
p
a
r
G
d
a
M

1/4
1/2
1
2
4
8
r
μ = μ [μc]
HJEP02(16)3
< 8 c for the three di erent choices of the central value c
: g, a, mt.

1/4
1/2
1
2
4
8
r
μ = μ [μc]
with c = g for the ttV V processes.
In table 4 we list, for all the processes, LO and NLO cross sections together with PDF
and scale uncertainties, and Kfactors for the central values. Again scale uncertainties
are evaluated by varying independently the factorisation and the renormalisation scales in
the interval g=2 <
f ; r < 2 g. The dependence of the LO and NLO cross sections on
=
r =
f is shown in
gure 12 in the range g=8 <
< 8 g. As expected, for all the
processes, the scale dependence is strongly reduced from LO to NLO predictions both in
the standard interval g=2 <
< 2 g as well as in the full range
g=8 <
< 8 g. For
the central scale
=
g, Kfactors are very close to unity. It is interesting to note that
NLO curves display a plateau around g=2 or g=4, corresponding to HT =8 and HT =16,
respectively.
We show now the impact of NLO QCD corrections for relevant distributions and we
discuss their dependence on scale choice and its variation. For all the processes we have
ttW +W [4f]
11:84+81:13:2%%
+2:3%
2:4%
ttZZ
NLO
LO
is given by the scale variation within
g=2 <
f ; r < 2 g, the second one by PDFs. The relative
statistical integration error is equal or smaller than one permille.
considered the distribution of the invariant mass of the topquark pair and the pT and the
rapidity of the (anti)top quark, of the topquark pair and of the vector bosons. Again, given
the large amount of distributions that is possible to consider for such a nal state, we show
only representative results. We remind the interested reader that additional distributions
can be easily produced via the public code MadGraph5 aMC@NLO.
For each gure, we display together the same type of distributions for the six di erent
processes: tt , ttZZ, ttW +W , ttW
Z, ttW
and ttZ .
We start with
gure 13,
which shows the m(tt) distributions. The format of the plot is the same used for most
of the distribution plots in subsection 2.1, where it is also described in detail. For m(tt)
distributions, we notice features that are in general common to all the distributions and
have already been addressed for ttV processes in subsection 2.1. For instance, the use
of
=
a leads to NLO values compatible with, but systematically smaller than, those
obtained with
=
g. Conversely, the choice
= mt leads to scale uncertainties bands
that overlaps with those obtained with
= g. The NLO corrections in ttZZ production
are very close to zero, for
=
g, and very stable under scale variation (see also table 4).
For all the processes, the two dynamical scales g and a yield atter Kfactors than those
from the xed scale mt.
In gure 14 we show the distributions for pT (tt). As for ttV processes (see gure 4),
these distributions receive large corrections in the tails. This e ect is especially strong for
the processes involving a photon in the
nal state, namely, tt
, ttZ
for all the three choices of
employed here, Kfactors are not at. Surprisingly, the
Kfactors for ttZZ, ttW
of pT (tt) when
Z and ttW +W
production show a larger dependence on the value
is a dynamical quantity, as can be seen from a comparison of the rst
( =
g) and second ( =
a) insets with the third insets (
= mt). From the fourth insets
of all the six plots, it is possible to notice how the scale dependence at NLO for
= g it
is much larger than for
=
a. Exactly as we argued for ttV processes, NLO ttV V +jets
merged sample a la FxFx should be used for an accurate prediction of these tails.
In gure 15 we show the distributions for pT (t). Most of the features discussed for m(tt)
in gure 13 appear also for these distributions. The same applies to the distributions of the
pT of the two vector bosons, which are displayed in gure 16. In the plots of gure 16 and
in all the remaining gures of this section we use the same format used in subsection 2.1 for
gure 10. Thus, di erential Kfactors will not be explicitly shown. In the rst and second
inset we show the ratio of the distributions of the pT of the two vector bosons, respectively
at NLO and LO accuracies. In the case of tt
production, 1 is the hardest photon, while
2 is the softest one. Similarly, in ttZZ production, Z1 is the hardest Z boson, while Z2 is
the softest one. As can be noticed, for each process this ratio is the same at LO and NLO
accuracy and thus it is not sensitive to NLO QCD corrections.
In
gure 17 we show the distributions for y(t) and y(t). The ttV V processes, with
the exception of ttW +W ,7 at LO exhibit a central asymmetry for top (anti)quarks. Top
quarks are more centrally distributed than top antiquarks in tt
, ttW
productions, while they are more peripherally distributed in ttZZ and ttW
Z production. In all
the ttV V processes, NLO QCD corrections lead to a relatively more peripheral distribution
of top quarks than antiquarks. This e ects yield to a nonvanishing central asymmetry for
ttW +W
production and almost cancel the LO central asymmetry of ttZ
production.
Here, we refrain to present results for the central asymmetries of ttV V processes, since it
is extremely unlikely that at the LHC it will be possible to accumulate enough statistics
to perform these measurements.
In gure 18 we show the distributions for y(V1) and y(V2). Comparing the rst and
second insets, only small di erences can be seen for the ratios of the distributions at LO
and NLO. Thus, unlike for the top quark and antiquark, the rapidity of the rst and the
second vector boson receive NLO relative di erential corrections that are very similar in
size. Both in the distributions of the rapidities of the top (anti)quark and of the vector
bosons, NLO QCD corrections in general induce non at Kfactors, also with the use of
dynamical scales.8
2.3
tttt production
In this section we present results for tttt production. We start by showing in gure 19 the
scale dependence of the LO (blue lines) and NLO (red lines) total cross section at 13 TeV.
As for the previous cases, we vary
=
r =
f by a factor eight around the central
value
= g (solid lines),
a (dashes lines) and, due to the much heavier nal state,
= 2mt (dotted lines). In this case we also show with a dotdashed line the dependence of
the NLO cross section on an alternative de nition of average scale
where possible additional partons appearing in the nal state do not contribute.
LO = N1 Pi=1;N mT;i,
a
7Analytically, this process is supposed to give an asymmetry. Numerically, it turns out that it can be
safely considered as zero.
8We explicitly veri ed it and it can be easily reproduced via the public version of MadGraph5
aMC@NLO, which has also been used for the phenomenological study presented here.
15
μc = 2mt
0
1/8

1/4
1/2
1
tttt (NLO)
tttt (LO)
5
h
p
a
r
dependence in the interval c=8 <
< 8 c for the four di erent choices of the central value c
As expected, predictions relative to g and
LO are very close. Conversely, a and
a
LO show a nonnegligible di erence. Note that the value of a and
a
LO is the same for
a
Born and and virtual contributions for any kinematic con guration. Thus, the di erence
between dashed and dotdashed lines is formally an NNLO e ect that arise from di erences
in the scale renormalisation for real radiation events only. To investigate the origin of this
e ect, we have explicitly checked that the di erence is mainly induced by the corresponding
change in the renormalisation scale and not of the factorisation scale. Similar behaviour is
also found in ttV and ttV V processes, yet since the masses of the
nalstate particles are
di erent and the s coupling order lower, g and
LO lines are more distant than in tttt
a
Since the LO cross section is of O( s4), it strongly depends on the value of the
renormalisation scale, as can be seen in
gure 19. This dependence is considerably reduced at
NLO QCD accuracy in the standard interval g=2 <
< 2 g. Conversely, for
the value of the cross section falls down rapidly, reaching zero for
g=8. This is a
signal that in this region the dependence of the cross section on
is not under control.
Qualitatively similar considerations apply also for the di erent choices of scales, as can be
seen in gure 19.
In eqs. (2.4) and (2.5), we list the NLO and LO cross sections evaluated at the scale
= g together with scale and PDF uncertainties. As done in previous subsections, scale
uncertainties are evaluated by varying the factorisation and renormalisation scales in the
standard interval g=2 <
f ; r < 2 g. As a result the total cross section at LHC 13 TeV
for the
= g central scale choice reads
NLO = 13:31+2255::83%% +56::86%% fb ;
LO = 10:94+8411::16%% +44::87%% fb ;
K factor = 1:22 :
(2.4)
(2.5)
(2.6)
HJEP02(16)3
Di erent choices for the central value and functional form of the scales, as well as the
interval of variation, lead to predictions that are compatible with the result above, see also
e.g. [16].
We now discuss the e ect of NLO QCD corrections on di erential distributions. We
analysed the distribution of the invariant mass, the pT and the rapidity of top (anti)quark
and the possible topquark pairs.
Again, given the large amount of distributions, we
show only representative results. All the distributions considered and additional ones
can be produced via the public code MadGraph5 aMC@NLO. For this process the scale
dependence of many distributions has been studied also in [16] and our results are in
agreement with those therein. In
gure 20 we show plots with the same formats as those
used and described in the previous sections. Speci cally, we display the distributions for
the total pT of the two hardest top quark and antiquark (pT (t1t1)), their invariant mass
(m(t1t1)), the rapidity of the hardest top quark y(t1) and the invariant mass of the tttt
system (m(tttt)). Also, in the last plot of gure 20, we show the pT distributions of the
hardest together with the softest top quarks, pT (t1) and pT (t2), and their ratios at NLO
and LO.
We avoid repeating once again the general features that have already been pointed out
several times in the previous two sections; they are still valid for tttt production. Here,
we have found, interestingly, that NLO corrections give a sizeable enhancement in the
threshold region for m(t1t1). It is worth to notice that also for this process NLO QCD
corrections are very large in the tail of the pT (t1t1) distribution, especially with the use
of dynamical scales. We have veri ed that in these regions of phase space the qg ! ttttq
contributions are important. Finally, as can be seen in the last plot, we nd that the ratios
of pT (t1) and pT (t2) distributions are not sensitive to NLO QCD corrections.
Total cross sections from 8 to 100 TeV
In addition to the studies performed for the LHC at 13 TeV, in this subsection we discuss
and show results for the dependence of the total cross section on the energy of the
protonproton collision. In gure 21 NLO QCD total cross sections are plotted from 8 to 100 TeV,
as bands including scale and PDF uncertainties. The corresponding numerical values are
listed in table 5. As usual, central values refers to
g, and scale uncertainties are
obtained by varying independently r and f in the standard interval g=2 < f ; r < 2 g.
In the upper plot of gure 21 we show the results for ttH production and ttV processes,
whereas tttt production and ttV V processes results are displayed in the lower plot. In both
plots we show the dependence of the Kfactors at
= g on the energy (the rst and the
second inset). The rst insets refer to processes with zerototalcharge nal states, whereas
the second insets refer to processes with charged nal states. The very di erent qualitative
behaviours between the two classes of processes is due to the fact that the former include
already at LO an initial state with gluons, whereas the latter do not. The gluon appears
in the partonic initial states of charged processes only at NLO via the (anti)quarkgluon
channel. At small Bjorkenx's, the gluon PDF grows much faster than the (anti)quark
PDF. Thus, increasing the energy of the collider, the relative corrections induced by the
(anti)quarkgluon initial states leads to the growth of the Kfactors and dominates in their
tt
ttW Z
ttZ
ttW
tttt
ttZ
ttW
tt
ttH
0:502+2:9% +2:7%
8:6%
2:2%
2:12+3:8% +1:9%
8:6%
1:8%
2:59+4:3% +1:8%
8:7%
1:8%
11:1+6:9% +1:2%
9:1%
1:4%
21:1+8:1% +1:1%
9:4%
1:3%
51:6+9:9% +0:9%
9:8%
1:1%
204+11:3% +0:8%
9:9%
1:0%
11:1%
+2:9%
2:7%
11:8+8:3%
11:2%
+2:3%
2:4%
14:4+12:2% +2:6%
12:8%
2:9%
66:6+9:5%
10:8%
+1:6%
2:0%
130+10:2% +1:5%
10:8%
1:8%
HJEP02(16)3
327+10:9% +1:3%
10:6%
1:6%
1336+10:3% +1:0%
9:9%
1:3%
2:77+6:4%
10:5%
+1:9%
1:5%
10:3+13:9% +1:3%
13:3%
1:3%
12+12:5% +1:2%
12:6%
1:2%
44:8+15:7% +0:9%
13:5%
0:9%
78:2+16:4% +0:8%
13:6%
0:9%
184+19:2% +0:8%
14:7%
0:9%
624+15:5% +0:7%
13:4%
1:0%
1:13+5:8% +3:1%
9:8%
2:1%
4:16+9:8%
10:7%
+2:2%
1:6%
4:96+10:4% +2:1%
10:8%
1:6%
17:8+15:1% +1:5%
12:6%
1:1%
30:2+18:3% +1:2%
14:1%
0:9%
66+18:9% +1:1%
14:3%
0:8%
210+21:6% +1:0%
15:8%
0:8%
1:39+6:9%
11:2%
+2:5%
2:2%
5:77+10:5% +1:8%
12:1%
1:9%
6:95+10:7% +1:8%
12:1%
1:9%
29:9+12:9% +1:3%
12:4%
1:5%
56:5+13:2% +1:2%
12:2%
1:4%
138+13:7% +1:0%
12:0%
1:1%
533+13:3% +0:8%
11:1%
1:0%
2:01+7:9%
10:5%
+2:6%
1:8%
6:73+12:0% +1:8%
11:6%
1:4%
7:99+12:8% +1:7%
11:9%
1:3%
27:6+18:7% +1:2%
14:4%
0:9%
46:3+20:2% +1:1%
15:1%
0:8%
98:4+21:9% +1:0%
15:9%
0:7%
318+22:5% +1:0%
17:7%
0:7%
1:71+24:9% +7:9%
26:2%
8:4%
13:3+25:8% +5:8%
25:3%
6:6%
17:8+26:6% +5:5%
25:4%
6:4%
130+26:7% +3:8%
24:3%
4:6%
297+25:5% +3:1%
23:3%
3:9%
929+24:9% +2:4%
22:4%
3:0%
4934+25:0% +1:7%
21:3%
2:1%
0:226+9:0%
11:9%
are calculated with percent accuracy, whereas for the processes with three
nalstate particles with per mill.
 
 
 
13 14
ttZ
ttW±
25 33
50
ttH
O
L
a
_
a
r
G
d
a
M
100
 
 
 
13 14
ttZZ
25 33



50
tttt
ttW±Z
ttZγ
ttW±γ
O
L
N
C
M
a
_
5
h
a
r
G
d
a
M
100
[p1O02
L
N
σ
10
1
101
rso 2
t
fca1.5
K 1
8
1
a
Kf 1
rso 2
t
fca1.5
K 1
8
ttV, ttH production at pp colliders at NLO in QCD
central μf = μr = μg , MSTW2008 NLO PDFs (68% cl)
uncertainties (added linearly). The upper plot refers to ttV processes and ttH production, the lower
plot to ttV V processes and tttt production. For nal states with photons the pT ( ) > 20 GeV cut
is applied.
ttW
available.
energy dependence. Also, as can be seen in gure 21 and table 5, these processes present
a larger dependence on the scale variation than the uncharged processes.
The di erences in the slopes of the curves in the main panels of the plots are also
mostly due to the gluon PDF. Charged processes do not originate from the gluongluon
initial state neither at LO nor at NLO. For this reason, their growth with the increasing of
the energy is smaller than for the uncharged processes. All these arguments point to the
fact that, at 100 TeV collider, it will be crucial to have NNLO QCD corrections for ttW ,
and ttW
Z processes, if precise measurements to be compared with theory will be
whereas ttV V processes are of O( s2 2).
The fact that tttt production is the process with the rapidest growth is again due to
percentage content of gluongluoninitiated channels, which is higher than for all the other
processes, see
gure 22. From the left plot of gure 21, it is easy also to note that the
scale uncertainty of tttt production is larger than for the ttV V processes. In this case,
the di erence originates from the di erent powers of s at LO; tttt production is of O( s4)
3
Analyses of ttH signatures
In this section we provide numerical results for the contributions of signal and irreducible
background processes to two di erent classes of ttH signatures at the LHC. In subsection 3.1
we consider a signature involving two isolated photons emerging from the decay of the
Higgs boson into photons, H !
H ! W W
and H !
involving two or more leptons, where ttH production can contribute via the H ! ZZ ,
decays. We perform both the analyses at 13 TeV and we adopt
. In subsection 3.2 we analyse three di erent signatures
ttV, ttH production at pp colliders at LO
μf = μr = μg , MSTW2008 LO PDFs
L
L
ttVV, tttt production at pp colliders at LO
μf = μr = μg , MSTW2008 LO PDFs
ttZ
50
ttH
100
O
L
N
a
5
h
a
r
G
d
a
M
ttZZ
tttt
100
O
L
N
a
r
HJEP02(16)3
 
13 14
25 33
 
13 14

25 33
Relative contribution of the gg channel to the total cross section at LO for
ttV; ttH; ttV V and tttt processes for pp collisions from 8 to 100 TeV centreofmass energy. For
nal states with photons the pT ( ) > 20 GeV cut is applied.
the cuts of [27].9 The preselection cuts, which are common for both the analyses, are:
pT (e) > 7 GeV ;
j ( )j < 2:5 ;
j (e) < 2:5j ;
pT (j) > 25 GeV ;
pT ( ) > 5 GeV ;
j (j)j < 2:4 ;
j ( )j < 2:4 ;
(3.1)
where jets are clustered via antikT algorithm [60] with the distance parameter R = 0:5.
Event by event, only particles satisfying the preselection cuts in eq. (3.1) are considered
and, for each jet j and lepton `, if
R(j; `) < 0:5 the lepton ` is clustered into the jet j. With the symbol `, unless otherwise speci ed, we always refer to electrons(positrons) and (anti)muons, not to (anti)leptons.
All the simulations for the signal and the background processes have been performed
at NLO QCD accuracy matched with parton shower e ects (NLO + PS). Events are
generated via MadGraph5 aMC@NLO, parton shower and hadronization e ects are realised in
Pythia8 [39], and jets are clustered via FastJet [61].10 Unless di erently speci ed, decays
of the heavy states, including
leptons, are performed in Pythia8. In the showering, only
QCD e ects have been included; QED and purely weak e ects are not included.
Furthermore, multiparton interaction and underlying event e ects are not taken into account.
In order to discuss NLO e ects at the analysis level, in the following we will also
report results for events generated at LO accuracy including shower and hadronization
e ects (LO + PS). As done for the xedorder studies in section 2, LO + PS and NLO + PS
central values are evaluated at
f =
r =
g and scale uncertainties are obtained by
varying independently the factorisation and the renormalisation scale in the interval g=2 <
f ; r < 2 g.
3.1
Signature with two photons
The present analysis focuses on the Higgs boson decaying into two photons in ttH
production, which presents as irreducible background the tt
production. In our simulation, top
9In our simulation we do not take into account particle identi cation e ciencies and possible
misiden
10In our simulation, btagging is performed by looking directly at B hadrons, which we keep stable.
1.09
LO
K
1:466+81:17:0%%
processes at 13 TeV. The
rst
uncertainty is given by scale variation, the second by PDFs. The assigned error is the statistical
Monte Carlo uncertainty.
quark pairs are decayed via Madspin for both the signal and the background, whereas the
HJEP02(16)3
loopinduced H !
branching ratio BR(H !
addition, the following cuts are applied:
decay is forced in Pythia8 and event weights are rescaled by the
) = 2:28
10 3, which is taken from [62].
In this analysis, at least two jets are required and one of them has to be btagged. In
100 GeV < m( 1 2) < 180 GeV ;
pT ( 1) >
2
m( 1 2) ; pT ( 2) > 25 GeV ;
R( 1; 2);
R( 1;2; j) > 0:4 ;
R( 1;2; `) > 0:4 ;
pT (`1) > 20 GeV ;
and an additional cut
R(`i; `j ) > 0:4
is applied if leptons are more than one. With 1 and 2 we respectively denote the hard
and the soft photon, analogously `1 indicates the hardest lepton. Cuts on lepton(s) imply
that the fully and semileptonic decays of the topquark pair are selected.
Results at LO + PS and NLO + PS accuracy are listed in table 6 for the signal and the
tt
background. Also, we display xed order results (LO, NLO) at production level only,
without including top decays, shower and hadronization e ects. In order to be as close as
possible to the analyses level, we apply the cuts in eqs. (3.1) and (3.2) that involve only
photons. Thus, the di erence between LO and NLO results of tt
in tables 4 and 6 are
solely due to these cuts.
In table 6, we show global Kfactors both at xed order (K := NLO=LO) and
including decays, shower and hadronization e ects, and all the cuts employed in the analysis
(KPS := NLO + PS=LO + PS). Comparing KPS and K it is possible to directly
quantify the di erence between a complete NLO simulation (KPS) and the simulation typically
performed at experimental level, i.e., a LO + PS simulation rescaled by a Kfactor from
production only (K). As shown in table 6, e.g., the second approach would
underestimate the prediction for tt
production w.r.t. a complete NLO + PS simulation. This
di erence is not of particular relevance at the level of discovery, which mostly relies on
an identi cation of a peak in the m( 1 2) (see also
gure 23), but could be important in
the determination of signal rates and in the extraction of Higgs couplings. Conversely, the
di erence between K and KPS is much smaller for the signal.
(3.2)
(3.3)
PS ttH1.5
Κ0.5
PS ttγγ 1.5
1
1
Κ0.5
10−4
10−6
1.5
PS ttH
Κ0.5
PS ttγγ 1.5
1
1
Κ0.5
NLO+PS (μg), LHC13
NLO+PS (μg), LHC13
4e−05
]
d
/
σ
/bb 3e−05
RΔ2e−05
d 1e−05
PS ttH1.5
Κ0.5
PS ttγγ 1.5
1
1
Κ0.5
10−4
n
i
T
p
d
/
dσ10−6
10−7
1
Κ0.5
ttγγ
LO unc.
NLO unc.
ttH(γγ)
O
L
L
N
N
a
a
5
5
h
h
p
p
a
a
r
r
G
LO unc.
NLO unc.
100 110 120 130
140
150 160 170 180
0
5
5
h
h
p
p
a
a
r
r
LO unc.
NLO unc.
0
200 250 300 350
0 20 40 60 80
100 120 140 160 180
pT(γ1) [GeV]
pT(γ2) [GeV]
In gure 23 we show representative di erential distributions at NLO + PS accuracy
for the signal (red) and background (black) processes. In the two insets we display the
di erential Kfactor for the signal (KtPtHS ) and the background (KtPtS ) using the same
layout and conventions adopted in the plots of section 2. In particular, we plot the invariant
mass of the two photons (m( 1 2)) their distance (
R( 1; 2)) and the transverse mo
mentum of the hard (pT ( 1)) and the soft (pT ( 2)) photon. We note that predictions for
key discriminating observables, such as the
R( 1; 2) and pT ( 2) are in good theoretical
control.
3.2
Signatures with leptons
H
and H
!
This analysis involves three di erent signatures and signal regions that includes two or
more leptons and it is speci cally designed for ttH production with subsequent H ! ZZ ,
decays. In the simulation, all the decays of the massive
particles are performed in Pythia8. In the case of the signal processes, the Higgs boson
is forced to decay to the speci c nal state (H
! ZZ , H
!
or H
!
+
)
and event weights are rescaled by the corresponding branching ratios, which are taken
W W ) = 2:15
10 1, BR(H
! ZZ ) = 2:64
10 2, BR(H
!
) = 6:32
10 2. The isolation of leptons from the hadronic activity is performed by
directly selecting only prompt leptons in the analyses, i.e., only leptons emerging from Z,
W or from
leptons which emerge from Z, W or Higgs bosons.11
We consider as irreducible background the contribution from ttW , ttZ= , ttW +W ,
ttZZ, ttW
Z and tttt production.12 Precisely, with the notation ttZ=
we mean the full
process tt`+` (` = e; ; ), where Z and photon propagators, from which the `+`
pair
emerges, can both go o shell and interfere.13 All the processes, with the exception of
ttZ= , have been also studied at xedorder accuracy in section 2.
In the analyses the following common cuts are applied in order to select at least two
(3.4)
Then, the three signatures and the corresponding signal regions are de ned as described
Signal region one (SR1): two samesign leptons
Exactly two samesign leptons with pT (`) > 20 GeV are requested. The event is
selected if it includes at least four jets with one or more of them that are btagged.
Furthermore it is required that pT (`1) + pT (`2) + Emiss > 100 GeV and, for the
T
dielectron events, jm(e e ) mZ j > 10 GeV and Emiss > 30 GeV, in order to suppress
T
background from electron sign misidenti cation in Z boson decays.
Signal region two (SR2): three leptons
Exactly three leptons with pT (`1) > 20 GeV, pT (`2) > 10 GeV, pT (`3 = e( )) >
7(5) GeV are requested. The event is selected if it includes at least two jets with one
or more of them that are btagged. For a Z boson background suppression, events
with an oppositesign same avour lepton pair are required to have jm(`+` )
mZ j >
10 GeV. Also, for this kind of events if the number of jets is equal or less than three,
the cut Emiss > 80 GeV is applied.
Signal region three (SR3): four leptons
analyses of [27].
) contributions.
Exactly four leptons with pT (`1) > 20 GeV, pT (`2) > 10 GeV, pT (`3;4 = e( )) >
7(5) GeV are requested. The event is selected if it includes at least two jets with one
or more of them that are btagged. Also here, for a Z boson background suppression,
events with an oppositesign same avor lepton pair are required to have jm(`+` )
mZ j > 10 GeV.
11We observed that applying hadronic isolation cuts as done in [27] we obtain results with at most
10% di erence with those presented here by selecting prompt leptons. Kfactors are independent of the
application of hadronic isolation cuts.
12In principle also ttW
and ttZ
production can contribute to the signatures speci ed in the following.
However, they are a small fraction of ttW and ttZ production and indeed are not taken into account in the
13To this purpose, we excluded Higgs boson propagators in order to avoid a double count of the ttH(H !
For both signal and background processes, results at LO + PS and NLO + PS accuracy
as well as KPSfactors are listed in table 7 for the three signal regions. Also, for each process
we display the value of the global Kfactor (listed also in section 2), which does not take
into account shower e ects, cuts and decays. A posteriori, we observe that in these analyses
the Kfactors are almost insensitive of shower e ects and the applied cuts. This is evident
from a comparison of the values of K and KPS in table 7, where the largest discrepancy
stems from the ttZ=
process in SR1. We also veri ed, with the help of Madspin, that
results in the SR3 (SR2 for ttW
) do not change when spincorrelation e ects are taken
into account in the decays.14 It is important to note that, a priori, with di erent cuts
and/or at di erent energies, K and KPS could be in principle di erent and spin correlation
e ects may be not negligible. Thus, a genuine NLO+PS simulation is always preferable.
4
In this paper we have presented a thorough study at NLO QCD accuracy for ttV and ttV V
processes as well as for ttH and tttt production within the same computational framework
and using the same input parameters. In the case of ttV V processes, with the exception of
tt
production, NLO cross sections have been studied for the rst time here. Moreover,
we have performed a complete analysis with realistic selection cuts on
nal states at NLO
QCD accuracy including the matching to parton shower and decays, for both signal and
background processes relevant for searches at the LHC for the ttH production. Speci cally,
we have considered the cases where the Higgs boson decays either into leptons, where ttV
and ttV V processes and tttt production provide backgrounds, or into two photons giving
the same signature as tt
We have investigated the behaviour of xed order NLO QCD corrections for several
distributions and we have analysed their dependence on (the de nition of) the
renormalisation and factorisation scales. We have found that QCD corrections on key distributions
cannot be described by overall Kfactors. However, dynamical scales in general, even
though not always, reduce the dependence of the corrections on kinematic variables and
thus lead to atter Kfactors. In addition, our study shows that while it is not possible
to identify a \best scale" choice for all processes and/or di erential distributions in ttV
and ttV V , such processes present similar features and can be studied together. For all the
processes considered, NLO QCD corrections are in general necessary in order to provide
precise and reliable predictions at the LHC. In particular cases they are also essential for
a realistic phenomenological description. Notable examples discussed in the text are, e.g.,
the giant corrections in the tails of pT (tt) distributions for ttV processes and the large
decrement of the topquark central asymmetry for tt
production. In the case of future
(hadron) colliders also inclusive cross sections receive sizeable corrections, which lead, e.g.,
to Kfactors larger than two at 100 TeV for ttV and ttV V processes with a charged
nal
state.
14SR2 and especially SR1 involves a rich combinatoric of leptonic and hadronic Z, W and
decays, which
render the simulation with spincorrelation nontrivial. However, we checked also here for representative
cases that spincorrelation e ects do not sensitively alter the results.
HJEP02(16)3
In the searches at the LHC for the ttH production with the Higgs boson decaying either
into leptons or photons, NLO QCD corrections are important for precise predictions of the
signal and the background. We have explicitly studied the sensitivity of NLO+PS QCD
corrections on experimental cuts by comparing genuine NLO+PS QCD predictions with
LO+PS predictions rescaled by global Kfactors from the xed order calculations without
cuts. A posteriori, we have veri ed that these two approximations give compatible results
for analyses at the 13 TeV RunII of the LHC with the cuts speci ed in the text. A priori,
this feature is not guaranteed for analyses with di erent cuts and/or at di erent energies.
In general, a complete NLO+PS prediction for both signal and background processes is
more reliable an thus preferable for any kind of simulation.
All the results presented in this paper have been obtained automatically in the publicly
available MadGraph5 aMC@NLO framework and they can be reproduced starting from
the input parameters speci ed in the text.
Acknowledgments
We thank the ttH subgroup of the LHCHXSWG and in particular Stefano Pozzorini for
many stimulating conversations.
We thank also all the members of the MadGraph5
aMC@NLO collaboration for their help and for providing a great framework for pursuing
this study. This work is done in the context of and supported in part (DP) by the ERC
grant 291377 \LHCtheory: theoretical predictions and analyses of LHC physics: advancing
the precision frontier" and under the Grant Agreement number PITNGA2012315877
(MCNet). The work of FM and IT is supported by the IISN \MadGraph" convention
4.4511.10, by the IISN \Fundamental interactions" convention 4.4517.08, and in part by
the Belgian Federal Science Policy O ce through the Interuniversity Attraction Pole P7/37.
Open Access.
Attribution License (CCBY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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