Double Parton Scattering in Associate Higgs Boson Production with Heavy Quarks at the LHC

doi:10.4236/jmp.2013.44A001

Paper Menu >>

Journal Menu >>

Journal of Modern Physics, 2013, 4, 1-5

http://dx.doi.org/10.4236/jmp.2013.44A001 Published Online April 2013 (http://www.scirp.org/journal/jmp)

Double Parton Scattering in Associate Higgs Boson

Production with Heavy Quarks at the LHC

Mohammad Yousif Hussein

Physics Department, College of Science, Bahrain University, Sakhir, Kingdom of Bahrain

Email: mhussein@sci.uob.bh

Received February 6, 2013; revised March 8, 2013; accepted March 20, 2013

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

Higgs boson production in association with heavy quarks is one of the most important discovery channels for Higgs

particles in the Standard Model and its super-symmetric extension at the LHC pp collider. We review the status of the

Higgs boson studies, with particular emphasis on the case bbh and tt production. We present results for the total

cross section at Large Hadron Collider (LHC) in both single and double parton scattering mechanism.

5.30.4 GeV

Keywords: Standard Model; Higgs Boson; Double Parton Scattering

1. Introduction

In the simplest version of the Standard Model (SM) of

particle physics, the breaking of the electroweak symme-

try introduces a single physical scalar particle, the Higgs

boson, which couples to both gauge boson and fermions.

Extensions of the Standard Model, like the Minimal Su-

persymmetric Standard (MSSM), introduce several scalar

and pseudoscalar Higgs boson.

Much progress has been made in the detection of a

Higgs boson, next-leading order corrections are now

known for most sub-processes [1-8], and knowledge of

parton distribution functions has improved as more deep

inelastic data become available and the range of possible

input parameter values decreased.

Recently, ATLAS [9] and CMS [10] collaborations

announced about the discovery of a new scalar particle at

the Large Hadron Collider (LHC), which is most likely

the Standard Model (SM) Higgs boson, with the mass

measured .

Although we need more data accumulation to conclude

it is truly the SM Higgs boson, these observations have

ignited a new trend of particle physics research.

After the discovery of the Higgs boson at the LHC, it

would be important to study various properties of it. In

particular, one would like to study the production of the

Higgs boson via all possible channels. One such category

of channels is the production of the Higgs boson in asso-

ciation with heavy quarks.

The associated production of a Higgs boson with a tt

air at the LHC, pptth, will play a very important

role in the Higgs boson mass range, both for discovery

and for precision measurements of the Higgs boson cou-

plings. This process will provide a direct measurement of

the top quark Yukawa coupling which could help to dis-

tinguish a SM Higgs boson from more complex Higgs

sector and shed light on the details of the generation of

fermions masses [11-17].

Although the associated production of a Higgs boson

with a pair of bb quarks has a small cross section in

the SM, but it can therefore be used to test the hypothesis

of enhanced bottom quark Yukawa coupling which is

common to many extensions of the SM, such as the

MSSM.

The coupling of the Higgs boson to bb pair is sup-

pressed in the Standard Model by the small factor, b

mv,





where 12

2 246





GeV.

In this context, we focus on the production of a Higgs

boson with a pair of top or bottom quark and anti-quark.

Our calculation corresponds to the inclusive cross section

for Higgs boson production in association with heavy

quarks, integrated over the momenta of t and

quarks.

When looking at extrapolation of the cross section at

high energies, one finds that the results are affected by

several uncertainties, as the knowledge of the parton

structure functions at very small

and the values of the

heavy quark mass and of the running coupling constant.

Although the expected inclusive cross section of

M. Y. HUSSEIN

production is hence still pretty uncertain at LHC energy,

all estimates point in the direction of rather large values,

as a consequence of the high parton luminosity. The

fairly large flux of partons makes it also plausible to ex-

pect a sizable rate of events, where two bb pair with

Higgs boson is produced contemporarily by different

partonic collisions in a given interaction. Although

at present stage all quantitative prediction for this much

more structured interaction process are unavoidably

pretty uncertain, the large cross sections foreseen at the

LHC is, in our opinion, a strong motivation to make an

attempt of giving a few quantitative indications on the

production rate of associated Higgs with heavy quark

pairs through multiparton interaction at the LHC, com-

paring with the rate to be expected by the more conven-

tional single parton scattering mechanism.

2. Double Parton Scattering Mechanism

The multiple parton scattering occurs when two or more

different pairs of parton scatter independently in the

same hadronic collision [8-23]. A schematic view of a

double parton scattering events in a p

p interaction is

shown in Figure 1.

With the only assumption of factorization of the two

hard parton processes A and B, the inclusive cross sec-

tion of a double parton-scattering in a hadronic collision

is expressed by:



, ;



 

,1 11

, 1122

,; ,

ˆddddd,

jlk l

mxx xx





xxxxxb





 









(1)

where 12ij

xb are the double parton distribution

function, depending on the fractional momenta 1

, 2

and the relative transverse distance b of the two parton

undergoing the hard processes A and B, the indices

and refer to the different parton species and



and

ˆA



are the partonic cross section. The factor 2m

for symmetry, specifically is for indistinguish-

able parton processes and

m



is for distinguishable



Figure 1. Diagram of a double parton scattering.

processes.

The double distributions 12ij

xb are the main

reason of interest in multiparton collisions. This distribu-

tion contains in fact all the information of probing the

hadron in two different points contemporarily through

the hard processes A and B.

The cross section for multiparton process is sizable

when the flux of partons is large, namely at small x.

Given the large flux one may hence expect that correla-

tions in momentum fraction will not be a major effect

and partons to be rather correlated in transverse space.

Neglecting the effect of parton correlations in x one

writes:









121 2

,; i

iji jj

xbxxF b (2)





where  the usual one body parton distribution is

function and







is a function normalized to one and

representing the pair density in transverse space. The

inclusive cross section hence simplifies to:

 

,ˆˆ,

Dij

kl ijkl

ijkl





 (3)





ˆij



where



and



ˆB



kl are the hadronic inclusive

cross section for the two partons labeled and un-

dergo the hard interaction labeled A and for two partons

and l to undergo the hard interaction labeled B;





iji j

klk l

bFb Fb





(4)

Are the geometrical coefficients with dimension an

inverse cross section and depending on various parton

processes. These coefficients are the experimentally ac-

cessible quantities carrying the information of the parton

Correlation in transverse momentum. The cross section

for multiple parton collisions has been further simplified

as:





ˆˆ

eff





1.7

14.51.7 mb







(5)

where all the information on the structure of the hadron

in transverse space is summarized in the value of the

scale factor. The experimental value measured by CDF

yields [19,20] 2.3eff . It is believed that

is largely independent of the center-of-mass energy of

the collision and on the nature of the partonic interactions.

The experimental evidence is not inconsistent with the

simplest hypothesis of neglecting correlations in mo-

mentum fractions.

3. Results for bbh Production

We evaluate the fully cross section for bbh production

by requiring that the transverse momentum of both final

state bottom and anti-bottom quarks be larger than 20

GeV. This corresponds to an experiment measuring the

M. Y. HUSSEIN 3

Higgs decay products along with two high pt bottom

quark jets. These cuts reduce the cross section by one or

two orders of magnitude, but also greatly reduce the

background and ensure that the Higgs boson was emitted

from a bottom quark and is therefore proportional to the

square of the b-quark Yakawa coupling.

-1

Single Scattering Mechanism

Double Scattering Mechanism

The cross section for leading order sub-process for

Higgs-boson production in association with bottom

quarks obtained using MRST parton distribution [21,22],

the packages MadGraph [24] and HELAS [25] and the

integration was performed by VEGAS [25] as function of

Higgs mass for the LHC with

σ (pb)

14 TeVs are dis-

played in Figure 2.

The cross-section for Higgs production in association

with bottom quarks are not large but may be useful if

high luminosity is available, since the Higgs boson can

be “tagged” by trigging on the bottom quarks.

40 60 80 100 120 140

(GeV)

Sizable rates of events where two bottom quarks asso-

ciate with Higgs boson are produced contemporarily at

the LHC, as a consequence of the large parton luminosity.

The corresponding integrated rate is evaluated by com-

bining the integrated cross section for Higgs boson and

ppH X

production at LHC energy.

If one uses the cross section for Higgs boson produc-

tion from , and the value for the scale fac-

tor



510 bbb





(the observed value is

1.7

1.7 mb





2.3

 one obtains the cross section for

a double parton collision producing a Higgs boson and a

14.5

eff



bb pair.

The large rate of bbpair at the LHC gives rise to a

relatively sizable production of Higgs boson associated

with bb quarks.

Figure 3 shows the double parton scattering to the

Higgs boson associated with bb quarks is very near in

value to single parton scattering mechanism, so that we

-1

-2

2.5

pp bbh













 2

σ (pb)

40 60 80 100 120 140 160

(GeV)

Figure 2. Leading order section (pb) for Higgs boson pro-

duction in association with bottom quarks at the LHC.

Figure 3. Total cross section for Higgs boson assocoated

with bottom quarks in the SM at LHC energy.

have to take this in our consideration in any kind of

search for Higgs discovery.

4. Results for tth Production

The possibility of discovering a Higgs boson in the range

115 - 130 GeV is becoming increasingly likely. The

Standard Model precision fits are consistent with a light

boson. Both the Fermilab and the CERN Large Hadron

Collider will focus on the search of light Higgs boson,

below the W-pair threshold, a Higgs boson mainly de-

cays hadronically into bb pairs.

The associated production of a Higgs with a pair of

tt quarks has drawn increasing attention. In spite of the

very small cross section, this production mode has an

extremely distinctive signature, and recent analyses have

shown that it can be within the reach of the LHC. This

process will provide a direct measurement of the top-

quark Yukawa coupling and will be instrumental in de-

termining ratios of Higgs couplings in a model inde-

pendent way.

Our calculation are found using MRST parton distri-

bution [24], the packages MadGraph [25] and HELAS

[26] and the integration was performed by VEGAS [27]

as function of Higgs mass for the LHC with 14TeVs

ppH X



are displayed in Figure 4.

If one uses the cross section for Higgs boson produc-

tion from ,



850 pbtt



 as a value for

the scale factor (the observed value is) one obtains the

cross section for a double parton collision producing a

Higgs boson and a tt pair.

The small rate of tt pair with Higgs boson at the

LHC gives rise to a relatively very small value for the

production of Higgs boson associated with tt quarks.

Figure 5 shows the double parton scattering to the

Higgs boson associated with tt quarks. Althought the

M. Y. HUSSEIN

800

600

400

200

tthpp

TeV





σ (fb)

100 120 140 160 180 200

(GeV)

Figure 4. Leading order section (pb) for Higgs boson pro-

duction in association with top quarks at the LHC.

4.0 × 10

-3

2.0 × 10

-3

σ (fb)

100 120 140 160 180

(GeV)

Double Scattering Mechanism

Figure 5. Total cross section for Higgs boson production

with top quarks in the double parton scatteri ng at the LHC.

rate of production cross section in double parton scatter-

ing mechanism is rather very small comparing with the

rate of production in single parton scattering, but still in

case of any change in the center of mass energy or lumi-

nosity of the collider may the effect be more clear in any

calculation for the search of Higgs boson.

5. Conclusions

In this work we have investigated bb production at

the LHC, which is important discovery channel for Higgs

boson in the SM and its extension in the MSSM at large

values of

bbh , where the bottom Yukawa coupling is

strongly enhanced.

Our calculations correspond to the cross section for

Higgs boson in association with two tagged b jets in sin-

gle and double parton scattering mechanism.

Although the double parton collision cross section is

not large, but it should be taken in consideration because

a sizable rate of events where pairs of quarks are pro-

duced at the LHC, as a consequence of the large parton

luminosity.

The technique used to calculate the cross section for

pp bbh is also applied to the study of the associated

production of tth . The cross section in double parton

scattering mechanism for tth case is very small and

will probably be beyond the LHC machine capabilities.

However, in the hadron collider environment, the large

QCD backgrounds may cause the observation impossible

for those events if Higgs bosons decay hadronically. In-

dividual channels with hadronic decays should be studied

on case by case.

REFERENCES

[1] T. Han and S. Willenbrock, “QCD Corrections to the

pp→WH and ZH cross Sections,” Physical Letters B, Vol.

273, 1991, p. 167.

[2] T. Han, G. Valencia and S. Willenbrock, “Structure Func-

tion Approach to Vector Boson Scattering in pp Scatter-

ing,” Physical Review Letters, Vol. 69, 1992, p. 3274.

[3] S. Dittmaier, M. Kramer and M. Spira, “Higgs Radiation

off Bottom Quarks at the Tevatron and the CERN LHC,”

Physical Review D, Vol. 70, 2004, Article ID: 0704010.

[4] S. Dawsen, C. B. Jakson, L. Rena and D. Wackeroth,

“Exclusive Higgs Boson Production with Bottom Quarks

at Hadron Colliders,” Physical Review D, 69, 2004, Arti-

cle ID: 074027.

[5] S. Dawson, “Radiative Corrections to Higgs Boson Pro-

duction,” Nuclear Physics B, Vol. 359, No. 2-3, 1991, pp.

283-300. doi:10.1016/0550-3213(91)90061-2

[6] A. Djouadi, M. Spira and P. M. Zerwas, “Production of

Higgs Bosons in Proton Colliders. QCD Corrections,”

Physical Letters B, Vol. 264, No. 3-4, 1991, pp. 440-446.

doi:10.1016/0370-2693(91)90375-Z

[7] D. Grandenz, M. Spira, and P. M. Zerwas, “QCD Correc-

tions to Higgs Boson Production at Proton Colliders,”

Physical Review Letters, 70, 1993, p. 1472.

[8] M. Spira, A. Djouadi, D. Grandenz and P. M. Zerwas,

“Production of Higgs Bosons in Proton Colliders. QCD

Corrections,” Physical Letters B, Vol. 264, No. 3-4, 1991,

pp. 440-446. doi:10.1016/0370-2693(91)90375-Z

[9] G. Aad, et al., “Observation of a New Particle in the

Search for the Standard Model Higgs Boson with the

ATLAS Detector at the LHC,” Physical Letters B, Vol.

716, No. 1, 2012, pp. 1-29.

doi:10.1016/j.physletb.2012.08.020

[10] S. Chatrchyan, et al., “Observation of a New Boson at a

Mass of 125 GeV with the CMS Experiment at the LHC,”

Physical Letters B, Vol. 716, No. 1, 2012, pp. 30-61.

doi:10.1016/j.physletb.2012.08.021

[11] S. Moch and M. Vogt, “Higher-Order Soft Corrections to

Lepton Pair and Higgs Boson Production,” Physical Let-

ters B, Vol. 631, 2005, p. 48.

M. Y. HUSSEIN

[12] E. Laenen and L. Mugnea, “Threshold Resummation for

Electroweak Annihilation from DIS Data,” Physical Let-

ters B, Vol. 632, 2005, p. 270.

[20] F. Halzen, P. Hoyer and W. J. Striling, “Evidence for

Multipe Parton Interaction from the Observation of

Multi-Muon Events in Drell-Yan Experiment,” Physical

Letters B, Vol. 188, 1987, pp. 375.

[13] T. Han, G. Valencia and S. Willenbrock, “Structure Func-

tion Approach to Vector Boson Scattering in pp Colli-

sion,” Physical Review Letters, Vol. 69, 1992, p. 3274.

[21] N. Paver and D. Treleani, “Multiquark Scattering and

Large-pT Jet Production in Hadronic Collisions,” Nuovo

Cimento A, Vol. 70, No. 3, 1982, pp. 215-228.

doi:10.1007/BF02814035

[14] E. Berger and J. Campbell, “Higgs Boson Production in

Weak Gusion at Next-to-Leading Order,” Physical Re-

view D, Vol. 70, 2004, Article ID: 073011. [22] M. Broun and D. Treleani, “The Double Parton Distribu-

tions in the Hard Pomeron Model,” European Journal of

Physic C, Vol. 18, No. 3, 2001, p. 511-522.

doi:10.1007/s100520100565

[15] J. Campell, R. Ellis, F. Maltoni and S. Willenbrock,

“Higgs Boson Production in Association with a Single

Bottom Quark,” Physical Review D, Vol. 67, 2003, article

ID: 095002. [23] F. Abe, et al., “Double Parton Scattering in p

̅p Collisions

at 1.8 TeV,” Physical Review D, Vol. 56, No. 7,

1997, pp. 3811-3832.

doi:10.1103/PhysRevD.56.3811

[16] S. Dawson, C. B. Jackson, L. Reina and D. Wackeroth,

“Higgs Boson Production with Bottom Quarks at Hadron

Colliders,” International Journal of Modern Physics A,

Vol. 20, No. 15, 2005, p. 3353.

doi:10.1142/S0217751X05026558

[24] A. D. Martin, R. G. Roberts, W. J. Stirling and R. S.

Thorne, “Parton Distribution at the LHC: W and Z Pro-

duction,” European Journal of Physic C, Vol. 14, 2000, p.

133. [17] D

awson, C. B. Jackson, L. H. Orr, L. Reine and D.

Wackeroth, “Theoretical Progress for the Associated

Production of a Higgs Boson with Heavy Quarks at Had-

ron Colliders,” European Journal of Physics C, Vol. 33,

2004, p. 5451.

[25] T. Stelzer and W. F. Long, “Automatic Generation of

Tree Level Helicity Amplitudes,” Computation Physical

Communications, Vol. 81, 1994, pp. 337.

[26] E. Murayama, I. Watanabe and K. Hagiwara, “HELAS:

Helicity Amplitude Subroutine for Feynman Diagram

Evaluations,” KEK Report, 1992, p. 91.

[18] J. Campbell, S. Dawson, S. Dittmaier, C. Jackson, M.

Kramer, F. Maltani, L. Reina, M. Spira, D. Wackeroth

and S. Willenbrock, “Higgs Boson Production in Asso-

ciation with Bottom Quarks,” hep-ph/0405302. [27] G. P. Lepage, “A New Algorithm for Adaptive Multi-

dimensional Integration,” Journal of Computation Phys-

ics, Vol. 27, No. 2, 1978, pp. 192-203.

doi:10.1016/0021-9991(78)90004-9

[19] C. Goebel, F. Halzen and D. H. Scott, “Double Drell-Yan

Annihilation in Hadron Collisions: Novel Tests of the

Constituents Picture,” Physical Review D, Vol. 22, 1980,

pp. 2789.