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Available online at www.sciencedirect.com

ScienceDirect

Nuclear Physics B 950 (2020) 114847

www.elsevier.com/locate/nuclphysb

Exploring the prominent channel: Charged Higgs pair

production in supersymmetric two-parameter

non-universal Higgs model

Nasuf Sonmez

Department of Physics, Faculty of Science, Ege University, 35040 Izmir, Turkey

Received 30

July 2019; received in revised form 28 October 2019; accepted 11 November 2019

Available

online 16 November 2019

Editor: Hong-Jian

Abstract

In this study, the charged Higgs pair production is calculated in the context of the supersymmetry at a

γγ-collider. The channel is explored in Two-parameter Non-Universal Higgs Model where the model pro-

vides

relatively light neutral and charged Higgs bosons. The computation is extended to one loop-level, and

the divergence arising in the loop-diagrams are cured with the radiative photon correction. The production

rate of the charged Higgs pair reaches up to ˆσ

LO+NLO

= 121 fb at

√

ˆs = 635 GeV. The analysis of the

cross-section is also given varying the parameters m

and tan β. The total convoluted cross-section with

the photon luminosity in an e

−

machine is calculated as a function of the center-of-mass energy up to

1TeV, and it gets up to 42 fb at

√

s = 900 GeV depending on the polarization of the initial electron and

laser photon.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

In particle physics, interactions between the fundamental particles are expressed by symme-

tries. The invariance of these symmetries leads to the conservation of physical quantities and

also imposes the equation of motion and the dynamics of the system. In this sense, the Stan-

dard Model (SM) is governed by local gauge symmetry, and it particularly has unitary symmetry

E-mail address: nasuf.sonmez@ege.edu.tr.

https://doi.org/10.1016/j.nuclphysb.2019.114847

The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

2 N. Sonmez / Nuclear Physics B 950 (2020) 114847

SU(3) × SU(2) × U(1). Besides local gauge symmetries, there is another one called Super-

symmetry (Susy) [1] which proposes a relationship between two basic classes of fundamental

particles: bosons (particles with an integer-valued spin) and fermions (particles with half-integer

spin). The Higgs boson was discovered at the LHC [2–4]. Thus, the SM wa

s completed. How-

ever, it is believed that the SM is a low energy approximation of a greater theory which deﬁnes

new physics at higher scales. Susy is one candidate of these models which has attracted much

attention.

The LHC running at

√

s = 7, 8, 13 TeV energies made it possible to test many low scale

Susy predictions. Unfortunately, no new particle has been discovered at the LHC. That re-

stricted the Susy parameter space [5–9]; therefore, the masses of the sparticles were pushed

to higher scales. It was concluded that the simple weak scale Susy picture wa

s not valid, and

thus, new scenarios were proposed in the Susy context. The Minimal Supersymmetric Standard

Model (MSSM) [10,11]is an extension of the SM that realizes supersymmetry with a minimum

number of new particles and new interactions. The simpliﬁed versions of the MSSM can be de-

ved from a grand uniﬁed theory (GUT) under various assumptions. The model was generally

deﬁned with the following parameters: the soft-breaking masses m

, m

1/2

and A

which are

assumed universal at the GUT scale, the higgsino mixing mass parameter μ, and the ratio of

the two vacuum expectation values of the two Higgs doublets tan β. Besides these parameters,

the sparticles get a contribution from the so-called soft breaking terms. These terms miracu-

lously give extra mass to these sparticles at the weak scale so that their masses are pushed

to higher scales. These soft breaking terms are usually assumed uni

versal at the GUT scale.

It is possible to assume non-universality for some of these parameters at the GUT scale with

different motivations. For example: in one-parameter Non-Universal Higgs Model (NUHM1),

the soft-breaking contrib

utions to the electroweak Higgs multiplets (m

and m

) are equal,

= m

= sign(m

)|m

|, but non-universal, m

(GUT) = m

(GUT) = m

. Another one

is called the two-parameter Non-Universal Higgs Model (NUHM2) [12,13], and this time the

soft-breaking contributions to the electroweak Higgs multiplets are not equal m

=m

This scenario ﬁts into all the current constraints on Susy, and most importantly, all electroweak

observables get low contribution overall from radiative corrections. Thus, the NUHM2 scenario

can be adjusted easily to get outside the limits obtained by the LHC. The masses of the squarks

and the sleptons can be specially arranged a

bove the TeV scale with the lightest electroweakinos

( ˜χ

0,±

) and the Higgses (h

, H

, A

, H

) being set deliberately below the TeV range. Among

these particles, charged Higgs (H

) boson emerges naturally in extended theories with at least

two Higgs ﬁelds. The observation of a single or pair production of charged Higgs boson is a hot

research topic, and it has been studied extensively in all high-energy experiments. Its observation

will be solid proof of an extended scalar sector.

The particle physics community has several proposals for the future colliders to study the

properties of the Higgs boson and investigate the extended scalar sector. In all these proposals, a

lepton collider is planned; therefore, the next one will be an e

−

-collider. Additionally, an e

−

collider can host a γγ-collider, basically high energy electrons are converted to high energy pho-

tons with a conversion rate of k ≈ 1by Compton back-scattering [14] technique. The LHC has

not found any trace about the extra Higgs bosons or the lightest electroweakinos. Therefore, one

may wonder what is the potential of the future colliders about the supersymmetry searches, par

ticularly, the charged Higgs pair production. The charged Higgs pair in lepton colliders were

studied extensively before in Refs. [15,16]. Since the production rate in e

−

-collisions is s-

channel suppressed, the cross-section of γγ → H

−

is larger than that of e

−

-collider. The

production of the charged Higgs pair was investigated before at the next-to-leading order (NLO)

N. Sonmez / Nuclear Physics B 950 (2020) 114847 3

for a γγ-collider in Refs. [17,18]by taking into account only Yukawa and later full squark

correction. However, the infrared divergence was not included there. The results showed that

the one-loop corrections are from -20% to +25%. Later, the process was handled in Ref. [19]

including the real radiative corrections. The calculation wa

s presented for various benchmark

points in MSSM, and the results showed that the correction is overall between -60% to +5% at

√

s = 1TeV. From the previous works which calculated the complete one-loop corrections, it is a

proper question to ask what is the contribution of one-loop diagrams in the light of the exclusion

limits set by the LHC and whether it is possible to observe the charged Higgs bosons in future

colliders. Therefore, this process needs to be ree

valuated.

In this study, the production of charged Higgs pair is studied, including one-loop corrections

plus radiative ones. The cross-section of the charged Higgs pair is calculated as a function of

the center-of-mass (c.m.) energy. The two polarization cases, ˆσ

and ˆσ

, are calculated at the

NLO level. Parameters of the model are varied, and the cross-section distributions are plotted.

Additionally, the distributions are presented by convoluting the total cross-section with the pho-

ton luminosity in an e

−

-collider with various polarization conﬁgurations of the machine. The

content of this paper is organized as follows: In Sec. 2, the parameter space of the NUHM2 is de-

ﬁned. In Sec. 3, one-loop Feynman diagrams, possible singularities in the calculation along with

the procedure to cure these divergences are discussed thoroughly. In Sec. 4, numerical results of

the total cross-section in the NUHM2 are deli

vered, and the conclusion is given in Sec. 5.

2. Two-parameters non-universal Higgs model

In Susy, the parameters at the GUT scale and the soft-breaking parameters are closely linked

with the electroweak symmetry breaking. The results from the LHC pushed the previous limits

on masses of the sparticles to high scales, and that resulted in the so-called “little hierarchy”

between the weak scale and the scale of sparticles masses. The high scale ﬁne-tuning of the

lar

ge logarithmic contributions and the weak scale ﬁne-tuning were needed to explain the little

hierarchy. The high scale tuning along with the weak scale tuning was discussed in detail in

Ref. [20]. The NUHM2 is an effective model which is valid up to the scale Q ≤ M

GUT

, and the

soft parameters at the GUT scale only serve to describe higher-dimensional operators of a more

fundamental theory so that there might be correlations that cancel the large logs. Then, the im-

plications on the weak scale become signiﬁcant, and ﬁne-tuning of the electroweak observables

is needed. The electroweak ﬁne-tuning parameter

, which is deﬁned in Ref. [21], is given below:



=max

|/(m

/2) (1)

where C

= m

/(tan β

− 1), C

=−m

tan β

/(tan β

− 1), and C

=−μ

. The ex-

pression of the other two contributions at the one-loop level C



(k)

and C



(k)

were deﬁned

in Ref. [21]. Evidently, the 

gives the largest contribution to the mass of Z-boson. Since

NUHM2 was inspired by GUT models where

and

belong to different multiplets, it is

argued that the GUT scale masses m

and m

could be trade-off for the weak scale parame-

ters μ and m

in Ref. [22]. To achieve small 

, it is required that the soft mass parameter

|, the mixing parameter of the Higgs-doublets μ, and the radiative contribution |

| have

to be around m

/2to within a factor of a few [21,23]. Then, the |m

weak

and μ

can have a

value of (100 − 300 GeV)

at any values of the parameters m

and m

1/2

in the non-universal

Higgs models. Therefore m

= 10 TeV and m

1/2

= 0.5 TeV are assumed. The largest radiative

correction, which is stop mixing, requires A

=±1.6 ·m

=±16 TeV, and ﬁnally μ = 6TeVis

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