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arXiv:hep-ph/0610340v1 25 Oct 2006

Edinburgh 2006/33

MPP-2006-137

Higgs-Boson Production in Association with

Heavy Quarks

Wolfgang Hollik∗and Michael Rauch†

∗Max-Planck-Institut für Physik, München, Germany

†School of Physics, SUPA, University of Edinburgh, Scotland, UK

Abstract. Associated production of a Higgs boson with a heavy, i.e. top or bottom, quark–anti-

quark pair provideobservationchannels for Higgs bosons at the LHC which can be used to measure

the respectiveYukawacouplings.Forthe lightsupersymmetricHiggsbosonwe presentSUSY-QCD

corrections at the one-loop level, which constitute a significant contribution to the cross section.

INTRODUCTION

Higgs-boson Yukawa couplings to fermions are proportional to the fermion masses and

hence are very small for the light quarks, u, d, s and c. In contrast, the top-quark mass is

of thesame order as the Higgs vacuum expectation value, leading to a top-quark Yukawa

couplingcloseto 1. Thebottom-quarkmass also leads to a rather weak Yukawacoupling

in the Standard Model. In the Minimal Supersymmetric Standard Model (MSSM), the

coupling to the lighter CP-even neutral Higgs boson h0can be enhanced for large values

of tan(β), the ratio of the two vacuum expectation values. Such large Yukawa couplings

make Higgs-boson production in association with heavy quarks [1] a phenomenologi-

cally interesting process. At O?α2

quark lines; the cross section is thus sensitive to the Yukawa coupling and can be used

to measure the respective Yukawa coupling. A precise determination requires to include

at least the next-order QCD corrections. Here we present for the case of MSSM Higgs

bosons the results from a calculation of the SUSY-QCD corrections, supplementing the

standard QCD corrections by the loop contributions with virtual gluinos and squarks.

sα?, the Higgs boson is emitted off one of the heavy-

BOTTOM QUARKS

The production of a Higgs boson in association with a bottom quark–anti-quark pair

was intensively studied in the literature [2, 3]. The analysis was soon extended [4, 5]

to include the lightest MSSM-Higgs boson h0. The diagram types are exactly the same

as in the Standard Model case; only the bottom-quark–Higgs coupling is changed to

its supersymmetric counterpart. The standard QCD corrections [6] to this process are

already known and reduce the dependence of the cross section on the factorization

and renormalization scales. The final-state bottom quarks are required to be explicitly

observed in the detector via b-tagging, in contrast to inclusive processes [7] without

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b-tagging. Therefore, a transverse-momentum cut on the bottom-quark jets, typically

pT≥ 20 GeV, is applied. The additional 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 Yukawa coupling.

Here we concentrate on the SUSY-QCD corrections with squarks and gluinos in the

loops. Part of these corrections were already calculated in ref. [8]. There an effective

b¯bh0-coupling was used which includes the one-loop vertex corrections, but no box-type

or pentagon diagrams were added in their analysis. We have performed a full one-loop

calculation of the SUSY-QCD corrections.

In certain regions of the MSSM parameter space a large contribution to the SUSY-

QCD corrections originates from the effective coupling of the bottom quark to the sec-

ond Higgs doublet. This changes the relation between bottom-quark mass and Yukawa

coupling and the additional contribution is commonly referred to as ∆bin the litera-

ture [9]. It is proportional to tan(β) and represents for large values of tan(β) the dom-

inant supersymmetric correction. If the ∆b-contribution is compared with full one-loop

results it is necessary to include it only to one-loop order as well and not use any re-

summed version, resulting in the replacement

mb→ mb(1−∆b)

,

(1)

which has been used when calculating ∆b-corrected tree-level cross sections.

In order to assess the relative differences between cross sections the following quan-

tities have been defined. The relative one-loop correction is given as

∆1=σ1−σ0

σ0

,

(2)

where σ0denotes the tree-level cross section and σ1the one-loop one including SUSY-

QCD corrections. Additionally,a ∆b-corrected tree-level cross section σ∆was calculated

by using the replacement of eq. (1) and treating the ∆bterm as a one-loop contribution.

Additionally, the contribution to the vertex from the term proportional to the second

mixing angle in the MSSM-Higgs sector, α, was included in σ∆according to ref. [4, 9,

10]. The relative correction using only these contributions is defined as

∆˜0=σ∆−σ0

σ0

.

(3)

The Feynman diagrams were generated using FeynArts [11], the matrix elements

calculated by FormCalc [12] and the loop integrals numerically evaluated by Loop-

Tools [13]. The convolution with the parton distribution functions was performed with

HadCalc [14] using the PDF set of ref. [15].

The left-hand side of Table 1 contains the individual contributions from the various

partonic processes to the hadronic process pp → b¯bh0and their sum, for the MSSM ref-

erence point SPS1a′[16]. The gluon-fusion process clearly dominates the total hadronic

cross section. This is because for the quark–anti-quark annihilation diagrams only an s-

channel topology exists, which is propagator-suppressed. For the gluon-fusion diagrams

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TABLE 1.

Process

d¯d → b¯bh0

u¯ u → b¯bh0

s¯ s → b¯bh0

c¯ c → b¯bh0

gg → b¯bh0

pp → b¯bh0

Hadronic cross sections for b¯bh0and t¯ th0production at the parameter point SPS1a′.

σ0[fb]

σ1[fb]

∆1[%]

∆˜0[%]

0.1070.104

−2.48

−1.95

0.1680.164

−2.56

−1.95

0.0280.028

−2.26

−1.95

0.0130.012

−2.20

−1.95

35.64733.734

−5.37

−1.95

Process

d¯d → t¯ th0

u¯ u →t¯ th0

s¯ s → t¯ th0

c¯ c → t¯ th0

gg →t¯ th0

pp → t¯ th0

σ0[fb]

42.7

71.9

σ1[fb]

37.6

63.4

∆1[%]

−11.77

−11.81

−11.58

−11.53

−3.30

7.5

2.8

6.6

2.5

273.7 264.7

35.96334.042

−5.34

−1.95 399.0374.8

−5.96

there is an additional t-channel diagram which does not suffer from such a suppression.

Additionally one can see that the ∆b-corrected tree-level cross section accounts only for

less than half of the total SUSY-QCD corrections for this parameter point, and therefore

a full calculation is necessary to determine the size of the additional contribution. The

details of this additional contribution will be discussed in a future publication [17].

TOP QUARKS

The production of a Higgs boson in association with a top quark–anti-quark pair [18]

proceeds in the same way as the one with a bottom quark–anti-quark pair and the same

Feynman diagrams appear, where the bottom-quark line is replaced by a top-quark line.

The standard QCD corrections to this process are also available in the literature [19].

A calculation of the SUSY-QCD corrections was performed recently in ref. [20]. As

the figures of this article include both standard and SUSY-QCD contributions a direct

comparison of the numerical results is difficult. The principal behavior when varying

MSSM parameters agrees. Our calculation was performed using the same tools as

mentioned beforehand in the bottom-quark case. No cuts were applied to the final state.

On the right-hand side of Table 1 the results for the MSSM parameter point SPS1a′

are presented. In this case the gluon-fusion contribution is still the dominant one, but

also the quark–anti-quark–annihilation subprocesses reach a significant size and cannot

be neglected any more. This is because to produce the final state a higher center-of-mass

energy than for bottom quarks is needed. The rapid decrease of the gluon density in

the proton with growing momentum fraction x partly cancels the effect of the s-channel

propagator suppression in quark–anti-quark annihilation. We find that the total size of

the SUSY-QCD corrections is of the order of several percent.

SUMMARY

Higgs-boson production in association with heavy, i.e. bottom or top, quarks is an

important way to measure the respective Yukawa couplings. In the MSSM besides

the standard QCD corrections also SUSY-QCD corrections appear. They modify the

total cross section significantly and should be taken into account to extract the Yukawa

coupling precisely from future experimental data.

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ACKNOWLEDGMENTS

We would like to thank T Plehn for careful reading of the manuscript. The work of MR

was supported by the Scottish Universities Physics Alliance (SUPA).

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