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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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reaction is the dominant production mode of neutral Higgs scalars (chiefly, the H0state)

at tanβ values above 7 or so, for any neutral Higgs mass of phenomenological interest [17],

this justifying our choice of privileging here the gg → b¯bH+H−channel. Finally, whereas

the already recalled MSSM relation MH± ≃ MA0 ≃ MH0 ≫ Mh0 clearly prevents the

appearance of a H0→ H+H−resonance in the diagrams proceeding via intermediate states

of the form gg → b¯bH0, this is no longer true in a general 2HDM, wherein one may well

have MH0 > 2MH±, with the consequent relative enhancement of the mentioned subset of

diagrams with respect to all others appearing in Fig. 1.

We will attempt the signal selection for the case of rather heavy charged Higgs bosons,

with masses above that of the top quark. The case for the existence of such massive Higgs

states has in fact become phenomenologically pressing, since rumours of a possible evidence

of light charged Higgs bosons being produced at LEP2 [18] have faded away. Instead, one

is now left from LEP2 with a model independent limit on MH±, of order MW±. Within

the MSSM, the current lower bound on a light Higgs boson state, of approximately 110

GeV [19], can be converted at two-loops into a minimal value for the charged Higgs boson

mass, of order 130–140 GeV, for tanβ ≃ 3–47. This bound grows rapidly stronger as tanβ

is decreased while tapering very gradually as tanβ is increased (staying in the 110–125GeV

interval for tanβ>

∼7). Besides, in the mass interval MH± < mt, charged Higgs bosons could

well be found at Tevatron (Run 2) [21], which has already begun data taking at√sp¯ p= 2

TeV at FNAL, by exploiting their production in top decays, t → bH+, and the tau-neutrino

detection mode, H−→ τ¯ ντ. In contrast, if MH±>

Higgs boson), one will necessarily have to wait for the advent of the LHC,√spp= 14 TeV,

at CERN. As hinted at in the beginning, we also make the assumption in our study that

∼mt(our definition of a ‘heavy’ charged

the charged Higgs boson mass is already known, e.g., from studies of the leading production

and decay channels, gg → t¯bH−and H−→ τ−¯ ντ or b¯t, during the first years of running of

the CERN hadron machine.

Under the above parameter assumptions, i.e., large tanβ (>

ues (>

∼mt), a sensible choice of decay channels [22] for our pair of charged Higgs bosons

would be to require one to decay via the leading mode, i.e., H+→ t¯b (with the t-quark

further decaying hadronically, so to allow for the kinematic reconstruction of the charged

Higgs boson resonance in a four-jet system) and the other via H−→ τ−¯ ντ (whose rate

increases with tanβ and that yields a somewhat cleaner trigger in the LHC environment,

∼10) and large MH± val-

7Recall that the tree-level relation between the masses of the charged and pseudoscalar Higgs boson,

M2

W±, is almost invariably quite insensitive to higher order corrections [20].

H±= M2

A0+ M2

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independently of whether the τ-lepton decays leptonically or hadronically, as opposed to

the above multi-jet and high hadron-multiplicity signature). As such decays would induce

an intermediate signal state made up by b¯bt¯bτ−¯ ντand since we will assume tagging all four

b’s, it is clear that the dominant irreducible background would be b¯bt¯t production followed

by the decay¯t →¯bW−→¯bτ−¯ ντ.

3 Calculation

The hard subprocess describing our signal is then

gg → b¯bH+H−, (1)

whereas for the main irreducible background we have to deal with

gg → b¯bt¯t. (2)

(We neglect here the computation of the quark-antiquark initiated components of both signal

and background, i.e., q¯ q → b¯bH+H−and q¯ q → b¯bt¯t, respectively, as they are negligible at

the LHC, in comparison to the gluon-gluon induced modes.) The matrix elements for (1)–(2)

have been calculated by using the HELAS [23] subroutines and MadGraph [24]. All unstable

particles entering the two processes (t,H±and W±) were generated not only off-shell (i.e.,

with their natural widths) but also in Narrow Width Approximation (NWA) for comparison.

For the MSSM and 2HDM Higgs bosons, the program HDECAY [25] has been exploited to

generate the decays rates eventually used in the Monte Carlo (MC) simulations. For the

MSSM, we have assumed the following set up for the relevant SUSY input parameters:

µ = 0, Aℓ = Au = Ad = 0 (with ℓ = e,µ,τ and u/d referring to u/d-type quarks) and

MSUSY= 1 TeV, the latter implying a sufficiently heavy scale for all sparticle masses, so

that no H±→ SUSY decay can take place8.

As a 2HDM configuration, we have basically maintained the previous setup in the rele-

vant input parameters of HDECAY, with the most important difference being the assumption

of a different relation between the input MA0 value and the derived MH0 one, by assuming

a linear relation between the H0and H±masses, i.e., MH0 = x H±, with x being a num-

ber larger than 2, while maintaining the MSSM relations among the H±and A0masses,

8The only possible exception in this mass hierarchy would be the Lightest Supersymmetric Particle

(LSP), whose mass may well be smaller than the MH± values that we will be considering, a state in which

however a charged Higgs boson cannot decay to, as R-parity and EM charge conservation would require the

presence of an additional heavy chargino.

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thereby allowing for the already intimated onset of H0→ H+H−resonant decays in dia-

grams 4,8,14,19,23,29,34 and 38 of Fig. 1. As already remarked upon, this is a crucial

phenomenological difference with respect to the MSSM, wherein such a decay threshold is

never reached over the unexcluded region of parameter space. Another important difference,

in a more general 2HDM, is the value of the triple Higgs coupling gH0H+H− which can be

much larger than what is the case in the MSSM.

Before giving the details of the 2HDM setup we are using let us recall the most general

CP-conserving 2HDM scalar potential which is symmetric under Φ1→ −Φ1 up to softly

breaking dimension-2 terms (thereby allowing for loop-induced flavour changing neutral

currents) [1],

V (Φ1,Φ2) = λ1(Φ†

1Φ1− v2

?

?

?

1)2+ λ2(Φ†

2Φ2− v2

2Φ2− v2

1Φ2)(Φ†

2)2

+λ3

(Φ†

1Φ1− v2

(Φ†

1) + (Φ†

2)

?2

2Φ1)

+λ4

1Φ1)(Φ†

2Φ2) − (Φ†

1Φ2) − v1v2

?

+λ5

Re(Φ†

?2+ λ6

?

Im(Φ†

1Φ2)

?2

(3)

where v2

1+v2

2= v2= 2M2

W/g2≃ (174 GeV)2. In general, the potential is thus parameterised

by seven parameters (the λiand tanβ = v2/v1) whereas in the MSSM only two of them are

independent. In the following we will replace five of the λiwith the masses of the Higgs

bosons (Mh0,MH0,MA0,MH±) and the mixing angle α of the CP-even Higgs bosons.

From the scalar potential the different three- and four-Higgs couplings can be obtained.

(See [26, 27] for a complete compilation of couplings in a general CP-conserving 2HDM.)

Using the Higgs masses and α as parameters together with λ3the gH0H+H− coupling takes

a particularly simple form (see for example [28])

gH0H+H−

= −i

g

MW

?

cos(β − α)

1

2sin2β[sin2α + 2sin(α − β)cos(α + β)](M2

?

M2

H± −M2

H0

2

?

+sin(α + β)

sin2β

?1

2(M2

H0 + M2

h0)+

+4λ3v2−

H0 − M2

h0)

??

. (4)

For the other three- and four-Higgs couplings we refer to [26, 27].

In the 2HDM that we will adopt below we will start from the MSSM parameter values

for MH0,MA0,Mh0,MH±,tanβ,α,(λ5− λ6)/2 using MA0 and tanβ as input. As already

mentioned we then change from MMSSM

H0

to M2HDM

1.7MH± while keeping the other Higgs boson masses and tanβ fixed. The choice Mh0 =

H0

= 2.2MH± and in addition Mh0 =

1.7MH± has been found to be favourable in order to get a larger gH0H+H− coupling and at

the same time avoid negative interference between H0and h0resonances. The remaining

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Table 2: Examples of values of the parameters in the Higgs potential used for different

values of MA0 together with the corresponding values of α and gH0H+H−.

MA0

λ1

λ2

λ3

λ4

λ5

λ6

αgH0H+H−

[GeV]

[GeV]

150−4.81618

−3.90929

1.69717

−4.02795

−2.75838

3.17924

4.816180.941863 4.131140.745433 0.5064−1235

−563

76

200

3.909291.52164 7.163751.32521 0.2686

250

−1.54105

−3.79044

2.2670710.97832.07065 0.0363

300

5.16558 7.63614 3.17816 9.195372.98173-1.539−1078

two parameters, α and (λ5− λ6)/2, are then determined by randomly picking one million

(α,(λ5− λ6)/2)-points, in the ranges [−π/2,π/2] and [−4π,4π] respectively, and keeping

the one which gives the largest effective coupling, gH0H+H− cosα, thereby also taking into

account the H0b¯b-coupling. In order to accept a point we also check that the following

conditions are fulfilled: the potential is bounded from below, the λi fulfill the unitarity

constraints [29], the contribution to ∆ρ < 10−3(although with the above setup for the

Higgs masses we are more or less guaranteed not to violate any experimental bounds on the

ρ-parameter [1]), and the combined partial width for the three H0→ h0h0,A0A0,H+H−

decays is smaller than MH0/2. (We have checked that the partial widths of the H0→

h0h0h0,h0A0A0,h0H+H−decay channels are negligible.)

Some examples of the actual values of the λiwe use in this study are given in Tab. 29

together with the corresponding values of α and gH0H+H−. From the table one sees that

the effective coupling gH0H+H− cosα decreases quite rapidly as MA0 increases, giving a

correspondingly smaller cross-section.(This will be shown in more detail below.) However,

it should be kept in mind that the 2HDM setup we are using is not the most general one

based on the scalar potential (3) and that there may be other parts of the parameter space

which we have not scanned that give a larger cross section. At the same time it should be

said that we have already tried different relations between the Higgs masses other than the

ones given above, yet we have not made any further detailed investigations.

To get an explicit example of the large differences between the more general 2HDM we

are considering and the MSSM, we compare the two using MA0 = 200 GeV and tanβ = 30

9The selection procedure outlined above did not lead to any acceptable solution for MA0>

∼310 GeV.

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as input values, as we will do below. In this case we get g2HDM

instead of the MSSM value, gMSSM

being much larger than αMSSM= −0.05774 the difference in effective coupling gH0H+H− cosα

is more than a factor hundred and as we will see below it has a large impact on the magnitude

of the cross section. (The H0widths will of course be different too in the MSSM and 2HDM

H0H+H− = −563 GeV in the 2HDM

H0H+H− = −1.8 GeV. With the value of α2HDM= 0.26859 not

just described: their effects have been included in the numerical analysis.)

As intimated already in Sect. 2, a non-running b-quark mass was adopted for both

the kinematics and the Yukawa couplings: mb = 4.25 GeV. For the top parameters, we

have taken mt = 175 GeV with Γt computed according to the model used (in the limit

MH± ≫ mt, we have Γt= 1.56 GeV in both the 2HDM and MSSM scenarios considered

here). EW parameters were as follows: αEM= 1/128, sin2θW = 0.232, with MZ0 = 91.19

GeV (ΓZ0 = 2.50 GeV) and MW± = MZ0 cosθW (ΓW± = 2.08 GeV). For the τ-lepton mass

we used mτ = 1.78 GeV, whereas all the other leptons and quarks were assumed to be

massless.

The integrations over the multi-body final states have been performed numerically with

the aid of VEGAS [30], Metropolis [31] and RAMBO [32], for checking purposes. Finite

calorimeter resolution has been emulated through a Gaussian smearing in transverse mo-

mentum, pT, with (σ(pT)/pT)2= (0.60/

pT)2+ (0.04)2for all jets and (σ(pT)/pT)2=

?

was reconstructed from the vector sum of the visible momenta after resolution smearing.

?

(0.12/

pT)2+ (0.01)2for leptons. The corresponding missing transverse momentum, pT

miss,

Furthermore, we have identified jets with the partons from which they originate and applied

all cuts directly to the latter, since parton shower and hadronisation were not included in

our study. The only exception is the τ-lepton decay which has been taken into account

using the Pythia [33] MC event generator.

As default PDFs we have adopted the set MRS98LO(05A) [34] with Q = µ =

√ˆ s as

factorisation/renormalisation scale for both signal and background. The same scale entered

the evolution of αS, which was performed at one-loop, with a choice of Λnf=4

QCDconsistent with

the PDF set adopted. In fact, we have verified that the spread in the inclusive cross sections,

for both signal and background, as obtained by using the five different parameterisations of

MRS98LO and also CTEQ4L [34] was within 6−7% of the values quoted for MRS98LO(05A)

in the remainder of the paper.

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4Selection

The signature that we are then considering is in practice:

4 b−jets + 2 light − jets + τ + pT

miss, (5)

wherein the two b-jets from the hard process are actually defined as the two most for-

ward/backward ones that also display a displaced vertex.

We have assumed a standard detector configuration by imposing acceptance and sepa-

ration cuts on all light-quark (including c’s) and b-jets, labeled as j and b, respectively, as

follows:

pT

b> 20 GeV,|ηb| < 2.5,pT

j> 20 GeV,|ηj| < 5,∆Rjj,jb> 0.4. (6)

The two most forward/backward b-jets (with pseudorapidities of opposite sign) are further

required to yield

Mbb> MH±

(7)

for their invariant mass. For τ-jets (we only consider hadronic decay modes) we impose:

pT

τ> 10 GeV,|ητ| < 2.5,∆Rjτ,bτ> 0.4. (8)

The setup corresponds to the standard ATLAS/CMS detectors. Presently it is not clear to

what extent this setup will also be applicable for the same apparata in the context of the

Super LHC (SLHC) option [35].

Having now excluded the two most forward/backward b-jets from the list of jets, we

impose hadronic W±- and t-mass reconstruction:

|Mjj− MW±| < 15 GeV,|Mbjj− mt| < 35 GeV, (9)

where the two light-quark jets entering the last inequality are of course the same fulfilling

the first one. Finally, the missing transverse momentum should be10:

pT

miss> 60 GeV. (10)

The combined effects of these cuts on the signal (1) in the MSSM and 2HDM models

is shown in Figs. 3 and 4 respectively in the case of retaining the finite width effects using

off-shell masses for the H±and W±. (The difference when instead using the NWA is very

10For simplicity we have kept this cut fixed, whereas in a more detailed analysis one would preferentially

make the cut depend on the mass of the charged Higgs boson.

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small and this option is therefore not shown.) As can be seen from the figures the effects of

the cuts on the magnitude of the cross sections is quite severe. On the other hand the cuts

are needed (especially in case of the MSSM) in order to beat down the background as is

illustrated in Fig. 5. From the figure it is also clear that the signal cross section reaches its

maximum around MH± = 200 GeV and that the magnitude of the signal varies by up to 2

orders of magnitude depending on which model we are considering. It should also be noted

that in the 2HDM setup we are using it was not possible to go above MH± ≃ 320 GeV

(corresponding to MH0 = 700 GeV) due to the unitarity contraints [29]. In the following we

will be considering the case MH± ≃ 215 GeV (corresponding to MA0 = 200 GeV) in more

detail.

After the above cuts have been implemented and the jet momenta assigned, one can

reconstruct the would-be charged Higgs boson mass, by pairing the three jets entering the

equation in the right-hand side of (9) with the left-over central jet, a quantity which we

denote by M4jets. The corresponding mass spectrum is presented in Fig. 6 for our two

customary setups of MSSM and 2HDM, assuming MH± = 215 GeV and tanβ = 30 as

representative values. The figure shows clear peaks at the charged Higgs boson mass for

the signal on top of a combinatorial background in both models whereas for the background

process there is no such peak. Thus, by selecting events with

180 GeV < M4jets< 250 GeV(11)

we can get an additional discrimination against the background.

Furthermore, using the visible τ-jet momentum and the missing transverse one, it is

possible to reconstruct the transverse mass, as

MT

τντ=

?

2pτpT

miss(1 − cos∆φ), (12)

with ∆φ the relative angle between the two momenta, a quantity which is ultimately cor-

related to the actual value of the mass resonance yielding τ−¯ ντpairs (H−in the signal and

W−in the background). We show this observable in Fig. 7 (where it is denoted by MT),

again, for our two customary setups of MSSM and 2HDM. From the figure it is clear that the

transverse mass for the signal in the two models extends all the way out to ∼ MH±. Com-

paring with the background, which starts to drop quite drastically around MT

τντ≈ MW±,

we see that it is advantageous to introduce a cut on the transverse mass of the order of

MT

τντ> MH±/2 (≃ 107 GeV). (13)

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This gives a very strong suppression of the background whereas the signal is only mildly

affected.

After having reconstructed the two charged Higgs bosons and applied the respective cuts

(11) and (13) we can form the (effectively, transverse) mass MT

4jets+τνof the combined two

charged Higgs boson system, giving the possibility to look for possible resonances. As can

be seen from the magnitudes of the cross sections in Fig. 8 the selection outlined above

gives a very clear signal in the 2HDM case with essentially no background, whereas in the

MSSM case the signal is still clear but very small. Of course, the cuts could be tightend to

give a very clear signal also in the MSSM case, but the absolute cross section would then be

even smaller. From the figure it is also clear that there is a significant difference in shape

between the two models, with the 2HDM showing a clear enhancement for MT

4jets+τν<

∼500

GeV due to the resonant contributions. However, given the limited statistics that will be

available at the LHC, it is not clear to what extent the difference in shape alone can be used

to extract any information about possible H0→ H+H−resonances and the corresponding

coupling. In addition the difference in shape will be smaller if the width of the H0Higgs

boson is larger and/or the detector resolution is worse than what we have assumed.

5 Conclusion

As we have shown, it is possible to outline a selection procedure that enables one to extract a

signal of heavy charged Higgs pair production in association with two b-quarks at tanβ>

∼30

in extensions of the standard model with two Higgs doublets of Type II. In a general case

the mass relations in the Higgs sector may be favourable such that a sizeable signal would

appear already at the LHC through the resonant channel gg → b¯bH0→ b¯bH+H−. However,

in the MSSM the resonance is not accessible over the allowed parameter region and the non-

resonant contributions turn out to be very small making it difficult to extract a signal even

after upgrading the luminosity at LHC by a factor ten (SLHC). The large difference in

cross section between the MSSM and a more general 2HDM shows that indeed the pair

production of charged Higgs production is sensitive to the H0H+H−coupling even though

it will probably be difficult to reconstruct a resonant transverse mass peak mainly due to

the limited statistics and possibly also due to the finite detector resolution.

In our study we have not included effects of the b-tagging efficiency. On the one hand,

requiring four b-tags will give a sizeable reduction (of the order of a factor ten) of the signal

as well as the backgrounds. On the other hand, the selection procedure outlined above was

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designed to get a signal in the case of the MSSM leading to unnecessarily tight cuts for the

general 2HDM case. Furthermore, being a leading order calculation, the cross section we

get for the signal is also sensitive to the choice of factorisation and renormalisation scales.

If we, instead of using the standard choice of the invariant mass of the hard subsystem, use

the mean transverse mass of the two b-quarks in the gg → b¯bH+H−process as scale, the

cross section increases by a factor 5. Such a scale choice also gives a better agreement with

the cross section for the ‘twin’ process b¯b → H+H−. In order to get a better handle on

the uncertainties due to scale choices a next-to-leading order calculation will eventually be

necessary. Nonetheless, we believe that our results already call for the attention of ATLAS

and CMS in further exploring the scope of the (S)LHC in reconstructing the form of the

Higgs potential in extended models through signals of charged Higgs boson pairs. Besides,

in presence of parton shower, hadronisation and detector effects, one may also realistically

attempt exploiting τ-polarisation techniques in hadronic decays of the heavy lepton [36] in

order to increase the signal-to-background rates, an effort that was beyond the scope of our

parton level analysis.

Acknowledgments

SM is grateful to The Royal Society of London (UK) for partial financial support in the

form of a Study Visit and thanks the High Energy Theory Group of the Department of

Radiation Science of Uppsala University for kind hospitality.

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Figure 2: Transverse momentum distribution (multiplied by ((pT

(mb=4.25 GeV) in gg → b¯bH+H−compared to factorised expectations for massless and

massive partons.

b)2+ m2

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b) of b-quarks

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Figure 3: Total cross sections as a function of MH± for process (1) yielding the signature (5),

including all decay BRs and with finite width effects, before (solid) and after the kinematic

cuts in (6)–(10), assuming LHC (dashed) detectors. For reference, the value tanβ = 30 is

adopted. The MSSM described in the text is here assumed.

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Figure 4: Total cross sections as a function of MH± for process (1) yielding the signature (5),

including all decay BRs and with finite width effects, before (solid) and after the kinematic

cuts in (6)–(10), assuming LHC (dashed) detectors. For reference, the value tanβ = 30 is

adopted. The 2HDM described in the text is here assumed.

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Figure 5: Total cross sections as a function of MH± for processes (1) (with finite width

effects) and (2) yielding the signature (5), including all decay BRs and after the kinematic

cuts in (6)–(10), assuming LHC detectors. For reference, the value tanβ = 30 is adopted.

The MSSM and the 2HDM described in the text are here compared to the background.

(Notice that the background retains a dependence upon MH± because of the optimisation

of the cut in (7).)

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Figure 6: Differential distribution in the invariant mass of the ‘four-jet system’ defined

in the text for processes (1) (with finite width effects) and (2) yielding the signature (5),

including all decay BRs and after the kinematic cuts in (6)–(10), assuming LHC detectors.

For reference, the values MH± = 215 GeV and tanβ = 30 are adopted. The MSSM and the

2HDM described in the text are here compared to the background.

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Figure 7: Differential distribution in transverse mass of the ‘tau-neutrino’ system defined

in the text for processes (1) (with finite width effects) and (2) yielding the signature (5),

including all decay BRs and after the kinematic cuts in (6)–(10), assuming LHC detectors.

For reference, the values MH± = 215 GeV and tanβ = 30 are adopted. The MSSM and the

2HDM described in the text are here compared to the background.

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Figure 8: Differential distribution in transverse mass of the ‘four-jets plus tau-neutrino’

system defined in the text for processes (1) (with finite width effects) and (2) yielding

the signature (5), including all decay BRs and after the kinematic cuts in (6)–(11) and

(13), assuming LHC detectors. For reference, the values MH± = 215 GeV and tanβ = 30

are adopted. The MSSM and the 2HDM described in the text are here compared to the

background.

27