W and Z/gamma* boson production in association with a bottomantibottom pair
ABSTRACT We present a study of l\nu b\bar{b} and l+ l b\bar{b} production at hadron
colliders. Our results, accurate to the nexttoleading order in QCD, are based
on automatic matrixelement calculations performed by MadLoop and MadFKS, and
are given at both the parton level, and after the matching with the Herwig
event generator, achieved with aMC@NLO. We retain the complete dependence on
the bottomquark mass, and include exactly all spin correlations of finalstate
leptons. We discuss the cases of several observables at the LHC which highlight
the importance of accurate simulations.
 [Show abstract] [Hide abstract]
ABSTRACT: We further develop a form factor formalism characterizing anomalous interactions of the Higgslike boson (h) to massive electroweak vector bosons (V) and generic bilinear fermion states (F). Employing this approach, we examine the sensitivity of pp > F >Vh associated production to physics beyond the Standard Model, and compare it to the corresponding sensitivity of h > V F decays. We discuss how determining the Vh invariantmass distribution in associated production at LHC is a key ingredient for modelindependent determinations of h V F interactions. We also provide a general discussion about the power counting of the form factor's momentum dependence in a generic effective field theory approach, analyzing in particular how effective theories based on a linear and nonlinear realization of the SU(2)_L x U(1)_Y gauge symmetry map into the form factor formalism. We point out how measurements of the differential spectra characterizing h > V F decays and pp > F > Vh associated production could be the leading indication of the presence of a nonlinear realization of the SU(2)_L x U(1)_Y gauge symmetry.07/2013;  SourceAvailable from: Ivan Donald ReidS Chatrchyan, V Khachatryan, AM Sirunyan, A Tumasyan, W Adam, T Bergauer, M Dragicevic, J Eroe, C Fabjan, M Friedl, [......], R Loveless, A Mohapatra, MU Mozer, I Ojalvo, GA Pierro, G Polese, I Ross, A Savin, WH Smith, J SwansonJournal of High Energy Physics 01/2013; · 5.62 Impact Factor

Article: W and Z production in association with light and heavyflavour jets at the LHC and the Tevatron
[Show abstract] [Hide abstract]
ABSTRACT: Measurements of W and Z production in association with jets provide a stringent test of perturbative QCD calculations. In addition, these measurements are of great relevance to searches for new particles and new interactions as these StandardModel processes often represent a significant background. In these proceedings, recent results on the W and Z production for light and heavyflavour jets at the Tevatron and the LHC are presented.05/2013;
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arXiv:1106.6019v1 [hepph] 29 Jun 2011
Preprint typeset in JHEP style  HYPER VERSION
CERNPHTH/2011147
CP31120
NSFKITP11114
ZHTH 13/11
W and Z/γ∗boson production in association with a
bottomantibottom pair
Rikkert Frederix
Institut f¨ ur Theoretische Physik, Universit¨ at Z¨ urich, Winterthurerstrasse 190,
CH8057 Z¨ urich, Switzerland
KITP, University of California Santa Barbara, CA 931064030, USA
Stefano Frixione∗
PH Department, TH Unit, CERN, CH1211 Geneva 23, Switzerland
ITPP, EPFL, CH1015 Lausanne, Switzerland
Valentin Hirschi
ITPP, EPFL, CH1015 Lausanne, Switzerland
Fabio Maltoni
Centre for Cosmology, Particle Physics and Phenomenology (CP3)
Universit´ e catholique de Louvain, B1348 LouvainlaNeuve, Belgium
Roberto Pittau
Departamento de F´ ısica Te´ orica y del Cosmos y CAFPE, Universidad de Granada
PH Department, TH Unit, CERN, CH1211 Geneva 23, Switzerland
KITP, University of California Santa Barbara, CA 931064030, USA
Paolo Torrielli
ITPP, EPFL, CH1015 Lausanne, Switzerland
Abstract: We present a study of ℓνb¯b and ℓ+ℓ−b¯b production at hadron colliders. Our re
sults, accurate to the nexttoleading order in QCD, are based on automatic matrixelement
calculations performed by MadLoop and MadFKS, and are given at both the parton level,
and after the matching with the Herwig event generator, achieved with aMC@NLO. We
retain the complete dependence on the bottomquark mass, and include exactly all spin
correlations of finalstate leptons. We discuss the cases of several observables at the LHC
which highlight the importance of accurate simulations.
Keywords: LHC, NLO, Monte Carlo.
∗On leave of absence from INFN, Sezione di Genova, Italy.
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Contents
1.Introduction1
2. Results3
3.Conclusions and outlook14
4. Acknowledgments15
1. Introduction
The discovery and identification of new degrees of freedom and interactions at highenergy
colliders relies on the detailed understanding of Standard Model (SM) background pro
cesses. Prominent among these is the production of electroweak bosons (W,Z) in associa
tion with jets, of which one or more possibly contain bottom quarks. The prime example
is the observation of the top quark at the Fermilab Tevatron collider, produced either in
pairs [1, 2] or singly [3, 4], since both of these mechanisms typically lead to W plus bjets
signatures. Other crucial examples involve the search for a SM Higgs in association with
vector bosons (WH/ZH), with the subsequent Higgs decay into a b¯b pair, a soughtfor
discovery channel both at the Tevatron [5] and at the LHC [6, 7]. Finally, in models which
feature an extended Higgs sector, such as the MSSM or more generally a twoHiggs dou
blet model, a typical Higgs discovery channel is through Hb¯b and Ab¯b final states, with
an H/A → τ+τ−decay. In this case, the SM process ℓ+ℓ−b¯b can provide an important
reference measurement.
Nexttoleadingorder (NLO) QCD calculations for the production of a vector boson
in association with jets have by now quite a successful record. Accurate predictions for W
plus up to four light jets [8, 9, 10, 11, 12, 13] and for Z plus up to three light jets [14, 8, 9, 15]
have become available in the past few years. Associated production with heavy quarks,
and in particular with bottom quarks, has been studied using various approximations. The
Wb¯b and Zb¯b processes have been calculated at the NLO for the first time in refs. [16]
and [17] respectively, by setting the bottomquark mass equal to zero. Such calculations
can be used only for observables that contain at least two bjets. The same processes
have been considered again in refs. [18, 19, 20], where a nonzero bottomquark mass has
been used; however, the matrix elements still involved onshell vector bosons, thereby
neglecting spin correlations of the leptons emerging from W and Z decays. In the case of
W production, this limitation has been recently lifted in ref. [21], which presents the NLO
calculation for the leptonic process ℓνb¯b. Other NLO calculations for final states with one
bjet, Wb and Zb [22, 23], and one bjet plus a light jet, Wbj and Zbj [24, 25], are also
– 1 –
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available in the fiveflavour scheme. All such calculations have played a role and/or have
been extensively compared to the data collected at the Tevatron [26, 27, 28, 29], and now
start to be considered in LHC analyses as well [30, 31].
In this paper we present a calculation of ℓνb¯b production that includes NLO QCD
corrections (analogous to that of ref. [21]), and the first calculation at the NLO of ℓ+ℓ−b¯b
production with massive bottom quarks; we retain the full spin correlations of the final
state leptons1. Furthermore, we match both of these results to the Herwig event generator
by adopting the MC@NLO formalism [32]. Therefore, our results include all the relevant
features which are important in experimental analyses, and can be used in order to obtain
NLO predictions for a large class of observables, including those with zero, one and two
bjets. All aspects of the calculations are fully automated and analogous to the calculation
recently appeared for Ht¯t/At¯t production [33]. Oneloop amplitudes are evaluated with
MadLoop [34], whose core is the OPP integrand reduction method [35] as implemented
in CutTools [36]. Real contributions and the corresponding phasespace subtractions,
achieved by means of the FKS formalism [37], as well as their combination with the one
loop and Born results and their subsequent integration, are performed by MadFKS [38].
The MC@NLO matching is also fully automated, and allows us to simulate for the first
time ℓνb¯b and ℓ+ℓ−b¯b production with NLO accuracy, including exactly spin correlations,
offshell and interference effects, and hadronlevel final states. All the computations are
integrated in a single software framework, which we have dubbed aMC@NLO in ref. [33].
We point out that the onshellW result of ref. [18] has recently been matched to showers
in ref. [39] in the framework of the POWHEG box [40].
The phenomenology of ℓνb¯b and ℓ+ℓ−b¯b final states is very rich and in fact transcends
the prosaic role of background for Higgs or topquark physics. Thanks to the aMC@NLO
implementation, several QCD issues interesting on their own can now be addressed theoret
ically and the results efficiently compared to experiments. In this work we limit ourselves
to providing a first evidence that reliable and flexible predictions for the ℓνb¯b and ℓ+ℓ−b¯b
processes need to include:
• NLO corrections;
• bottom quark mass effects;
• spincorrelation and offshell effects;
• showering and hadronisation.
Detailed studies of these processes as backgrounds to specific signals, such as singletop
and Hb¯b or Ab¯b production respectively, are left to forthcoming investigations.
This paper is organised as follows. In the next section we present several distributions
relevant to ℓνb¯b and ℓ+ℓ−b¯b production at the LHC, and report the results for total rates
at both the Tevatron and the LHC. By working with a nonzero bottom mass, we are able
1In the rest of this paper, ℓνb¯b and ℓ+ℓ−b¯b production as predicted by our simulations may also be
denoted by Wb¯b and Zb¯b respectively.
– 2 –
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to obtain predictions for the cases in which one or two b’s are not observed, and can thus
have arbitrarily small transverse momenta. We also give one example of the comparisons,
at the level of hadronic final states, between the HW and HZ signals and their respective
irreducible backgrounds which we have computed in this paper. We draw our conclusions
in sect. 3.
2. Results
At the leading order (LO) in QCD ℓνb¯b and ℓ+ℓ−b¯b production at hadron colliders proceed
through different channels. Both final states can be obtained via a DrellYantype mecha
nism, i.e., q¯ q(′)annihilation in association with a gluon splitting in a b¯b pair, see fig. 1(a).
Zb¯b, however, can also be produced by gluon fusion, see fig. 1(b), a channel that at the
LO contributes a 30% of the total rate at the Tevatron, but turns out to be the dominant
one (80%) at the LHC, owing to the larger gluon luminosity there. As we shall see in the
following, the fact that Wb¯b and Zb¯b production are dominated by different channels at
the LHC leads to important differences in the kinematical properties of final states, and in
particular of bjets.
We start by presenting results for the total cross sections at both the Tevatron,√s =
1.96 TeV, and the LHC,√s = 7 TeV; the ℓνb¯b results are the sums of the ℓ+νb¯b and ℓ−¯ νb¯b
ones (due to virtualW+and W−production respectively). In our computations we have
set the lepton masses equal to zero, and is therefore not necessary to specify their flavour,
which we generically denote by ℓ (for the charged leptons) and ν (for the neutrinos); we
always quote results for one flavour. For the numerical analysis we have chosen:
µ2
F= µ2
R= m2
ℓℓ′ + p2
T(ℓℓ′) +m2
b+ p2
2
T(b)
+m2
b+ p2
2
T(¯b)
, (2.1)
with ℓℓ′= ℓν and ℓℓ′= ℓ+ℓ−in the case of Wb¯b and Zb¯b production respectively; the
value of the bquark mass is that of the pole mass, mb= 4.5 GeV. We have used LO
and NLO MSTW2008 fourflavour parton distribution functions [41] for the corresponding
cross sections, and the SMparameter settings can be found in table 1. Our runs are fully
inclusive and no cuts are applied at the generation level, except for mℓ+ℓ− > 30 GeV in
ParametervalueParametervalue
mZ
mW
mb
mt
α(LO,4)
s
α(NLO,4)
s
91.118
80.419
4.5
172.5
0.133551
0.114904
α−1
GF
CKMij
ΓZ
ΓW
132.50698
1.16639·10−5
δij
2.4414
2.0476(mZ)
(mZ)
Table 1: Settings of physical parameters used in this work, with dimensionful quantities given in
GeV.
– 3 –
Page 5
Figure 1: Representative diagrams contributing to ℓνb¯b and ℓ+ℓ−b¯b production at the leading
order. ℓνb¯b production can proceed only via a q¯ q′channel, diagram (a). For ℓ+ℓ−b¯b production the
q¯ q channel, diagram (a), is dominant at the Tevatron, while the gg channel, diagram (b), largely
dominates at the LHC.
Cross section (pb)
Tevatron√s =1.96 TeV LHC√s =7 TeV
LO NLOK factor LONLOK factor
ℓνb¯b 4.638.04 1.74 19.4 38.92.01
ℓ+ℓ−b¯b 0.8601.5091.759.6616.1 1.67
Table 2: Total cross sections for ℓνb¯b and ℓ+ℓ−b¯b production at the Tevatron (p¯ p collisions at
√s = 1.96 TeV) and the LHC (pp collisions at√s = 7 TeV), to LO and NLO accuracy. These
rates are relevant to one lepton flavour, and the results for ℓνb¯b production are the sums of those
for ℓ+νb¯b and ℓ−¯ νb¯b production. The integration uncertainty is always well below 1%.
the ℓ+ℓ−b¯b sample. The predicted production rates at the Tevatron and at the LHC are
given in table 2 where, for ease of reading, we also show the fully inclusive K factors. The
contribution of the gg → Zb¯b+X channels is clearly visible in these results: at the Tevatron
σ(ℓ+ℓ−b¯b)/σ(ℓνb¯b) is quite small (and of the same order of the ratio of the fullyinclusive
cross sections σ(Z)/σ(W)), whereas at the LHC ℓ+ℓ−b¯b and ℓνb¯b differ only by a factor of
two.
We now study the impact of NLO QCD corrections on differential distributions, at
both the parton level and after showering and hadronisation, and in doing so we limit
ourselves to the case of the LHC, where the kinematical differences between Wb¯b and Zb¯b
production are more evident. The parton shower in aMC@NLO has been performed with
fortran Herwig [42, 43, 44], version 6.5202.
We start by summarizing our results for bjet rates. Jets are reconstructed at the parti
2Automation of the matching to parton shower in the MC@NLO formalism to Herwig++ [45] and to
Pythia [46] (see refs. [47] and [48] respectively) is currently under way.
– 4 –
Page 6
Figure 2: Fractions of events (in percent) that contain: zero bjets, exactly one bjet, and exactly
two bjets. The rightmost bin displays the fraction of bjets which are bbjets. The two insets show
the ratio of the aMC@NLO results over the corresponding NLO (solid), aMC@LO (dashed), and
LO (symbols) ones, separately for Wb¯b (upper inset) and Zb¯b (lower inset) production.
cle level. In the case of MC simulations, this means giving all finalstate stable hadrons3in
input to the jet algorithm. We adopt the antikTjet clustering algorithm [49] with R = 0.5,
and require each jet to have pT(j) > 20 GeV and η(j) < 2.5. A bjet is then defined as a
jet that contains at least one bhadron; a bbjet is a jet that contains at least two bhadrons
(hence, a bbjet is also a bjet). This implies that we make no distinction between the b
quark and antiquark contents of a jet. We point out that at least another definition of
bjets exists [50] which has a better behaviour in the mb→ 0 limit, in the sense that it
gives (IRsafe) results consistent with the naive picture of “quark” and “gluon” jets. In
practice, this is relevant only in the pT ≫ mblimit. Since this region is not our primary
interest in this paper, we stick to the usual definition; however, it should be obvious that
any jet definition can be used in our framework.
In fig. 2 we present bjet rates, as the fractions of events that contain zero, exactly
one, or exactly two bjet(s). In the case of MCbased simulations, there are also events
with more than two bjets and more than one bbjet, but they give a relative contribution
to the total rate equal to about 0.4% (for Wb¯b) and 0.6% (for Zb¯b), and are therefore not
reported here. The rightmost bin of fig. 2 shows the fraction of bjets which are bbjets.
There is an inset for each of the two histograms shown in the upper part of fig. 2. Each
of the insets presents three curves, obtained by computing the ratio of the aMC@NLO
results over the NLO (solid), aMC@LO4(dashed), and LO (symbols) corresponding ones.
3In order to simplify the Herwig analyses, weaklydecaying B hadrons are set stable.
4We call aMC@LO the analogue of aMC@NLO, in which the shortdistance cross sections are computed
at the LO rather than at the NLO. Its results are therefore equivalent to those one would obtain by using,
e.g., MadGraph/MadEvent [51] interfaced to showers.
– 5 –
Page 7
Figure 3: Invariant mass distribution of finalstate lepton pairs, as predicted by aMC@NLO.
The bjet fractions are fairly similar for Wb¯b and Zb¯b production, and the effects of the
NLO corrections are consistent with the fullyinclusive K factors. On the other hand, the
bbjet contribution to the bjet rate is seen to be more than three times larger for ℓνb¯b
than for ℓ+ℓ−b¯b final states. This fact is again related to the different mechanisms for the
production of a b¯b pair in the two processes considered here. At variance with the case of
ℓνb¯b production, in a ℓ+ℓ−b¯b final state the two b’s may come from the separate branchings
of two initialstate gluons, and thus the probability of them ending in the same jet is much
smaller than in the case of a g → b¯b finalstate branching. We conclude this discussion
by pointing out that the zero and onebjet rates can only be obtained with a nonzero
bquark mass, since the one or two “untagged” b’s must be integrated down to pT= 0, and
hence mb?= 0 is required in order to screen initialstate collinear divergences. This fact
is a severe test condition for the computer programs used in the computations, because it
may induce numerical instabilities. We stress that we did not impose lowpT cuts on any
of the finalstate particles in MadLoop, MadFKS, and in the generation of hard events
in aMC@NLO; our results are therefore completely unbiased, which is what gives us the
possibility of computing quantities such as those reported in table 2 and in fig. 2.
We now turn to studying differential distributions, and start by considering those
defined in terms of finalstate leptons. Observables sensitive to the hadronic activity of
the events, be either relevant to bjets or to Bhadrons, will follow later. In the case of
MCbased simulations, several leptons can appear in the final state. We use the MCtruth
information to select the two which emerge from the hard process, and we shall simply
refer to them as “the leptons” henceforth. A more realistic analysis may select leptons on
the basis of their hardness, measured e.g. with their pT’s; in practice, for the processes we
are considering here (and thanks to the fact that the bhadrons have been set stable) the
two approaches are equivalent.
In fig. 3 the invariant mass of the finalstate lepton pairs is shown. The effect of the γ∗
contribution to ℓ+ℓ−b¯b production is clearly visible at small invariant masses. In this plot,
with limit ourselves to presenting only the aMC@NLO results, since the other simulations
– 6 –
Page 8
Figure 4: Transverse momentum of the charged leptons in ℓνb¯b (left panel) and ℓ+ℓ−b¯b (right
panel) production, shown separately for positive and negative charges. The upper and middle
insets follow the same patterns as those in fig. 2. The lower inset (magenta solid histogram) is
the ratio of the aMC@NLO results relevant to positivelycharged leptons over those relevant to
negativelycharged ones.
give results which are essentially identical to the present ones.
In figs. 4 and 5 the transverse momenta and the pseudorapidities of the charged leptons
are shown separately according to their electric charges. In the two upper insets we have
used the same patterns and conventions as in fig. 2 – these will be used throughout this
paper. In the case of Wb¯b production, the effects of the NLO corrections are especially
pronounced at large pT’s, where they are the signal of new partonic subprocesses opening
up at this order, and in particular of those which include an initialstate gluon, such as
qg. Results after matching with showers consistently show a similar behaviour. The same
large enhancement is not present in the case of Z production, which receives gluoninitiated
contributions already at the LO; again, this trend is seen also after matching with showers.
The lowest insets (solid magenta curves) show the ratios of the aMC@NLO results relevant
to positivelycharged leptons over those relevant to negativelycharged ones. In the case of
Wb¯b production the behaviour is similar to what has been described recently in ref. [52],
while for Zb¯b this distribution is flat, as expected.
A complementary aspect of the different parton luminosities that contribute to Wb¯b
and Zb¯b production can be appreciated by looking for example at the transverse momentum
distributions of the ℓν and ℓ+ℓ−pairs (i.e. of the virtual W and Z bosons respectively),
shown in the left panel of fig. 6. In the case of ℓνb¯b final states, the aMC@LO and LO
results are very close to each other, which is not the case for ℓ+ℓ−b¯b production. This is
due to the fact that the gginitiated channel in the latter case is responsible for much more
QCD radiation in MCbased simulations than the q¯ q channel (the latter being identical to
the mechanism that induces Wb¯b production). This larger amount of radiation hardens the
virtualZ pTspectrum predicted by aMC@LO, making it more similar to the aMC@NLO
result than in the case of Wb¯b production. The NLO pTspectra of the virtual vector bosons
– 7 –
Page 9
Figure 5: As in fig. 4, for the pseudorapidity of the charged leptons.
are closer to the aMC@NLO results, because at that order one does get contributions from
gluoninitiated channels to both ℓνb¯b and ℓ+ℓ−b¯b final states, and thus the relative changes
obtained when matching with parton showers have a milder impact. This is an example
of the “stabilizing” pattern that one observes when higherorder perturbative results are
taken into account. On the other hand, the rapidity distributions of the lepton pairs do
not change significantly under QCD radiation, as is shown in the right panel of fig. 6.
We remark that we do not find any significant enhancement in the largepT tails of
vector bosons when going from the NLO to the aMC@NLO predictions, at variance with
the POWHEG Wb¯b result of ref. [39] which necessitates an adhoc perturbative tuning for
this reason. It should further be stressed that the almost perfect coincidence between the
aMC@LO and LO results for pT(ℓν) may not occur by simply changing the tuning of the
shower parameters in Herwig: indeed, we have verified that the spectrum predicted by
Pythia 6 is slightly different w.r.t. the aMC@LO or LO ones. It is also interesting to
notice that the features discussed here and that affect the low and intermediatepTregions
of lepton pairs are not visible in the case of the individual lepton pTspectra, fig. 4. We have
verified that kinematical correlations are such that, for a fixed small or intermediate value
of pT(ℓ±), one integrates over a pT(ℓ+ℓ−) range that causes the local differences between
the aMC@LO and LO results for the latter transverse momentum to be averaged out.
The left panel of fig. 7 presents the cosθ∗distribution, computed by separating the
positively and negativelycharged lepton contributions. We remind the reader that such
an observable is defined as the cosine of the angle between the chosen charged lepton, and
the direction of flight of the parent vector boson, in the rest frame of the latter. Clearly
visible are the strong angular correlations and charge asymmetry in the ℓνb¯b case. For
ℓ+ℓ−b¯b production such correlations and asymmetries, while present, are much milder, and
likely not observable in a real experiment. For both processes, the aMC@NLO results are
basically identical to those of aMC@LO, NLO, and LO, and thus we refrain from showing
the latter here.
– 8 –
Page 10
Figure 6: Transverse momentum (left panel) and rapidity (right panel) of the ℓν and ℓ+ℓ−pairs
(i.e. of the virtual W and Z bosons respectively) in ℓνb¯b and ℓ+ℓ−b¯b production. The insets follow
the same patterns as those in fig. 2.
In the right panel of fig. 7, where we consider only leptons with positive electric charge
to be definite, we plot the ratio of the lepton transverse momentum over the same quantity,
obtained by imposing a phasespace (i.e., flat) decay of the parent vector boson; hence,
this ratio is a measure of the impact of spin correlations on the inclusivelepton pT. We
see that differences between correlated and uncorrelated decays can be as large as 20%,
and vary across the kinematical range considered. This confirms that the inclusion of spin
correlation effects is necessary when an accurate description of the production process is
required. We stress again that our computations feature spin correlations exactly at the
matrixelement level, including oneloop ones. It is interesting to observe that, while in the
case of Zb¯b production all four calculations give similar results (see the lower inset), this
happens in Wb¯b production only for pT(ℓ+) ? 50 GeV (see the upper inset). At pTvalues
larger than this, aMC@NLO and NLO predict ratios that differ from the corresponding
aMC@LO and LO ones. Once again, this is a manifestation of the significant impact of
gluoninitiated, NLO partonic processes on Wb¯b cross sections.
In figs. 8 and 9 the transverse momenta and the pseudorapidities of the two hardest
bjets are shown. Differences in normalisation are consistent with what we expect on the
basis of inclusive K factors; differences in shapes are typically small, but visible. We point
out that for an event to contribute to the hardestbjet observables shown here it is sufficient
that one bjet be present in the event; the other b quark emerging from the hard process
can have arbitrarily small momentum.
In the left panel of fig. 10, the ∆R separation between the two hardest bhadrons
(for the MCbased simulations) or between the b and¯b quarks (for the NLO and LO
computations) is shown. Differences between the Wb¯b and Zb¯b processes are manifest. In
the former case the two b’s originate from a finalstate gluon splitting, and they will thus
tend to be quite close in pseudorapidity. On the other hand, the two b’s in Zb¯b production
can arise from the uncorrelated branchings of the initialstate gluons in the gg channel, and
– 9 –
Page 11
Figure 7: Left panel: cosθ∗distribution of finalstate charged leptons for different charges. All
histograms have been obtained with aMC@NLO. See the text for the observable definition. Right
panel: ratio of the results for the pT of the positivelycharged lepton over the same quantity com
puted by neglecting production spin correlations. The insets follow the same patterns as those in
fig. 2.
Figure 8: Transverse momentum of the hardest (left panel) and secondhardest bjet (right panel)
in Wb¯b and Zb¯b production. The insets follow the same patterns as those in fig. 2.
in this way they will naturally acquire a large separation in pseudorapidity, which is directly
related with large∆R values. However, a b¯b pair arising from a finalstate gluon branching
can be easily separated in pseudorapidity by QCD radiation. This is the reason why the
partonlevel LO result in the case of Wb¯b production is so different from the other three
predictions (as shown by the symbols in the upper inset). Both partonlevel NLO (through
radiation present at the matrixelement level) and aMC@LO (through radiation due to
parton showers) results are in fact much closer to aMC@NLO than partonlevel LO result
is. This does not happen in the case of Zb¯b production, since as discussed before the b and
¯b quarks can be wellseparated in pseudorapidity already at the LO. It should be stressed
– 10 –
Page 12
Figure 9: As in fig. 8, for the pseudorapidity of the hardest and the secondhardest bjet.
Figure 10: Left panel: ∆R separation between the two hardest bhadrons (aMC@NLO and
aMC@LO) or the b and¯b quarks (NLO and LO) in the event. Right panel: invariant mass of the
bjets, inclusive over all bjets in the event. The insets follow the same patterns as those in fig. 2.
that the bhadrons that contribute to the ∆R separation shown in fig. 10 are not subject
to any lower cuts in pT. Thus, one expects that the effects of extra radiation be diminished
when imposing a pT cut or, which is equivalent, by studying the same distribution in the
case of bjets. We have verified that this is indeed the case, i.e. that when a minimumpTcut
is imposed on the two bhadrons the pattern of NLO QCD corrections in Wb¯b production is
more similar to that observed in Zb¯b production. This is another example of the possibility
of testing detailed properties of QCD radiation by considering lowpTevents. It should be
clear that from the theoretical viewpoint such studies can be sensibly performed only by
retaining the full bmass dependence.
The right panel of fig. 10 shows the mass of the bjets in the events. The observable
is inclusive over all bjets, which implies that a given event may enter more than once
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Figure 11: Transverse momentum fraction carried by bjets. See the text for details.
in the plot.
mjb≈ 12 GeV. In the case of Zb¯b production this effect is almost invisible, a consequence
of the fact that the fraction of events where a bjet is actually a bbjet is much smaller than
for Wb¯b production, see fig. 2. The distribution discussed here measures the activity inside
a jet, and one cannot expect fixedorder partonlevel results, where a jet consists of one
or two particles, to be particularly sensible in this case. In fact, we see that fixedorder
results are very different from MCbased ones. On the other hand, the differences in shape
when going from aMC@LO to aMC@NLO are small, in particular for Zb¯b production, as
expected for observables which are insensitive to emissions at large relative pT’s. We also
point out that the knee at mjb≈ 12 GeV would appear as a feature of gluon jets if the bjet
definition of ref. [50] were used. This stresses again the fact that, at small and moderate
pT’s, the usual definition gives more intuitive results. On the other hand, at large jet pT’s
the onset of the bbjet contribution to mjbis largely smeared out.
In fig. 11 we show the ratio of the total transverse momentum PT[jb] of bjets, over the
total transverse hadronic momentum PT5. In the context of partonlevel computations, by
“hadrons” we simply understand QCD partons. At the partonlevel LO, the configurations
with one bbjet or with two bjets (each of which contains one b quark) give contribution
at PT[jb]/PT= 1. Configurations with one bjet that contains only one b quark contribute
to 0.5 < PT[jb]/PT < 1 if the other b quark has pT < 20 GeV (i.e., it is softer than a jet
is required to be), while values PT[jb]/PT < 0.5 can be obtained when the other b quark
has pT> 20 GeV and η(b) > 2.5 (i.e., it is outside the bjet tagging region in pseudora
pidity). What was said above implies that PT[jb]/PT = 1 is an infraredsensitive region,
which gives rise to Sudakov logarithms at higher order; this explains the behaviour of the
partonlevel NLO results there. Furthermore, the LO contributions to the PT[jb]/PT< 0.5
region decrease when increasing the maximumpseudorapidity cut on jets. This is only
marginally the case at the NLO (because of the presence of a hard light parton in the real
emission contributions), which explains the longer tail of the latter results w.r.t. the LO
Striking is the onset of the bbjet contribution in the Wb¯b result around
5We stress that PT is defined without including the underlying event and pileup contributions.
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Figure 12: Invariant mass of the pair of the two leading bjets. WH(→ ℓνb¯b), ZH(→ ℓ+ℓ−b¯b),
ℓνb¯b, and ℓ+ℓ−b¯b results are shown, with the former two rescaled by a factor of ten.
ones. The arguments above obviously do not apply to the context of an event generator;
this is confirmed by the similarity of the aMC@NLO and aMC@LO results. Firstly, at
PT[jb]/PT= 1 Sudakov logarithms are properly resummed. Secondly, the extra radiation
generated by parton showers implies that quite a few hadrons will lie outside bjets, hence
shifting further the PT[jb]/PTresults to the left of those relevant to partonlevel NLO com
putations. This shift is also present when passing from the aMC@LO to the aMC@NLO
predictions in Wb¯b production, while in the case of Zb¯b production these two results are
very similar (up to an overall rescaling by the inclusive K factor). We are finding here the
same pattern already discussed for a few observables in this paper. Namely, the opening of
gluoninitiated partonic channels at the NLO in Wb¯b production implies a richer hadronic
activity w.r.t. the corresponding LO case, which is only marginal in the case of Zbb produc
tion owing to the dominance of the gg channel already at the LO there. Hence, the relative
enhancement of the hadronic activity outside the bjets when going from aMC@LO to
aMC@NLO is stronger for Wb¯b production than is for Zb¯b production.
Finally, as a simple application to Higgs searches of the calculations presented in this
paper, we show in fig. 12 the invariant mass of the two leading bjets in WH(→ ℓνb¯b),
ZH(→ ℓ+ℓ−b¯b), ℓνb¯b, and ℓ+ℓ−b¯b events. The former two processes (the “signal”) have
been simulated with MC@NLO [32]6, with a Higgs mass mH = 120 GeV. The tail at
m[jb,1,jb,2] > mHis due to the fact that the jet momenta are typically larger than those of
the bhadrons they contain, owing to the contributions of other finalstate hadrons emerging
from initialstate showers. This is compensated by the fact that the bhadron momenta
are only a fraction of those of their parent b quarks, the complementary fraction being
6In the process of validating aMC@NLO, we had checked that it gave results identical to MC@NLO for
all the processes implemented in the latter. Hence, we could have equally well employed aMC@NLO to
simulate the signal here.
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Page 15
lost to radiation which may end up outside the jets. These two effects smear the Higgs
peak. Furthermore, in some events the b quarks entering the two hardest bjets do not arise
from the Higgs decay, but from a g → b¯b branching in the shower phase. Although rare
indeed, these events may result in invariant masses much larger than the Higgs pole mass.
The comparison given here is just an example of an analysis in which both the signal and
its irreducible backgrounds can be computed at the same precision with (a)MC@NLO,
improving upon both fixedorder and LObased Monte Carlo descriptions.
3. Conclusions and outlook
In this work we have presented results for the ℓνb¯b and ℓ+ℓ−b¯b production processes,
accurate to the NLO in QCD and that include the matching to parton showers according
to the MC@NLO formalism. Our approach is fully general, completely automated, and
opens the way to performing comparisons with experimental data from the Tevatron and
the LHC at the highest theoretical accuracy attainable nowadays.
By studying a limited but representative set of observables, we have shown that several
are the elements to be kept into account in order to achieve reliable and flexible predictions
for this class of processes: spin correlations of the final state leptons emerging from the
decays of the vector bosons, heavyquark mass effects, and a realistic description of the
final states, obtained thanks to the interface with a shower and hadronisation program. As
we have seen, NLO QCD corrections have a highly nontrivial impact, since they lead not
only to large enhancements of total rates, but also to significant changes in the shapes of
distributions. In this respect, the opening at the NLO of new partonic channels, and in
particular of those involving gluons, plays a fundamental role. In general and apart from
wellunderstood cases in which pure perturbative results are not meaningful, one observes
that at the NLO level fixedorder and MCbased results are closer to each other than the
corresponding LO ones. This is in keeping with naive expectations based on perturbation
theory, and it is significant in that it shows that the very large corrections affecting the
processes considered here do not pose problems when the matching with parton shower
Monte Carlos is carried out according to the MC@NLO method.
Thanks to the aMC@NLO implementation, several QCD issues interesting on their
own can now be addressed. One example over all is the study of NLO corrections, mass
effects and radiation pattern in finalstate gluon splitting, for which Wb¯b production offers
a particularly clean environment. Gluon splitting in the initial state and the role of the b
PDF (and therefore of different schemes for the predictions of total and differential cross
sections) can be assessed by considering Zb¯b production. The outcome of such a study
can then be applied to the Hb¯b case. In particular, available predictions in the fiveflavour
scheme at the NNLO for the fullyinclusive production of a Z in association with bottom
quarks [53], and for Z+1 bjet at the NLO [23], can now compared with our fourflavour
scheme results. In addition, QCD radiation effects on highpTb¯b pairs, which can be merged
into one jet, are also of interest in boostedHiggs searches [54]. Finally, spin correlation
effects may also be investigated to gather more insight on the production mechanisms
in QCD, and possibly to distinguish them from other competing hard reactions, such as
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