Page 1

arXiv:1101.1383v1 [hep-ph] 7 Jan 2011

Extraction of Top Backgrounds in the Higgs Boson Search with the

H → WW⋆→ ℓℓ + Emiss

Bruce Mellado,1, ∗Xifeng Ruan,2,3, †and Zhiqing Zhang3, ‡

T

Decay with a Full-Jet Veto at the LHC

1Department of Physics, University of Wisconsin, Madison, WI 53706, USA

2Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China

3Laboratoire de l’Acc´ el´ erateur Lin´ eaire, Universit´ e Paris-Sud et IN2P3-CNRS, Orsay, France

The search for a Standard Model Higgs boson with the H → WW⋆→ ℓℓ + Emiss

application of a full-jet veto yields a strong sensitivity in the mass range 130 < mH < 200 GeV.

One of the residual backgrounds is related to processes involving top quarks. A method for the

extraction of top backgrounds is evaluated at the parton and hadronic levels based on the data-

driven extraction of the jet veto survival probability. The uncertainty of the proposed method is

about 15%.

T

decay and the

PACS numbers: 11.15.Ex,14.80.Bn

I.INTRODUCTION

In the Standard Model (SM) of electroweak interactions, there are four types of gauge vector bosons (gluon, photon,

W±and Z) and twelve types of fermions (six quarks and six leptons) [1–4]. These particles have been observed

experimentally. At present, all the data obtained from the many experiments in particle physics are in agreement

with the SM. In the SM there is one particle, the Higgs boson, that is responsible for generating masses to all of the

particles in the theory, the gauge bosons as well as the fermions [5–10]. In this sense, the Higgs particle occupies a

unique position.

The search using the decay mode H → WW(∗)→ ℓνℓν,(ℓ = e,µ) gives strong sensitivity to the SM Higgs boson

in the intermediate mass range of 130 < mH < 200 GeV [11–15]. The feasibility of Higgs boson searches at the

LHC has been extensively studied and reported by the CMS and ATLAS collaborations in Refs. [16–19] for different

proton-proton center-of-mass energies and integrated luminosities scenarios.

The extraction of the non-resonant WW production and the Higgs boson signal with the H → WW⋆→ ℓℓ+Emiss

decay, where Emiss

T

is the missing transverse energy from the escaping neutrinos, requires a good understanding of top

backgrounds. The region of the phase-space with the best signal-to-background ratio corresponds to a full-jet veto,

i.e. that no hadronic jets be observed above a transverse momentum threshold and within a certain pseudorapidity

range. These requirements are defined by the characteristics of the experiments and the experimental conditions. The

requirement of a full-jet veto is motivated by the need to suppress top backgrounds, the cross-sections of which grow

more rapidly with the center-of-mass energy than the Higgs signal processes. Therefore, it is necessary to understand

the jet veto survival probability of the top background processes. This is a complex observable. For its determination

it is desirable to rely on data or to have the least amount of Monte Carlo (MC) dependence.

In Ref. [18] a method for the extraction of the jet veto survival probability from data was explored. In this work this

quantity was extracted from a control sample made of one high transverse momentum and isolated lepton, large Emiss

and at least two jets, the invariant mass of which was required to be close to the W mass. Systematic errors of the

order of 100% were reported. Here we consider the extraction of the jet veto survival probability of top backgrounds

from a control sample that comprises two high transverse momentum leptons, Emiss

This part of phase-space is dominated by top backgrounds. The isolation of top processes experimentally happens in

a restricted region of the phase-space. This may introduce a significant bias in the calculation of the jet veto survival

probability. This bias and the corresponding theoretical uncertainty are evaluated here. In this method, the full-jet

veto survival probability for top backgrounds is expressed as the square of the veto survival probability in events with

one b-tagged hadronic jet multiplied by a Matrix Element correction.

This paper is organized as follows: Section II gives account of the modelling of the top backgrounds; Section IIIA

describes the event selection used; Section IIIB discusses the jet veto survival probability at leading order (LO). The

T

T

T

and a b-tagged hadronic jet.

∗Electronic address: bmellado@wisc.edu

†Electronic address: ruanxf@mail.ihep.ac.cn

‡Electronic address: zhangzq@lal.in2p3.fr

Page 2

2

impact of QCD higher order corrections and hadronization is discussed in Section IIIC.

II.DESCRIPTION OF TOP PROCESSES

As pointed out in Refs. [20, 21] the description of top-related processes in the presence of jet vetoes or topological

requirements is not trivial. A description of this final state in terms of the sum of the square-amplitudes of tt and

single top production (qb → tW diagrams) is not appropriate for certain parts of the phase-space of interest here.

This has been proven to be the case even when finite width effects in the top quark decays are taken into account.

Effects have been quantified in the particular context of the Higgs boson search with the H → WW⋆→ ℓℓ + Emiss

decay [20, 21]. When calculating the survival probability against a jet veto in a detector it is appropriate to use the

full set of diagrams that contribute to pp → W+W−bb processes. Events with two large transverse momentum leptons

and large Emiss

T

emerging from the pp → W+W−bb processes cannot be split into double resonant, single resonant

and non-resonant processes. This problem would be solved with the computation of QCD corrections at next-to-

leading-order (NLO) to the complete set of pp → W+W−bb diagrams and their implementation in MC@NLO [22] or

POWHEG [23, 24]. Before the appearance of such a tool it is necessary to resort to the LO description. The first

results of a NLO QCD calculation for the full set of pp → W+W−bb have been reported recently [25]. This represents

significant progress towards a proper description of corners of the phase-space of interest here.

The automated program MADGRAPH [26] is used to generate MC events corresponding to the various processes

considered here. The impact of QCD higher order corrections and hadronization is evaluated with the package

MC@NLO [22]. The impact of hadronization and QCD higher order corrections are obtained with the Monte Carlo

truth (hadronic) without the application of detector effects. In both cases default settings are used. The CTEQ6L1 and

CTEQ6M [27] parton density parameterizations are used, when appropriate. The renormalization and factorization

scales are set to the top mass. No constraint is applied on the transverse momentum of the b-partons and these are

required to be separated by ∆R > 0.4. The decays of the W boson are treated with the narrow width approximation.

For the computation of the non-resonant pp → W+W−bb process all diagrams containing top quark lines are

excluded. This is necessary in order to evaluate the double-counting that occurs when extracting top-related back-

grounds for the extraction of the WW signal. For the calculation of cross-sections with this process the factorization

and renormalization scales are set to the W mass.

T

Process7 TeV 14TeV

103

99.6

0.50

pp → W+W−bb

pp → tt → W+W−bb

pp → W+W−bb (non-resonant)

625

597

3.03

TABLE I: Cross-sections (in pb) at LO for the processes pp → W+W−bb, pp → tt → W+W−bb and non-resonant

pp → W+W−bb. Results are shown for two different values of the center-of-mass energy of the proton-proton collision.

The MADGRAPH [26] package is used to calculate the cross-sections.

Table I shows the cross-sections in pb at LO for the processes pp → W+W−bb, pp → tt → W+W−bb and non-

resonant pp → W+W−bb. The results in Table I do not include the branching ratios of the W bosons to leptons.

III. PARTON-LEVEL STUDIES

In this section we consider the extraction of the full-jet veto survival probability using parton-level. The impact of

QCD higher order corrections and hadronization will be considered in Section IIIC.

A. Event Selection

The following requirements are imposed on the final state considered here:

• s1 Two opposite sign leptons (electrons or muons) with pT> 20 GeV in the pseudorapidity range |η| < 2.5,

• s2 Large transverse missing transverse energy, Emiss

T

> 30 GeV.

Page 3

3

When performing studies at the parton-level the Emiss

W decay and b-tagging is performed by tossing a random number. If more than two partons are b-tagged the parton

that has the largest random number assigned is chosen. The remaining parton is denoted as probe parton. When

evaluating the feasibility of top events with a b-tagged jet a 60% tagging efficiency is assumed in the range |η| < 2.5.

Experimentally, the b-tagging efficiency is a function of the jet transverse momentum. Following this procedure without

a correction would introduce undesirable biases that would need to be corrected with MC. Therefore, when choosing

probe parton it is appropriately deconvoluted with the pT dependence of the experimental b-tagging efficiency.

The control sample studied here to extract top backgrounds is defined by the additional requirement of a high pT

and central b-parton. In addition to the requirements specified above the following condition is imposed:

T

is defined as the transverse momentum of neutrinos of the

• s3 At least one b-tagged parton with pT> 30 GeV in the range |η| < 2.5.

B. Jet Veto Survival Probability and the Definition of the Method

The study of the jet veto survival probability (jvsp) is initially performed at the parton-level using LO matrix

elements. The jvsp for events with a large pT gluon in the final state is significantly smaller. The impact of QCD

higher order corrections and hadronization will be considered below.

In this section we define various quantities pertaining to the jvsp in events with top backgrounds at LO. It is

convenient to define the P1 as the probability of a parton of a particular type to miss a region of phase-space of

interest. This region of the phase-space is defined with a lower bound on the transverse momentum, pv

maximum value of the parton pseudorapidity, ηv, with the superscript v referring to veto. These are defined by

experimental considerations. The hadron-level transverse momentum threshold that is usually applied experimentally

is pv

pv

Tis expected to be somewhat higher than the nominal value of the threshold that is set experimentally. These two

thresholds are related to each other via the experimental inefficiency of observing jets in a range in the vicinity of pv

The jvsp is defined in the control region as the sum of two contributions:

T, and a

T= 20 GeV.1In this transverse momentum range the jet finding is not fully efficient.2The effective value of

T.

P1=

??pv

T

0

?|ηv|

0

dσcuts

dpTbd|ηb|dpTbd|ηb| +

?∞

0

?∞

|ηv|

dσcuts

dpTbd|ηb|dpTbd|ηb|

?

/σcuts

tot, (1)

where the integration over the pT and |η| of the b parton is assumed and

σcuts

tot =

?∞

0

?∞

0

dσcuts

dpTbdpTb

dpTbdpTb, (2)

σcutsis the cross-section of the top related backgrounds after the application of the requirements described in Sec-

tion IIIA where the integration of the pseudorapidity of the partons is implied. The expression for the full-jet veto

survival probability at LO can be written as:

P2 =

?? ?pv

?∞

?∞

T

0

?|ηv|

?∞

? ?|ηv|

?pv

?∞

0

dσcuts

dpTbdpTbd|ηb|d|ηb|dpTbdpTbd|ηb|d|ηb|

?∞

?∞

+ 2

0

0

T

0

|ηv|

dσcuts

dpTbdpTbd|ηb|d|ηb|dpTbd|ηb|dpTbd|ηb|

dσcuts

dpTbdpTbd|ηb|d|ηb|dpTbd|ηb|dpTbd|ηb|

+

0|ηv|0|ηv|

?

/σcuts

tot. (3)

The calculation of P1and P2is performed after the application of requirements s1 and s2 (see Section IIIA). It is

important to note that the second term in Expression (1) and the last two terms in Expression (3) become significantly

smaller than the first terms for values of |ηv| > 3. These terms become negligible for |ηv| > 4.

1The transverse energy of a reconstructed jet does not in general correspond to an exact value of the parton pT. At LO, requiring no

parton with pT> 30 GeV has a similar efficiency as requiring that no jet with pv

MC.

2In the conditions of ATLAS jet finding becomes fully efficient for pT> 40 GeV.

T> 20 GeV is reconstructed after hadronization in the

Page 4

4

The survival probability relevant to the control sample used here is defined as:

PBtag

1

=

??pv

T

0

?|ηv|

0

dσBtag

dpTd|η|dpTd|η| +

?∞

0

?∞

|ηv|

dσBtag

dpTd|η|dpTd|η|

?

/σBtag

tot , (4)

where

described in Section IIIA, including the requirement that the event has at least one b-tagged parton (requirements

s1-s3 in Section IIIA). It is worth noting that the second term in Expression (4) is significantly smaller than the

first.

Similar survival probabilities can be defined also with real data. Indeed when these probabilities are much smaller

than one for low pT thresholds as we will see later in Table II, one can assume PExp

where ǫ0is an experimental efficiency of observing a low pT jet in the region of interest. Therefore

dσBtag

dpTd|η|and σBtag

tot

are the double differential and the total cross-section after the application of the requirements

2

≈ ǫ2

0P2and PBtag,Exp

1

≈ ǫ0PBtag

1

PExp

2

≈

?

PBtag,Exp

1

?2

P2

?

PBtag

1

?2. (5)

Here experimental uncertainties related to the hadronic energy scale and jet finding inefficiencies at near the transverse

momentum threshold would cancel out. In this case no statement is made with regards to the effective transverse

momentum at parton-level. This is not a concern since the goal of the extraction of the jvsp is not to compare the

data with a QCD calculation. The latter would require a detailed understanding of the experimental aspects just

mentioned and it is beyond the scope of the top extraction method proposed here. It is important to note that the

hadronic energy scale uncertainty still have a certain indirect impact on the stability of the results (see Tab. II).

pv

T[ GeV]

20.0

22.5

25.0

27.5

30.0

32.5

35.0

37.5

40.0

P1

0.07 0.005

0.08 0.007

0.10 0.010

0.11 0.013

0.13 0.018

0.15 0.025

0.17 0.032

0.20 0.040

0.23 0.051

P2

P2

0.89

0.89

0.94

0.95

0.93

0.90

0.94

0.99

1.01

1/P2 PBtag

1

PBtag

1

1.29

1.27

1.27

1.27

1.25

1.21

1.18

1.16

1.14

/P1 (PBtag

1

)2/P2

1.50

1.45

1.51

1.53

1.46

1.32

1.31

1.32

1.30

0.09

0.10

0.12

0.14

0.16

0.18

0.21

0.23

0.26

TABLE II: Results of jet veto survival probabilities for pp → W+W−bb processes (see Section II) at 7TeV center-of-mass

energy. Results are shown for different values of the transverse momentum for the jet veto.

pv

T[ GeV]

20.0

22.5

25.0

27.5

30.0

32.5

35.0

37.5

40.0

P1

0.06 0.003

0.07 0.004

0.08 0.007

0.10 0.010

0.12 0.014

0.14 0.019

0.16 0.026

0.18 0.034

0.21 0.042

P2

P2

1.05

1.11

1.03

0.97

1.01

1.01

0.99

0.99

1.03

1/P2 PBtag

1

PBtag

1

1.19

1.19

1.19

1.19

1.19

1.17

1.14

1.12

1.09

/P1 (PBtag

1

)2/P2

1.49

1.58

1.47

1.36

1.44

1.38

1.28

1.24

1.23

0.07

0.08

0.10

0.12

0.14

0.16

0.18

0.21

0.23

TABLE III: Same as Tab. II for tt production only.

The data-driven prediction will rely on the rate of top-related events observed in data:

NExp

Top(ℓℓ + Emiss

T

,0j) ≈ NExp

Top(ℓℓ + Emiss

T

)

?

PBtag,Exp

1

?2

P2

?

PBtag

1

?2, (6)

Page 5

5

pv

T[ GeV]

20.0

22.5

25.0

27.5

30.0

32.5

35.0

37.5

40.0

P1

0.07 0.005

0.09 0.007

0.10 0.010

0.12 0.013

0.14 0.018

0.15 0.022

0.18 0.030

0.20 0.038

0.22 0.047

P2

P2

1.12

1.04

1.01

1.07

1.05

1.08

1.04

1.04

1.04

1/P2 PBtag

1

PBtag

1

1.23

1.20

1.22

1.21

1.22

1.19

1.15

1.14

1.11

/P1 (PBtag

1

)2/P2

1.71

1.51

1.50

1.55

1.55

1.51

1.37

1.34

1.28

0.09

0.10

0.12

0.14

0.17

0.18

0.20

0.22

0.25

TABLE IV: Results of jet veto survival probabilities for pp → W+W−bb at 14TeV center-of-mass energy. Results are shown

for different values of the transverse momentum for the jet veto.

where NExp

application of a full-jet veto and the number of top background events observed in data without the application of

any requirements on the jet multiplicity in the final state, respectively. The rejection of processes not related to top

backgrounds for the measurement of NExp

T

) is implied. This is not considered here. However, one can

anticipate that the production of two isolated leptons and large Emiss

is dominated by top-related processes. In this master formula uncertainties related to the luminosity measurement

and the residual theoretical uncertainties of the total cross-section of top processes cancel out.

If we rewrite P2as NMC

T

,0j)/NMC

T

form:

Top(ℓℓ + Emiss

T

,0j) and NExp

Top(ℓℓ + Emiss

T

) are the number of predicted top background events after the

Top(ℓℓ + Emiss

T

at center-of-mass energies studied in this paper

Top(ℓℓ + Emiss

Top(ℓℓ + Emiss

), Expression (6) can be shown in a general data-driven

NExp

Top(ℓℓ + Emiss

T

,0j) ≈

NExp,control

Top

NMC,control

Top

NMC

Top(ℓℓ + Emiss

T

,0j), (7)

with

NExp/MC,control

Top

= NExp/MC

Top

(ℓℓ + Emiss

T

)

?

PBtag,Exp/MC

1

?2

. (8)

Namely the extracted top background in data in the signal region is nothing but the corresponding top background

contribution in MC scaled by the ratio of data over MC events in the control region. The advantage of our method

expressed in terms of the survival probabilities in (6) lies in a number of cancellation in systematic uncertainties

mentioned above.

Table II displays the results of jet veto survival probabilities for pp → W+W−bb processes (see Section II) at 7TeV

center-of-mass energy. Results are shown for different values of the transverse momentum for the jet veto. The second,

third columns show the values of P1and P2, respectively. The fourth column displays the ratio P2

does not necessarily lead to a useful observable, the ratio P2

1/P2helps us understand the potential angular correlations

between the b-partons. A deviation from unity is indicative of a correlation. This seems to be the case for low values

of pv

T= 30 GeV. This correlation appears due to kinematics, in events

where the products of the reaction go in the forward region (asymmetric collisions). The fifth column show the value

of PBtag

1

and PBtag

1

/P1, respectively. The latter quantifies the bias introduced by determining the jvsp from a part of

the phase-space where a b-parton is required. The bias seems moderate and constitutes 15% for pv

last column displays the final correction factor (PBtag

1

)2/P2that will be used in Expression (6).

It is relevant to note that the dependence of (PBtag

1

)2/P2 on the transverse momentum threshold is mild. The

results are stable within better then 15%. This effectively leads us to conclude that the effect of hadronic energy scale

uncertainties will have little impact on (PBtag

1

)2/P2.

Table III shows the same results as in Tab. II but for tt production only. The values of the jvsp in Tab. III are

significantly lower than for the full pp → W+W−bb treatment. This is expected. What is particularly relevant for

the robustness of the method is the fact that the ratio (PBtag

1

bias with respect to that observed for the full pp → W+W−bb processes.

Table IV shows the results for the pp → W+W−bb at 14TeV center-of-mass energy. The results for (PBtag

display a mild increase with respect to the results obtained for 7TeV.

Because the transverse momentum spectrum of partons is relatively steep it is relevant to check the impact of the

detector resolution. The energy of partons is smeared according to a single Gaussian distribution to mimic a resolution

with a stochastic term of 0.75/√E. The results for (PBtag

1

1/P2. Although P1

Tand the effect yields ≈ 5% correction for pv

T= 30 GeV. The

)2/P2changes little. The ratio P2

1/P2shows a smaller

1

)2/P2

)2/P2are stable within a few percent.

Page 6

6

As seen in Tab. II the kinematic bias introduced by requiring b-tagging in a restricted region of the phase-space is

not trivial and needs to be corrected in Expression (6). In order to evaluate the stability of the results against changes

in the transverse momentum of b-tagging results are obtained for pT= 25,35 GeV. These variations are significantly

larger than the energy scale uncertainties for low pT jets. The results for (PBtag

within 15%. In order to check the stability of the results for the range in |η| chosen for the b-tagging the range is

changed to |η| < 2. The results for (PBtag

range of the jet veto is changed to |η| < 4. The results for (PBtag

It is concluded that the results for (PBtag

1

)2/P2at pv

space discussed here. Variations in the QCD scales results in much smaller variations of the results for (PBtag

These variations are consistent with the statistics of the MC samples generated for the studies reported here.

The contamination from the non-resonant (or continuum) WW process in the b-tagged control sample is 0.2%. It

is important to evaluate the fraction of the non-resonant WW background that is subtracted due to the procedure

discussed here. For this purpose we perform parton-level studies with the LO Matrix Elements described in Section II.

The full jvsp is estimated to be P2 = 0.5. This implies that the effective cross-section of the non-resonant pp →

W+W−bb process that escapes corresponds to 0.25pb (before leptonic branching ratios and cuts). This constitutes

about 1% of the total non-resonant WW cross-section at LO (before leptonic branching ratios and cuts, as well).

1

)2/P2and pv

T= 30 GeV are stable

1

)2/P2and pv

T= 30 GeV are stable within 10%. Finally, the pseudorapidity

)2/P2and pv

T= 30 GeV are stable within 15% for the region of the phase-

1

T> 30 GeV show little change.

1

)2/P2.

C.Impact of QCD Higher Order Corrections, Hadronization and Pile-up

Because the results for (PBtag

of QCD higher order corrections and hadronization are checked here with a large sample of tt events produced with

MC@NLO. The jvsp defined in Section IIIB were obtained for a transverse momenta thresholds of pT = 20 GeV

(both for the jet veto and the b-tagging). In order to minimize the effect of final state radiation of gluons off the

b-parton it is required that the jvsp be calculated with jets that pass the requirement of ∆R > 1 with respect to the

tagging b-parton. In this setup (PBtag

1

)2/P2decreases by approximately 10%.

The effect of additional soft proton-proton collisions, or pile-up has been studied in the past for different scenar-

ios [16, 17, 19]. The impact of pile-up needs to be subtracted from the control sample in data before applying the

master formula.

Experimentally the value of (PBtag

1

)2/P2that needs to be implemented in Expression (6) does not need to come

from the parton-level study shown here. The ratio (PBtag

1

)2/P2may be affected by a number of experimental biased

that need to be described with a full-detector simulation, even though their impact is expected to be small. This

pertains to the transverse momentum dependence of b-tagging, pseudorapidity dependence of the hadronic energy

scale, the impact of pile-up, etc...

1

)2/P2vary little with respect to that obtained with pp → tt → W+W−bb the impact

IV.CONCLUSIONS AND PROSPECTS

Top processes are an important background for Higgs boson search with the H → WW⋆→ ℓℓ + Emiss

order to isolate the Higgs boson search a full-jet veto needs to be applied. In this paper a method for the extraction

of the jet veto survival probability of top backgrounds is proposed. The full-jet veto survival probability for top

backgrounds is expressed as the square of the veto survival probability in events with one b-tagged hadronic jet

multiplied by a Matrix Element correction, (PBtag

1

)2/P2. The values of (PBtag

complete set of Matrix Elements pp → W+W−bb to pp → tt → W+W−bb. Therefore, in practice this Matrix Element

correction can be obtained with a tt Monte Carlo.

The stability of (PBtag

1

)2/P2is about 15%. A rigorous evaluation of the impact of QCD higher order corrections

on (PBtag

1

)2/P2would require a complete calculation for the complete set of pp → W+W−bb diagrams. This exercise

will be possible in the near future since the first results of a NLO QCD calculation for the full set of pp → W+W−bb

are already available [25].

T

decay. In

1

)2/P2vary little when going from the

Acknowledgments

The authors would like to thank N. Kauer and Y. Pan for discussions. This work was supported in part by the

DoE Grant No. DE-FG02-95ER40896. The work of B.M. is also supported by awards from the Wisconsin Alumni

Page 7

7

Research Foundation and the Vilas Foundation.

[1] S. L. Glashow, Nucl. Phys. 22, 579 (1961).

[2] S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967).

[3] A. Salam, Proceedings to the Eighth Nobel Symposium, May 1968, ed: N. Svartholm (Wiley, 1968) 357.

[4] S. L. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. D2, 1285 (1970).

[5] F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964).

[6] P. W. Higgs, Phys. Lett. 12, 132 (1964).

[7] P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964).

[8] P. W. Higgs, Phys. Rev. 145, 1156 (1966).

[9] G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Phys. Rev. Lett. 13, 585 (1964).

[10] T. Kibble, Phys. Rev. 155, 1554 (1967).

[11] M. Dittmar and H. Dreiner, Phys. Rev. D55, 167 (1997).

[12] N. Kauer, T. Plehn, D. L. Rainwater and D. Zeppenfeld, Phys. Lett. B503, 113 (2001).

[13] B. Mellado, W. Quayle and S. L. Wu, Phys. Rev. D76, 093007 (2007).

[14] V. Barger, G. Bhattacharya, T. Han and B. A. Kniehl, Phys. Rev. D 43, 779 (1991).

[15] D. Rainwater and D. Zeppenfeld, Phys. Rev. D 60, 113004 (1999).

[16] A. Airapetian et al. (The ATLAS Collaboration), Detector and Physics Performance Technical Design Report, CERN-

LHCC/99-14/15 (1999).

[17] G. Aad et al. (The ATLAS Collaboration), Expected Performance of the ATLAS Experiment, CERN-OPEN-2008-020,

arXiv:0901.0512 (2009).

[18] G. Aad et al. (The ATLAS Collaboration), Tech. Rep. ATL-PHYS-PUB-2010-005, CERN, Geneva (2010).

[19] G. L. Bayatian et al. (The CMS Collaboration), CMS Physics Technical Design Report, V.2: Physics Performance,

CERN/LHCC 2006-021.

[20] N. Kauer and D. Zeppenfeld, Phys. Rev. D65, 014021 (2001).

[21] N. Kauer, Phys. Rev. D70, 014020 (2004).

[22] S. Frixione and B. R. Webber (2002).

[23] P. Nason, JHEP 11, 040 (2004).

[24] S. Frixione, P. Nason and C. Oleari, JHEP 11, 070 (2007).

[25] A. Denner, S. Dittmaier, S. Kallweit and S. Pozzorini, arXiv:1012.3975 (2010).

[26] J. Alwall et al., JHEP 09, 028 (2007).

[27] J. Pumplin et al., JHEP 0207 (2002) 012.