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arXiv:hep-ph/0308215v4 4 Dec 2003

SHEP-03-07

TSL/ISV-2003-0271

August 2003

Pair production of charged Higgs bosons in association

with bottom quark pairs at the Large Hadron Collider

S. Moretti1

School of Physics & Astronomy, University of Southampton,

Highfield, Southampton SO17 1BJ, UK

J. Rathsman2

High Energy Physics, Uppsala University, Box 535, 751 21 Uppsala, Sweden

Abstract

We study the process gg → b¯bH+H−at large tanβ, where it represents the dominant

production mode of charged Higgs boson pairs in a Type II 2-Higgs Doublet Model,

including the Minimal Supersymmetric Standard Model. The ability to select this

signal would in principle enable the measurements of some triple-Higgs couplings,

which in turn would help understanding the structure of the extended Higgs sector.

We outline a selection procedure that should aid in disentangling the Higgs signal

from the main irreducible background. This exploits a signature made up by ‘four b-

quark jets, two light-quark jets, a τ-lepton and missing energy’. While, for tanβ>

∼30

and over a significant MH± range above the top mass, a small signal emerges already

at the Large Hadron Collider after 100 fb−1, ten times as much luminosity would

be needed to perform accurate measurements of Higgs parameters in the above final

state, rendering this channel a primary candidate to benefit from the so-called ‘Super’

Large Hadron Collider option, for which a tenfold increase in instantaneous luminosity

is currently being considered.

Keywords:

Beyond Standard Model, Two Higgs Doublet Models, Supersymmetry, Charged Higgs Bosons.

1stefano@hep.phys.soton.ac.uk

2johan.rathsman@tsl.uu.se

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1 Introduction

Charged Higgs bosons appear in the particle spectrum of a general 2-Higgs Doublet Model

(2HDM). We are concerned here with the case of a Type II 2HDM [1], possibly in presence of

minimal Supersymmetry (SUSY), the combination of the two yielding the so-called Minimal

Supersymmetric Standard Model (MSSM). To stay with the Higgs sector of the extended

model, unless two or more neutral Higgs states3are detected at the Large Hadron Collider

(LHC), only the discovery of a spinless charged Higgs state would unquestionably confirm

the existence of new physics beyond the Standard Model (SM), since such a field has no

SM counterpart. In the MSSM, e.g., if MH±,MA0,MH0 ≫ Mh0 and tanβ is below 10 or so,

the only available Higgs state (h0) is indistinguishable from the one of the SM: this is the

so-called ‘decoupling scenario’4.

Not surprisingly then, a lot of effort has been put lately, by theorists and experimen-

talists alike, in clarifying the Higgs discovery potential of the LHC in the charged Higgs

sector [2]. (This is particularly true within the MSSM scenario, where one could also ex-

ploit interactions between the Higgs and sparticle sectors [3] in order to extend the reach of

charged Higgs bosons at the LHC, beyond the standard channels.) Results are now rather

encouraging, as charged Higgs bosons could indeed provide the key to unveil the nature of

EWSB over a large area in MH± and tanβ, as they may well be the next available Higgs

boson states, other than the h0, provided tanβ is rather large (above 10 or so). Once the

H±and h0Higgs bosons will have been detected, the next step would be to determine

their interactions with SM particles, among themselves and also with the other two neu-

tral Higgs states, H0and A0. While the measurement of the former would have little to

teach us as whether one is in presence of a general Type II 2HDM or indeed the MSSM,

constraints on the latter two would certainly help to clarify the situation in this respect. In

fact, triple-Higgs vertices enter directly the functional form of the extended Higgs potential

and, once folded within a suitable Higgs production process, may lead to the measurement

of fundamental terms of the extended model Lagrangian. As the H±states have a finite

3Of the initial eight degrees of freedom pertaining to a complex Higgs doublet, only five survive as real

particles upon Electro-Weak Symmetry Breaking (EWSB), labeled as h0,H0, A0(the first two are CP-

even or ‘scalars’ whereas the third is CP-odd or ‘pseudoscalar’) and H±, as three degrees of freedom are

absorbed into the definition of the longitudinal polarisation for the gauge bosons Z0and W±, upon their

mass generation after EWSB.

4One of the Higgs masses, usually MA0 or MH±, and the ratio of the Vacuum Expectation Values (VEVs)

of the up-type and down-type Higgs doublets (denoted by tanβ) are the two parameters that uniquely define

the MSSM Higgs sector at tree-level.

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Electro-Magnetic (EM) charge, the first Lagrangian term of relevance would be the one

involving two such states and a neutral Higgs boson: chiefly, the vertices H+H−Φ0, where

Φ0= h0and H0.5This requires the investigation of hard scattering processes with two

charged Higgs bosons in the final state, as their direct couplings to valence quarks in the

proton would be very small, hence inhibiting processes like: e.g., q¯ q′→ H±∗→ H±Φ0.

2 Hadroproduction of charged Higgs boson pairs

A summary of all possible production modes of charged Higgs boson pairs at the LHC

in the MSSM can be found in Ref. [4]. Three channels dominate H+H−phenomenology

at the LHC: (i) q¯ q → H+H−(via intermediate γ∗/Z0∗production but also via Higgs-

strahlung off incoming b¯b pairs) [5]; (ii) gg → H+H−(primarily via a loop of top and

bottom (s)quarks) [6]; (iii) qq → qqH+H−(via vector boson fusion) [4]. Corresponding

cross sections are found in Fig. 2 of Ref. [4]. For all phenomenologically relevant tanβ

values it is essentially the first process which dominates. One important aspect should be

noted here though, concerning the simulation of the b¯b component of the q¯ q → H+H−

process, which can become the dominant contribution to the cross section of process (i) at

very large tanβ values. In fact, the use of a ‘phenomenological’ b-quark parton density,

as available in most Parton Distribution Function (PDF) sets currently on the market,

requires crude approximations of the partonic kinematics, which result in a mis-estimation

of the corresponding contribution to the total production cross section. (The problem is

well known already from the study of the leading production processes of charged Higgs

bosons at the LHC, namely,¯bg →¯tH+and gg → b¯tH+: see, e.g., [8, 10].) In practice, the

b-(anti)quark in the initial state comes from a gluon in the proton beam splitting into a

collinear b¯b-pair, resulting in large factors of ∼ αSlog(µF/mb), where µFis the factorisation

scale. These terms are then re-summed to all orders,

?

nαn

Slogn(µF/mb), in evaluating

the phenomenological b-quark PDF. In contrast, in using a gluon density while computing

the ‘twin’ process (iv) gg → b¯bH+H−(see Fig. 1 for the associated Feynman graphs), one

basically only includes the first terms (n = 1) of the corresponding two series, when the b

and¯b in the final state are produced collinearly to the incoming gluon directions. It turns

out that, for µF≫ mb, as it is the case here if one uses the standard choice of factorisation

scale µF>

∼2MH±, the re-summed terms are large and over-compensate the contribution

5We are here only considering CP-conserving extensions of the SM Higgs sector such that there is no

“H+H−A0-vertex”.

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of the large transverse momentum region available in the gluon-induced case. In the end,

differences between the two cross sections as large as one order of magnitude are found, well

in line with the findings of Refs. [8] and [10], if one considers that two g → b¯b splittings are

involved here.

One way to reconcile the large differences in the cross section for the two processes,

gg → b¯bH+H−and b¯b → H+H−, is to use a significantly lower factorisation scale, as argued

in [11, 12, 13, 14] for similar processes. Following the suggestion in part A.1. of [15], we look

at the transverse momentum distribution of the b-quarks in the process gg → b¯bH+H−, as

shown in Fig. 2, to get an indication of the most suitable factorisation scale for b¯b → H+H−.

From the figure we see that a proper choice for the latter, when MH± = 215 GeV, is of the

order µF = 0.1√ˆ s ≃ 40 GeV (at this point the distribution reaches about half of its

“plateau” value6) rather than, e.g., µF =

√ˆ s. Using such a lower scale we do get a much

better agreement between the leading order (LO) cross sections for the two processes, as

shown in Tab. 1 in the case of the MSSM specified below (MA0 = 200 GeV and tanβ = 30)

if the renormalisation scale (µR) is also changed accordingly. However, one should also

bear in mind that both processes are subject to possibly large QCD corrections and that

the choice of (factorisation and/or renormalisation) scales that minimises the differences

between the two descriptions in higher orders of H+H−production may alternatively be

viewed as the most suitable one. Or else, one may arguably choose a scale that minimises

the size of the higher order corrections themselves in either process independently of the

other. All such additional values may eventually turn out to be different from the one

extracted from Tab. 1. Such exercises in higher orders cannot unfortunately be performed

in the present context, as next-to-leading order (NLO) corrections to the two processes of

interest are unavailable. Yet, some guidance may be afforded again by the study of the single

charged Higgs production modes already referred to. In fact, NLO corrections to¯bg →¯tH+

were first computed in Ref. [7] and then later confirmed in [11]. Following Ref. [11], it is

clear that a choice for the renormalisation scale µRas low as the one recommended for the

factorisation one µF is not sustainable for¯bg → tH+at NLO, no matter the choice for

the latter: see Fig. 5 of [11]. Besides, if one fixes, e.g., µR= (mt+ MH±)/2 but varies

µF, the minimal difference between the NLO and the LO results for¯bg → tH+is found at

large µF, at values around or even larger than mt+ MH±(again, see Fig. 5 of Ref. [11]).

Be the most suitable combination of scales as it may, we take here a pragmatical attitude

6This number is not too dissimilar from the one recommended in [13] on the basis of the same argument

applied to the single H±production mode gg → b¯tH+, as M/4, where M is the ‘threshold mass’ mt+MH±.

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Table 1: Cross sections for gg → b¯bH+H−and b¯b → H+H−as functions of the factorisation

(µF) and renormalisation (µR) scales (at leading order the b¯b → H+H−cross section does

not depend on µR) in the MSSM specified below (MA0 = 200 GeV and tanβ = 30).

µF

√ˆ s

?mT

?mT

√ˆ s

0.1√ˆ s

µR

√ˆ s

√ˆ s

?mT

σ(gg → b¯bH+H−) [fb]

1.4

σ(b¯b → H+H−) [fb]

b?†

b?†

2.3

b?†

8.2

7.5

4.4

†Here, the exact definition is: ?mT

b? =

?

m2

b+ ((pT

b)2+ (pT

¯b)2)/2.

and use the standard setup µF = µR=

conservative choice in terms of the overall normalisation for gg → b¯bH+H−(Tab. 1) – as

it becomes minimal – and keeping in mind that its cross section can be up to a factor ∼ 5

larger depending on the choice of factorisation and renormalisation scales.

√ˆ s throughout, as this corresponds to the most

Under any circumstances, a clear message that emerged from NLO computations of

¯bg → tH+with respect to the LO ones of gg → b¯tH+is that the former (duly incorporating

a running NLO b-quark mass in the Yukawa coupling to the charged Higgs boson) agree

better with the latter if these use the pole b-quark mass instead, see Fig. 4 of Ref. [11]. By

analogy, in the reminder of our paper, we will make the same assumption (of a pole b-quark

mass entering the b¯tH+vertex) in our gg → b¯bH+H−process at LO. Finally, while a well

defined procedure exists in order to compute both inclusive and exclusive cross sections

when combining the b¯b- and gg-initiated processes, through the subtraction of the common

logarithm terms [8] and/or by a cut in phase space [9], it should be noticed that process (iv)

is the only contributor when one exploits the tagging of both the two b-quark jets produced

in association with the charged Higgs boson pair.

It is precisely the intention of this note that of pursuing a similar strategy in order

to extract a possible b¯bH+H−signal, as it has already been shown the beneficial effects of

triggering on the ‘spectator’ b-jet in the gg → t¯bH−case, in order to improve on the discovery

reach of charged Higgs bosons at the LHC [16]. Furthermore, if vertices of the type H+H−Φ0

are to be studied experimentally, one should appreciate the importance of the gg → b¯bΦ0

subprocess (from which two charged Higgs bosons would stem out of the above triple-Higgs

coupling: see diagrams 4,8,14,19,23,29,34 and 38 in Fig. 1) by recalling that the latter

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