Charged Higgs in MSSM and Beyond

Yasar Hicyılmaza,1, Levent Selbuzb,2, Levent Solmaza,3 and Cem Salih Unc,4

aDepartment of Physics, Balıkesir University, TR10145, Balıkesir, TurkeybDepartment of Engineering Physics, Ankara University, TR06100, Ankara, TurkeycDepartment of Physics, Uludag University, 16059, Bursa, Turkey

Abstract

We conduct a numerical study over the constrained MSSM (CMSSM), Next-to-MSSM(NMSSM) and U(1) extended MSSM (UMSSM) to probe the allowed mass rangesof the charged Higgs boson and its dominant decay patterns, which might comeinto prominence in near future collider experiments. We present results obtainedfrom a limited scan for CMSSM as a basis and compare its predictions with theextended models. We observe within our data that a wide mass range is allowed as0.5(1) . mH± . 17 TeV in UMSSM (NMSSM). We find that the dominant decaychannel is mostly H± → tb such that BR(H± → tb) ∼ 80%. While this moderemains dominant over the whole allowed parameter space of CMSSM, we realizesome special domains in the NMSSM and UMSSM, in which BR(H± → tb) . 10%.In this context, the decay patterns of the charged Higgs can play a significant role todistinguish among the SUSY models. In addition to the tb decay mode, we find thatthe narrow mass scale in CMSSM allows only the decay modes for the charged Higgsboson to τν (∼ 16%), and their supersymmetric partners τ ν (∼ 13%). On the otherhand, it is possible to realize the mode in NMSSM and UMSSM in which the chargedHiggs boson decays into a chargino and neutralino pair up to about 25%. This decaymode requires non-universal boundary conditions within the MSSM framework tobe available, since CMSSM yields BR(H± → χ0

1χ±1 ) . 1%. It can also be probed

in near future collider experiments through the missing energy and CP-violationmeasurements. Moreover, the chargino mass is realized as mχ±1

& 1 TeV in NMSSM

and UMSSM, and these solutions will be likely tested soon in collider experimentsthrough the chargino-neutralino production. Focusing on the chargino-neutralinodecay patterns, we also present tables which list the possible ranges for the chargedHiggs production and decay modes.

1E-mail: yasarhicyilmaz@balikesir.edu.tr2E-mail: selbuz@eng.ankara.edu.tr3E-mail: lsolmaz@balikesir.edu.tr4E-mail: cemsalihun@uludag.edu.tr

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1 Introduction

After the null results for the new physics, the current experiments have focused on theHiggs boson properties and analyses have been quite enlarged such that the Higgs bosoncouplings and decays are now being studied precisely. The Higgs boson itself is a stronghint for the new physics and there are some drawbacks of the Standard Model (SM) suchas the gauge hierarchy problem [1] and the absolute stability of the SM Higgs potential [2].In addition, most of the models beyond the SM (BSM) need to enlarge the Higgs sector sothat their low scale phenomenology includes extra Higgs bosons which are not present inthe SM. Among many well motivated BSM models, supersymmetric models take arguablya special place, since they are able to solve the gauge hierarchy problem, provide plausiblecandidates for the dark matter (DM) and so on. Besides, the Higgs sector in such modelsrequires two Higgs doublets and so the low scale Higgs sector includes two CP-even Higgsbosons (h,H), one CP-odd Higgs boson (A) and two charged Higgs bosons (H±).

While the lightest CP-even Higgs boson is expected to exhibit very similar properties tothe SM-like Higgs boson at the decoupling limit (mH ∼ mA ∼ mH± mh), its couplingsto the SM particles can still deviate from the SM and thus, it can be constrained bysuch deviations [3]. Similarly, the heavier Higgs bosons can be constrained if they cansignificantly decay into the SM particles. For instance, if the CP-odd Higgs boson decaysmostly into a pair of τ−leptons, then its mass can be constrained as mA & 1 TeV dependingon tan β [4]. In addition, the flavor changing decays of B−meson also yield importantimplications for these Higgs bosons. The Bs → µ+µ− process receives some contributionsfrom A−boson proportional to (tan β)6/m4

A [5], and the strong agreement between theexperimental results (BR(Bs → µ+µ−) = 3.2+1.5

−1.2 × 10−9 [6]) and the SM (BR(Bs →µ+µ−) = (3.2± 0.2)× 10−9 [7]) strictly constrains the A−boson phenomenology.

Among these extra Higgs bosons, the charged Higgs boson plays a crucial role, since theSM does not have any charged scalar. It can be produced at the current collider experimentsalong with other particles as pp→ (t,W±, tb, . . .)H±, where p stands for the proton. Eventhough its production is rather difficult and production cross-section is small in comparisonto the other particles, the charged Higgs boson can be visible with large center of massenergy and luminosity in near future collider experiments. In this context, the track ofits decays can be directly related to the new physics. Furthermore, this distinguishingcharged particle may reveal itself in many manifestations and different supersymmetricmodels may favor different predictions. Even though the usual dominant decay mode isH± → tb when mH± & mt + mb in the CMSSM, models with extended particle contentand/or gauge group can open window for other probable and important decay modes. Inaddition, richer phenomenology can be revealed when the charged Higgs boson is allowedto decay into new supersymmetric particles. For instance, if the H± → χ0

i χ±j mode is open,

one can also measure the CP-asymmetry throughout such processes [8].Based on different decay patterns of the charged Higgs boson, we analyzed the charged

Higgs boson in this work within three different models which are the minimal supersym-metric extension of the SM (MSSM), U(1) extended MSSM (UMSSM) and Next-to-MSSM(NMSSM). We restrict our analyses to constrained versions of these models, in which thelow scale observables can be determined with only a few input parameters defined at thegrand unification scale (MGUT). Of course, a more detailed study can be performed fromweak scale side which is a tedious work and this is beyond the scope of this paper. Through-out the analyses the CMSSM framework will be considered as the base and implications of

1

the other two models will be discussed in a way that also compares them with CMSSM. Itis important to stress that the different imprints of the charged Higgs boson can be used todistinguish a model from another and this may be useful for future charged Higgs studies.

The outline of the rest of the paper is the following: We will briefly describe themodels under concern in Section 2. After we summarize the scanning procedure, employedexperimental constraints in Section 3, Section 4 discusses the mass spectrum in terms ofthe particles, which can participate in the charged Higgs boson decay modes. The resultsfor the production and decay modes of the charged Higgs boson are presented in Section5. We also present tables containing rates for the charged Higgs boson production andits decay modes over some benchmark points in this section. Section 6 summarizes andconcludes our findings.

2 Models

2.1 MSSM

The superpotential in MSSM is given as

WMSSM = µHuHd + YuQHuU + YdQHdD + YeLHdE (1)

where µ is the bilinear mixing term for the MSSM Higgs doublets Hu and Hd; Q and Ldenote the left handed squark and lepton dublets, while U,D,E stand for the right-handedu-type squarks, d-type squarks and sleptons respectively. Yu,d,e are the Yukawa couplingsbetween the Higgs fields and the matter fields shown as subscripts. Higgsino mass term µ isincluded in the SUSY preserving Lagrangian in MSSM, and hence it is allowed to be at anyscale from the electroweak (EW) scale to MGUT. In this sense, even though it is relevantto the EW symmetry breaking, its scale is not constrained by the EW symmetry breakingscale (∼ 100 GeV). This is called the µ−problem in MSSM. In addition to WMSSM, the softSUSY breaking (SSB) Lagrangian is given below

−LSUSYMSSM = m2

Hu|Hu|2 +m2

Hd|Hd|2 +m2

Q|Q|2 +m2

L|L|2

+m2U|U |2 +m2

D|D|2 +m2

E|E|2 +

∑a

Maλaλa + (BµHuHd + h.c.)

+ AuYuQHuU c + AdYdQHdDc + AeYeLHdEc (2)

where the field notation is as given before. In addition, m2φ with φ = Hu, Hd, Q, L, U , D, E

are the SSB mass terms for the scalar fields. Au,d,e are the SSB terms for the trilinear scalarinteractions, while B is the SSB bilinear mixing term for the MSSM Higgs fields. Afteradding the SSB Lagrangian, the Higgs potential in MSSM becomes more complicated thanthe SM, and the masses of the physical Higgs bosons can be found in terms of µ, mHu ,mHd

and tan β, where tan β = vu/vd is the ratio of the vacuum expectation values (VEVs)of the MSSM Higgs fields. The tree level Higgs boson masses can be found as [9];

2

mh,H =1

2

(m2A +M2

Z ∓√

(m2A −M2

Z)2 + 4M2Zm

2A sin2(2β)

)m2H± = m2

A +M2W

m2A = 2|µ|2 +m2

Hu+m2

Hd

(3)

where MZ and MW are the masses of the Z− and W−bosons respectively. As it is well-known, the lightest CP-even Higgs boson tree level mass is problematic in MSSM, since it isbounded by MZ from above as m2

h .M2Z cos2(2β). This conflict can be resolved by adding

the loop corrections to the Higgs boson mass. Utilizing the loop corrections to realize 125GeV Higgs boson at the low scale requires either multi-TeV stop mass or relatively largeSSB trilinear A−term [10]. In this context the 125 GeV Higgs boson constraint leads toheavy spectrum in SUSY particles especially in the CMSSM framework where all scalarmasses are set by a single parameter at MGUT. Besides, if the mass scales for the extraHiggs bosons are realized as mA ∼ mH ∼ mH± & 1 TeV, it requires large mHu and mHd

as seen from Eqs.(3). It also brings the naturalness problem back to the SUSY models,since the consistent electroweak symmetry breaking scale requires µ ≈ mHu over most ofthe fundamental parameter space of the models. It also arises the µ−problem in MSSMmentioned above.

The µ−term is also important since it is the Higgsino masses at the low scale. Inthis context, if µ term is significantly low in comparison to the gaugino masses M1 andM2, the LSP neutralino can exhibit Higgsino-like properties, and it yields different DMphenomenology. Nature of the DM can be investigated by considering the neutralino massmatrix given as

MMSSMχ0 =

M1 0 −g1vd√2

g1vu√2

0 M2g2vd√

2−g2vu√

2

−g1vd√2

g2vd√2

0 −µ

g1vu√2

−g2vu√2

−µ 0

(4)

in the basis (B, W , hd, hu), where B and W denote Bino and Wino respectively, whichmay be called electroweakinos, while hd and hu represent the Higgsinos from Hd and Hu

superfields respectively. Similarly, the chargino mass matrix can be written as

Mχ± =

M2

1√2g2vu

1√2g2vd µ

. (5)

The properties and relevant phenomenology involving with the chargino and neutralinocan be understood by comparing M1, M2 and µ. If µ > M1,M2 then both LSP neutralino

3

and the lightest chargino exhibit gaugino properties and the gauge couplings are dominantin strength of the relevant interactions. When µ < M1,M2, the LSP neutralino and thelightest chargino are mostly formed by the Higgsinos, and the Yukawa couplings also takepart in interactions as well as the gauge couplings. Since, the charged Higgs is, in principle,allowed to decay into a pair of a neutralino and a chargino, the self interaction couplingsin the Higgs sector are also important in such decay processes, when the chargino andneutralino are Higgsino-like.

2.2 NMSSM

The main idea behind NMSSM is to resolve the µ−problem of MSSM in a dynamic waythat an additional S field generates the µ−term by developing a non-zero VEV. It can berealized by replacing the term with µ−term in WMSSM given in Eq.(1) with a trilinear termas hsSHuHd, where S is chosen preferably to be singlet under the MSSM gauge group. Ifthere is no additional term depending on the S−field, then the Lagrangian also remainsinvariant under Pecce-Quinn (PQ) like symmetry which transforms the fields as follows

Hu → eiqPQθHu Hd → eiqPQθHd S → e−2iqPQθ

Q→ e−iqPQθQ L→ e−iqPQθL U,D,E → U,D,E(6)

Such a symmetry in the Lagrangian can help to resolve the strong CP-problem [11].However, in NMSSM, the Pecce-Quinn symmetry is broken by the µ−term spontaneously,since it happens by the VEV of the S field. In this case, there has to be a massless Goldstoneboson, which can be identified as axion. Such a massless field is strongly constrained bythe cosmological observations [12]. Moreover, hs is restricted into a very narrow range(10−10 & hs . 10−7) experimentally, and in order to yield µ ∼ O(100) GeV VEV of Sshould be very large, and it brings back the naturalness problem.

The situation of the massless Goldstone boson arose from the spontaneous breaking of

the PQ symmetry, is to add another S dependent term as1

3κS3, which explicitly breaks

the PQ symmetry, while Z3 symmetry remains unbroken. However, despite avoiding themassless axion in this case, the effectively generated µ−term spontaneously breaks thediscrete Z3 symmetry, which arises the domain-wall problem. This problem can be resolvedby adding non-renormalizable higher order operators which break Z3 symmetry, whilepreserving the Z2 symmetry at the Planck scale. (For a detailed description of the domain-wall problem and its resolution, see [13]). In our work we assume that the domain-wallproblem is resolved and we consider the following superpotential in the NMSSM framework;

WNMSSM = WMSSM(µ = 0) + hsSHuHd +1

3κS3 (7)

and the corresponding SSB Lagrangian is

LSUSYNMSSM = LSUSY

MSSM(µ = 0)−m2SS∗S −

[hsAsSHuHd +

1

3κAκS

3 + h.c.

](8)

where LSUSYMSSM(µ = 0) is the SSB Lagrangian for MSSM given in Eq.(2) with µ = 0, mS is

the mass for the scalar component of S, while As and Aκ are trilinear SSB terms for thescalar interactions. According to the superpotential and the SSB Lagrangian, the second

4

term in Eq.(7) is responsible for generating the µ−term effectively as µeff ≡ hsvs/√

2 andthe first term in the paranthesis of Eq.(8) is Bµ correspondence. Although the particlecontent is simply enlarged by including an extra singlet field in NMSSM, the neutral scalarcomponent of this field can mix with the CP-even and CP-odd Higgs boson of MSSM,while the charged Higgs sector remains intact. After the EW symmetry breaking, theNMSSM Higgs sector includes three CP-even Higgs bosons, two CP-odd Higgs bosons andtwo charged Higgs bosons. A detailed discussion for the Higgs sector can be found in Ref.[14]. Once the mass matrix for the CP-even Higgs boson states is diagonalized, the lightestmass eigenvalue can be found as

m2h = MZ

(cos2(2β) +

hsg

)(9)

where the first term covers the MSSM part of the Higgs boson, while the second termencodes the contributions to the tree-level Higgs boson mass from the singlet. In thissense, the necessary loop corrections to the Higgs boson mass may be relaxed and lightermass spectrum for the SUSY particles can be realized. As the lightest CP-even Higgsboson, other Higgs bosons receive contributions from the singlet, and the tree-level massfor the charged Higgs boson can be obtained as [15]

m2H± = M2

W +2hsvs

sin(2β)(As + κvs)− hs(v2u + v2d) (10)

In addition to the Higgs sector, the neutralino sector of NMSSM has five neutralinosincluding to the supersymmetric partner of S field - so-called singlino - in addition to theMSSM neutralinos. The mass matrix for the neutralinos in the basis (B, W , Hu, Hd, S)is obtained as

MNMSSMχ0 =

00

MMSSMχ0 (µ = µeff ) −hsvu

−hsvd

0 0 −hsvu −hsvd 2κvs

(11)

where MMSSMχ0 (µ = µeff ) is the MSSM neutralino masses and mixing as given in Eq.(4),

while the extra column and row represent the mixing of the singlino with the MSSMneutralinos. As seen from the M55

χ0 , the singlino mass is found as MS = 2κvs. Eventhough it is left out from the first 4× 4 matrix of the MSSM neutralinos, the singlet sectoris still effective, since the mass term for the Higgsinos is determined by the VEV of S fieldas µeff = hsvs/

√2. If one assumes the lightest mass eigenvalue ofMχ0 is also the lightest

supersymmetric particle (LSP), species of the LSP can yield dramatically different darkmatter (DM) implications than those obtained in the MSSM framework, especially whenthe singlino is realized so light that it can significantly mix with the other neutralinos information of the LSP neutralino. The chargino sector remains intact, since NMSSM doesnot introduce any new charged field to the particle content; hence, the chargino massesand mixing are given with the same matrix given in Eq.(5). Note that VEV of the singletfield is indirectly effective in the chargino sector through the Higgsino mass, which can beseen by replacing µ with µeff in Eq.(5).

5

2.3 UMSSM

In the previous subseciton, where we discussed NMSSM, even though its non-zero VEVmight be expected to break a gauged symmetry spontaneously, there was no symmetrywhose breaking is triggered with VEV of S except the global PQ and Z3 symmetries. Inthis sense, one can associate a gauged symmetry to vs by extending the MSSM gaugegroup with a simple abelian U(1)′ symmetry [16, 17]. Such extensions of MSSM form aclass of U(1)′ models (UMSSM), and its gauge structure can be originated to the GUTscale, when the underlying symmetry group at MGUT is larger than SU(5). The mostinteresting breaking pattern, which results in UMSSM, can be realized when the GUTsymmetry is identified with the exceptional group E6:

E6 → SO(10)× U(1)ψ → SU(5)× U(1)χ × U(1)ψ → GMSSM × U(1)′ (12)

where GMSSM = SU(3)c × SU(2)L × U(1)Y is the MSSM gauge group, and U(1)′ can beexpressed as a general mixing of U(1)ψ and U(1)χ as

U(1)′ = cos θE6U(1)χ + sin θE6U(1)ψ. (13)

In a general treatment, all the fields including the MSSM ones are allowed to havenon-zero charges under the U(1)′ gauge group; thus, despite the similarity with NMSSM,the invariance under the U(1)′ symmetry does not allow the term κS3 as well as µHuHd.The charge configurations of the fields for U(1)ψ and U(1)χ models are given in Table 1.The charge configuration for any U(1)′ model can be obtained with the mixing of U(1)ψand U(1)χ, which is quantified with the mixing angle θE6 , through the equation providedbelow Table 1.

Model Q U c Dc L Ec Hd Hu S

2√

6 U(1)ψ 1 1 1 1 1 -2 -2 4

2√

10 U(1)χ -1 -1 3 3 -1 -2 2 0

Qi = Qiχ cos θE6 +Qi

ψ sin θE6 .

Table 1: Charge assignments for the fields in several models.

Moreover, vs is now responsible for the spontaneous breaking of the U(1)′ symmetry,and hence the µeff term can be related to the breaking mechanism of a larger symmetry.The particle content of UMSSM is slightly richer than the MSSM. First of all, in additionto S field, there should be also another gauge field associated with the U(1)′ group, whichis denoted by Z ′. Even though the current analyses provide strict bounds on Z ′ (MZ ≥2.7 − 3.3 TeV [18], MZ ≥ 4.1 TeV [19]), the signal processes in these analyses are basedon the leptonic decay modes of Z ′ as Z ′ → ll, where l stands for the charged leptons ofthe first two families. However, as shown in a recent study [20], Z ′ may barely decay intotwo leptons; hence such strict bounds can be relaxed. Moreover, its neutral superpartner(B′) is also included in the low energy spectrum as required by SUSY. It is interesting thatthere is no specific mass bound on B′, and it can be as light as O(100) GeV consistent withthe current experimental constraints [21, 22]. Since B′ is allowed to mix with the other

6

neutralinos, the LSP neutralino may reveal its manifestation through the U(1)′ sector inthe collider and DM direct detection experiments.

Since the MSSM fields are non-trivially charged under the extra U(1)′ group, the modelmay not be anomaly free. To avoid possible anomalies, one may include exotic fields whoseparticipation into the triangle vertices leads to anomaly cancellation. However, such fieldsusually yield heavy exotic mass eigenstates at the low scale. If one chooses a superpotentialin which these exotic fields do not interact with the MSSM fields directly, their effects in thesparticle spectrum are quite suppressed by their masses. In this case, the model effectivelyreduces to UMSSM without the exotic fields. After all, the superpotential is

W = YuQHuU + YdQHdD + YeLHdE + hsSHdHu (14)

and the corresponding SSB Lagrangian can be written as

− LSUSYUMSSM = LSUSY

MSSM +m2S|S|2 +MB′B

′B′ + (AshsSHuHd + h.c.) (15)

Employing Eqs.(14 and 15), the Higgs potential can be obtained as

V tree = V treeF + V tree

D + V treeSUSY (16)

with

V treeF = |hs|2 [|HuHd|2 + |S|2 (|Hu|2 + |Hd|2)]

V treeD =

g218

(|Hu|2 + |Hd|2)2 +g222

(|Hu|2|Hd|2 − |HuHd|2)

+g′2

2(QHu|Hu|2 +QHd

|Hd|2 +QS|S|2)

V treeSUSY = m2

Hu|Hu|2 +m2

Hd|Hd|2 +m2

S|S|2 + (AshsSHuHd + h.c.) ,

(17)

which yields the following tree-level mass for the lightest CP-even Higgs boson mass:

m2h = M2

Z cos2 2β +(v2u + v2d

) [h2S sin2 2β

2+ g2Y ′

(QHu cos2 β +QHd

sin2 β)]. (18)

The second term in the square paranthesis of Eq.(18) reflects the contribution fromthe U(1)′ sector, where gY ′ is the gauge coupling associated with U(1)′, QHu and QHd

arethe charges of Hu and Hd under the U(1)′ group. After these contributions, the tree-levelHiggs boson mass can be obtained as large as about 140 GeV for low tan β, while it can beas heavy as about 115 GeV, when tan β is large [20]. Similarly, other Higgs bosons receivecontributions from the U(1)′ sector, and the charged Higgs boson mass can be obtained astree-level as

m2H± = M2

W +

√2hsAsvssin(2β)

− 1

2h2s(v

2d + v2u) (19)

In addition to the Higgs sector, the neutralino sector is also enlarged in UMSSM. Sinceit has a field whose VEV breaks U(1)′ symmetry, its fermionic superpartner mixes withthe MSSM neutralinos, as in the NMSSM case. Moreover, since UMSSM possesses an

7

extra U(1) symmetry, the gaugino partner of the gauge field (Z ′) also mixes with the otherneutralinos. In sum, there are six neutralinos in UMSSM, and their masses and mixingcan be given in (B′, B, W , hu, hd, S) basis as

Mχ0 =

M ′1 0 0 g′YQHd

vd g′YQHuvu g′YQSvs0 00 0

g′YQHdvd MMSSM

χ0 (µ = µeff ) − 1√2hsvu

g′YQHuvu − 1√2hsvd

g′YQSvs 0 0 − 1√2hsvu −

1√2hsvd 0

(20)

where M ′1 is the SSB mass of B′, and the first row and column code the mixing of B′

with the other neutralinos. The middle part represents the MSSM neutralino masses andmixing, while the last column and row displays the mass and mixing for the MSSM singletfield as in the case of NMSSM. Similar to NMSSM, UMSSM does not propose any newcharged particle; hence, the chargino sector remains the same as that in MSSM.

3 Scanning Procedure and Experimental Constraints

We have employed SPheno 3.3.3 package [23] obtained with SARAH 4.5.8 [24]. In thispackage, the weak scale values of the gauge and Yukawa couplings are evolved to the unifi-cation scale MGUT via the renormalization group equations (RGEs). MGUT is determinedby the requirement of the gauge coupling unification, described as g1 = g2 for CMSSM andNMSSM, while it is as g1 = g2 = gY ′ for UMSSM. Note that the UMSSM framework isnot anomaly-free, but its RGE’s are being used, since the U(1)’ models reduce to UMSSMeffectively due to possible heavy exotic states. This treatment can be improved with theinclusion of such exotic states in the RGEs. Even though g3 does not appear in theseconditions for MGUT, it needs to take part in the gauge coupling unification condition.Concerning the contributions from the threshold corrections to the gauge couplings at theGUT scale arising from some unknown breaking mechanisms of the GUT gauge group, g3receives the largest contributions [25], and it is allowed to deviate from the unification upto about 3%. If a solution does not require this condition within this allowance, SPhenodoes not generate an output for such solutions by default. Hence, the existence of an out-put file guarantees that the solutions are compatible with the unification condition, andg3 deviates no more than 3%. With the boundary conditions given at MGUT, all the SSBparameters along with the gauge and Yukawa couplings are evolved back to the weak scale.Note that each model yields different RGEs coded by SARAH in different model packagesfor SPheno. We employ the packages called after the model names as MSSM, NMSSM andUMSSM. During our numerical investigation, we have performed random scans over thefollowing parameter spaces of CMSSM, NMSSM and UMSSM:

8

CMSSM NMSSM UMSSM

0 ≤ m0 ≤ 5 (TeV) 0 ≤ m0 ≤ 3 (TeV) 0 ≤ m0 ≤ 3 (TeV)

0 ≤ M1/2 ≤ 5 (TeV) 0 ≤ M1/2 ≤ 3 (TeV) 0 ≤ M1/2 ≤ 3 (TeV)

1.2 ≤ tan β ≤ 50 1.2 ≤ tan β ≤ 50 1.2 ≤ tan β ≤ 50

−3 ≤ A0/m0 ≤ 3 −3 ≤ A0/m0 ≤ 3 −3 ≤ A0/m0 ≤ 3

µ > 0 0 ≤ hs ≤ 0.7 0 ≤ hs ≤ 0.7

1 ≤ vs ≤ 25 (TeV) 1 ≤ vs ≤ 25 (TeV)

−10 ≤ As, Aκ ≤ 10 (TeV) −10 ≤ As ≤ 10 (TeV)

0 ≤ κ ≤ 0.7 −π2≤ θE6 ≤ π

2

(21)

where m0 is the universal spontaneous supersymmetry breaking (SSB) mass term for thematter scalars. This mass term is also set as mHu = mHd

= m0 in CMSSM, while mHu andmHd

are calculated through the EWSB conditions, which leads to mHu 6= mHd6= m0 in

NMSSM and UMSSM. Similarly, M1/2 is the universal SSB mass term for the gaugino fields,which includes one associated with the U(1)′ gauge group in UMSSM. tan β = 〈vu〉/〈vd〉is the ratio of VEVs of the MSSM Higgs doublets, A0 is the SSB term for the trilinearscalar interactions between the matter scalars and MSSM Higgs fields. Similarly, As isthe SSB interaction between the S and Hu,d fields, and Aκ is the SSB term for the tripleself interactions of the S fields. hs and κ have defined before. Note that κ = 0 in theUMSSM case. Finally, vs denotes the VEV of S fields. Recall that the µ−term of MSSMis dynamically generated such that µ = hsvs/

√2. Its sign is assigned as a free parameter

in MSSM, since REWSB condition can determine its value but not sign. For simplicity, weforced it to be positive in NMSSM and in UMSSM by hs and vs. Finally, we set the topquark mass to its central value (mt = 173.3 GeV) [26]. Note that the sparticle spectrumis not very sensitive in one or two sigma variation in the top quark mass [27], but it canshift the Higgs boson mass by 1− 2 GeV [28].

The requirement of radiative electroweak symmetry breaking (REWSB) provides im-portant theoretical constraints, since it excludes the solutions withm2

Hu= m2

Hd[9]. Besides,

based on our previous experience from the numerical analyses over the parameter spacesof various SUSY models, REWSB requires m2

Huto be more negative than m2

Hdat the low

scale (see for instance [28]). In addition, the solutions are required to bring consistentvalues for the gauge and Yukawa couplings, gauge boson masses, top quark mass [29] etc.Such constraints are being imposed into SPheno by default. In addition, the solutionsmust not yield color and/or charge breaking minima, which restricts the trilinear scalarinteraction coupling in our scans as |A0| ≤ 3m0, where m0 is the universal mass term atthe GUT scale for the SUSY scalars. Another important constraint comes from the relicabundance of the stable charged particles [30], which excludes the regions where chargedSUSY particles such as stau and stop become the lightest supersymmetric particle (LSP).In our scans, we allow only the solutions for which one of the neutralinos is the LSP andREWSB condition is satisfied.

In scanning the parameter space, we use our interface, which employs Metropolis-Hasting algorithm described in [31]. After collecting the data, we impose the mass boundson all the sparticles [32], and the constraint from the rare B-decays such as Bs → µ+µ−

[6], Bs → Xsγ [33], and Bu → τντ [34]. In addition, the WMAP bound [35] on therelic abundance of neutralino LSP within 5σ uncertainty. Note that the current results

9

from the Planck satellite [36] allow more or less a similar range for the DM relic abundancewithin 5σ uncertainty, when one takes the uncertainties in calculation. These experimentalconstraints can be summarized as follows:

mh = 123− 127 GeV

mg ≥ 1.8 TeV

MZ′ ≥ 2.5 TeV

0.8× 10−9 ≤ BR(Bs → µ+µ−) ≤ 6.2× 10−9 (2σ)

mχ01≥ 103.5 GeV

mτ ≥ 105 GeV

2.99× 10−4 ≤ BR(B → Xsγ) ≤ 3.87× 10−4 (2σ)

0.15 ≤ BR(Bu → τντ )MSSM

BR(Bu → τντ )SM≤ 2.41 (3σ)

0.0913 ≤ ΩCDMh2 ≤ 0.1363 (5σ)

(22)

In addition to those listed above, we also employ the constraints on the SM-like Higgsboson decay processes obtained from the ATLAS [37] and CMS [38] analyses. We expecta strong impact from current bounds for BR(B → Xsγ) on the parameter space. Figure1 displays the results for the impacts from the B → Xsγ and h→ ZZ processes (where hdenotes the SM-like Higgs boson) with plots in the BR(Bs → Xsγ) −mH± and BR(h →ZZ)−mH± planes for CMSSM. All points are compatible with the REWSB and neutralinoLSP conditions. Green points satisfy the mass bounds and the constraints from the raredecays of B-meson. The blue points form a subset of green and they are consistent with theconstraints from the SM-like Higgs boson decay processes. Note that the constraint fromBR(Bs → Xsγ) is not applied in the left plane, but the bounds from this processes arerepresented with the horizontal solid lines. Similarly, the constraint from BR(h→ ZZ) isnot employed in the right plane, and the horizontal lines indicate the experimental bounds(0.024 ≤ BR(h → ZZ) ≤ 0.029) within 2σ uncertainty[33, 37, 38]. As we expect, theconstraint from the BR(Bs → Xsγ) process excludes a significant portion of the parameterspace (green points below the bottom horizontal line); however, its impact barely affectsthe mass bound on the charged Higgs boson. We can find the mH± & 800 GeV allowedby this constraints (see also [39]). On the other hand, the main impact on the parameterspace (and hence on the charged Higgs boson mass) comes from those for the SM-like Higgsboson decays. The BR(h → ZZ) −mH± plane shows that the h → ZZ process excludesmore than half of the parameter space (green and blue points below the bottom horizontalline in the right panel). According to the results in the BR(h → ZZ) −mH± plane, thesolutions with mH± . 2 TeV are excluded by the h→ ZZ process. Note that the universalboundary conditions of CMSSM restricts results more, and if non-universality is employed,the lower mass for the charged Higgs boson can be found at about 1 TeV consistently withthe current constraints including that from the h → ZZ process [40]. Thus, our resultswill also mean that some possible signal channels require to impose non-universal boundary

10

conditions in the MSSM framework to be available.

Figure 1: CMSSM plots in the BR(Bs → Xsγ) −mH± and BR(h → ZZ) −mH± planes.All points are compatible with the REWSB and neutralino LSP conditions. Green pointssatisfy the mass bounds and the constraints from the rare decays of B-meson. The bluepoints form a subset of green and they are consistent with the constraints from the SM-like Higgs boson decay processes. Note that the constraint from BR(Bs → Xsγ) is notapplied in the left plane, but the bounds from this processes are represented with thehorizontal solid lines. Similarly, the constraint from BR(h → ZZ) is not employed in theright plane, and the horizontal lines indicate the experimental bounds from this process(0.024 ≤ BR(h→ ZZ) ≤ 0.029) within 2σ uncertainty[33, 37, 38].

Figure 2: Plots for the impacts of BR(Bs → Xsγ) (left) and BR(h → ZZ) (right) on theparameter space of NMSSM (top) and UMSSM (bottom). The color coding is the same asFigure 1.

On the other hand, one can investigate the impacts of these constraints on the fun-

11

damental parameter space of NMSSM and UMSSM as shown in Figure 2 with plots forthe impacts of BR(Bs → Xsγ) (left) and BR(h → ZZ) (right) on the parameter spaceof NMSSM (top) and UMSSM (bottom). The color coding is the same as Figure 1. Theresults in Figure 2 shows that the constraint from h → ZZ has a strong impact in bothmodels. However, even though this constraint excludes more than half of the solutions,it does not bound the charged Higgs mass from below, in contrast to CMSSM. Note thatlighter mass scales for the Charged Higgs boson can be allowed, if one employs relativelymilder bounds from the h→ ZZ process.

We have emphasized the bounds on the Higgs boson [41] and the gluino [42], since theyhave drastically changed since the LEP era. We have employed the two-loop RGEs incalculation of the Higgs boson mass. The uncertainty in the Higgs boson mass calculationarises mostly from the uncertainties in values of the strong gauge coupling and top quarkmasses, which yield about 3 GeV deviation in the Higgs boson mass calculation [43]. Inaddition, the large SUSY scale (MSUSY) worsens the uncertainty in the Higgs boson masscalculation [44]. Note that there are more precise calculations available to improve theresults for the Higgs boson mass (see for instance [45]). In addition, we have employed theLEP II mass bounds on the lightest chargino and stau. Although the mass bounds haverecently been updated on these particles [46, 47], these bounds are model dependent andbased on specific decay channels of the chargino. While we employ the LEP II bounds onour plots, their masses will be discussed briefly later. In addition, the current mass boundson Z ′ is established as MZ′ & 4.1 TeV [18]. On the other hand, this bound can vary modeldependently, and a most recent study [48] has shown that MZ′ & 2.5 TeV can survive, ifZ ′ is leptophobic. Based on our previous study [20], which was conducted in the similarparameter space, the leptonic decay processes of Z ′ is found as BR(Z ′ → ll) . 14%. Sincethe leptonic decays of Z ′ are found rather low, we set the mass bound on Z ′ as MZ′ ≥ 2.5TeV. The mass bound on Z ′ depends on the gauge coupling associated with U(1)′ groupwhich varies with θE6 . Thus, some of the solutions represented in our study can be excludedby the experimental analyses [18].

When the LSP is required to be one of the neutralinos, the DM relic abundance con-straint will be highly effective to shape the fundamental parameter space, since the relicabundance of LSP neutralino is usually realized greater than the current measurement overmost of the fundamental parameter space. Once one can identify the regions compatiblewith the current WMAP and Planck results, they can be analyzed further against theresults from the direct detection [49], indirect detection [50] and collider experiments [51].However, all these detailed analyses are out of the scope of our study. We apply only therelic abundance constraint on the LSP neutralino to show that the regions of interest forthe charged Higgs boson phenomenology can also be compatible with the relic abundancebound from the current measurements, and they can be also tested under the light of theDM constraints in possible future studies. In this context, the DM implications obtainedwithin our analyses can be improved with more thorough analyses devoted to DM. TheDM observables in our scan are calculated by micrOMEGAs [52] obtained by SARAH [24].

We will apply the constraints mentioned in this section subsequently, and thus, beforeconcluding this section, it might be necessary to mention the color convention which we willuse in the next sections in presenting the results. The following is the list that summarizeswhat color satisfies which constraints:

Grey: REWSB and Neutralino LSP conditions.

12

Red: REWSB, neutralino LSP and Higgs boson mass constraint.

Green: REWSB, neutralino LSP, Higgs boson mass constraint, SUSY particle mass bounds,and B-physics constraints.

Blue: REWSB, neutralino LSP, Higgs boson mass constraint, SUSY particle mass bounds,B-physics constraints, LHC constraints on the Higgs boson couplings.

Black: REWSB, neutralino LSP, Higgs boson mass constraint, SUSY particle mass bounds,B-physics constraints, LHC constraints on the Higgs boson couplings, and WMAPand Planck constraints on the relic abundance of neutralino LSP within 5σ.

From black to grey, each color is always on top of the previous one in the order as listedabove in a way that the black always stays on top of all other colors in the plots.

4 Fundamental Parameter Space and Mass Spectrum

Figure 3: Plots in the m0−mH± and M1/2−mH± planes for CMSSM (left panel), NMSSM(middle panel) and UMSSM (right panel). All points are consistent with the REWSB andneutralino LSP. Our color convention is as listed at the end of Section 3.

In this section, we consider the fundamental parameter space, shaped by the experi-mental constraints discussed in the previous section, and discuss the charged Higgs massalong with the mass spectrum for other particles, which might be relevant to decay modesof the charged Higgs boson. Figure 3 displays our results with plots in the m0 − mH±

and M1/2 − mH± planes for CMSSM (left panel), NMSSM (middle panel) and UMSSM(right panel). All points are consistent with the REWSB and neutralino LSP. Our colorconvention is as listed at the end of Section 3. In the CMSSM case, as seen from the leftpanel, the charged Higgs can be as heavy as about 8 TeV in the range of the fundamentalparameters given in Eq.(21).

These results in CMSSM arise from the fact that CMSSM yields mostly bino-like LSPneutralino µM2 ∼ 2M1 [53], where µ is the Higgsino mass parameter, while M2 and M1

13

are the SSB masses of Wino and Bino, respectively. The problem with bino-like DM is thatits relic abundance is usually much larger than the current measurements of the WMAP[35] and Planck [36] satellites, and one needs to identify some coannihilation channels whichtake part in reducing LSP neutralino’s relic abundance down to the current ranges [54].However, the void direct signals for supersymmetry from the LHC experiments yield quiteheavy spectrum in the low scale implications of CMSSM, and the mass scales are usuallyout of the possible coannihilation scenarios. On the other hand, even if the neutralinosector is extended only a single flavor, the region of the parameter space allowed by theDM observations becomes quite wide open [22], as a result of mixing the extra flavor statewith the MSSM neutralinos. However, as seen from the bottom left panel of Figure 3, thecharged Higgs boson cannot be lighter than about 1.5 TeV when one employs the LHCconstraints (green). Even though we do not find solutions for mH± . 2 TeV after applyingall the constraints listed in Section 3, some recent studies [55] have shown that mH± & 1.5TeV can be consistent with the DM constraints. Such a lower bound on the charged Higgsboson mass mostly arises from the rare B-meson decay process, Bs → Xsγ, where Xs is asuitable bound state of the strange quark. The strong agreement between the experimentalmeasurements (BRexp(Bs → Xsγ) = (3.43 ± 0.22) × 10−4 [33]) and the Standard Modelprediction (BRSM(Bs → Xsγ) = (3.15± 0.23)× 10−4 [56]) strongly enforces a lower boundon the charged Higgs boson mass. However; as have been shown before, these constraintsfrom the rare B-meson decays restrict the charged Higgs boson mass as mH± & 800 GeV.The strongest restriction comes from the h → ZZ process, which excludes the solutionswith mH± . 2 TeV (blue points). In contrast to the results in CMSSM, the mass range ofthe charged Higgs boson is quite wide in NMSSM and UMSSM, as is seen from the middleand right panels respectively, and the solutions can yield mH± from about 1 to 15 TeV, afterthe experimental constraints are employed. This wide mass range partly arises from thenon-universality in mHd

and mHu in NMSSM and UMSSM. In addition, such a wide regionallowed by the DM observations reflects the significant effect of extending the neutralinosector of MSSM even with one extra flavor state. The recent studies have shown that newflavor states, which are allowed to mix with the MSSM neutralinos can significantly alterthe DM implications [22]. The fundamental parameter space for NMSSM and UMSSM arerestricted based on our previous studies [20, 61], which explored the regions with acceptablefine-tuning in the fundamental parameter space of UMSSM.

The other fundamental parameters are A0 and tan β, and the results in terms of theseparameters are represented in Figure 4 with plots in the tan β −mH± and A0/m0 −mH±

planes for CMSSM (left panel), NMSSM (middle panel) and UMSSM (right panel). Thecolor coding is the same as Figure 3. As seen from the top panels, tan β is a strongparameter in mH± , and one can realize heavy charged Higgs boson only when tan β . 10in the CMSSM and NMSSM frames, while it is restricted to moderate values as 20 .tan β . 30 in UMSSM. On the other hand, there is no specific restriction in A0, and asseen from the bottom panels, it is possible to realize whole allowed range of mH± for anyA0.

After presenting the fundamental parameter space of the models, we consider the massspectrum, that reveals which particles the charged Higgs boson may kinematically beallowed to decay. First we present the stop and sbottom masses in Figure 5 with plots inthe mt1 −mH± and mb1

−mH± planes for CMSSM (left panel), NMSSM (middle panel)and UMSSM (right panel). If the solutions with mH± & mt + mb can be realized, thenthe charged Higgs boson can participate in the processes H± → tb. As seen from the

14

Figure 4: Plots in the tan β − mH± and A0/m0 − mH± planes for CMSSM (left panel),NMSSM (middle panel) and UMSSM (right panel). The color coding is the same as Figure3.

Figure 5: Plots in the mt1−mH± and mb1−mH± planes for CMSSM (left panel), NMSSM

(middle panel) and UMSSM (right panel). The color coding is the same as Figure 3.

middle and right panels, if the charged Higgs boson is allowed to be heavy enough, thereis a possibility for the decay process H± → tb. However, since the relevant backgroundgenerated by the decay processes involving with the top-quark significantly suppresses thepossible signals from stop [62], such decays of the charged Higgs boson may not provide adetectable track.

Figure 6 displays our results with another pair of supersymmetric particles, stau andsneutrino, which the charged Higgs boson can decay, with plots in the mτ1 − mH± andmν − mH± planes for CMSSM (left panel), NMSSM (middle panel) and UMSSM (rightpanel). The color coding is the same as Figure 3. The current bound on a charged sleptoncan be expressed as mτ & 400 GeV [63]. Such bounds rely on the chargino-neutralino

15

production, which differs from model to model; thus it can vary depending on the massspectrum. Considering the model dependence of such bounds, even if we employed theLEP2 bounds, the LHC and DM constraints bound the stau mass from below as mτ & 500GeV in all CMSSM, NMSSM and UMSSM as seen from the top panels. Similarly thesneutrino mass is also bounded as mν & 1 TeV.

Figure 7 shows the neutralino masses and the charged Higgs boson mass with plots inthe mχ0

1−mH± and mχ0

i−mH± planes for CMSSM (left panel), NMSSM (middle panel) and

UMSSM (right panel), where i stands for the number identifying the heaviest neutralinoin models as i = 4 for CMSSM, i = 5 for NMSSM, and i = 6 for UMSSM. The colorcoding is the same as Figure 3. All models allow the LSP neutralino to be only as heavyas about 1.5 TeV. The upper bound on the neutralino LSP mass arises from the rangeassigned to M1/2 in scanning the fundamental parameter spaces of the models. The lowerbound, on the other hand, arises mostly from the heavy bound on the gluino mass, whilethe other constraints may also have minor effects. Without the relic density constraint, theneutralino LSP mass can be as low as about 400 GeV in CMSSM, while lower bound canbe as low as about 100 GeV in NMSSM and UMSSM (blue). However, the WMAP andPlanck bounds on the relic abundance of neutralino LSP can be satisfied when mχ0

1& 500

GeV in all models. The heaviest neutralino χ0i in CMSSM (i = 4) cannot be lighter than

about 2 TeV, while its mass is bounded from above as mχ04. 3 TeV. While NMSSM

and UMSSM reveal similar bound from below at about 500 GeV, the heaviest neutralinomass in these models can be realized in multi-TeV scale as mχ0

5. 5 TeV in NMSSM and

mχ05. 10 TeV in UMSSM.

Since the decay modes of H± including a neutralino happens along with also a chargino,we conclude this section by considering the chargino masses in the models as shown inFigure 8 with plots in the mχ±1

−mH± and mχ±2−mH± planes for CMSSM (left panel),

NMSSM (middle panel) and UMSSM (right panel). The color coding is the same as Figure3. The solutions in the CMSSM framework are allowed by the constraints only when theyyield mχ±1

& 1 TeV (seen from the black points). Even though it is kinematically allowed

Figure 6: Plots in the mτ1 −mH± and mν −mH± planes for CMSSM (left panel), NMSSM(middle panel) and UMSSM (right panel). The color coding is the same as Figure 3.

16

Figure 7: Plots in the mχ01−mH± and mχ0

i−mH± planes for CMSSM (left panel), NMSSM

(middle panel) and UMSSM (right panel), where i stands for the number identifying theheaviest neutralino in models as i = 4 for CMSSM, i = 5 for NMSSM, and i = 6 forUMSSM. The color coding is the same as Figure 3.

Figure 8: Plots in the mχ±1−mH± and mχ±2

−mH± planes for CMSSM (left panel), NMSSM

(middle panel) and UMSSM (right panel). The color coding is the same as Figure 3.

(mH± ∼ mχ01

+ mχ±1), CMSSM may not provide significant decay processes in which the

charged Higgs boson decays into a chargino and neutralino. On the other hand, the sameconstraints can allow lighter chargino solutions in NMSSM and UMSSM as mχ±1

& 500

GeV, while the heavier mass scales for the charged Higgs boson (& 10 TeV) are alsoallowed. In this context, NMSSM and UMSSM may distinguish themselves from CMSSM,if they can yield significant H± → χ0χ± processes. The bottom panels show also thesecond chargino may be effective in the charged Higgs decay modes, since the heaviercharged Higgs boson is allowed and the constraints bound the second chargino mass frombelow as mχ±2

& 2 TeV in CMSSM.

17

5 Production and Decay Modes of H±

Direct production processes of the charged Higgs boson at the LHC is rather difficult, sinceits production rate is proportional to the Yukawa couplings of the Higgs bosons with thequarks from the first two families. It is rather suppressed even when the charged Higgsboson is light, because the Yukawa couplings associated with the first two-family matterfields are quite small. On the other hand, the charged Higgs bosons can be producedthrough the top-pair productions if they are sufficiently light that the t → H±b processis kinematically allowed. In such processes, the charged Higgs boson can leave its marksthrough the H± → τ±b decay processes. In the cases with heavy charged Higgs bosons,the charged Higgs boson is produced at the LHC in association with either top-quark [64]or W±− boson [65]. The production processes associated with top-quark do not provideclear signal due to a large number of jets involved in the final states. Nevertheless, thosewith W± boson might be expected to be relatively clear signal, but such processes aresuppressed by the irreducible background processes from the top-pair production processes[66]. In this context, it is not easy to detect the charged Higgs boson at the LHC. Eventhough an exclusion limit is provided for the charged Higgs boson, it can be excluded upto mH± ∼ 600 GeV only for low tan β (∼ 1) [64], which allows lighter charged Higgs bosonsolutions when tan β is large.

Before considering the possible decay modes, we present the possible production chan-nels for the charged Higgs production over some benchmark points in Table 2. These valueswere obtained after implementing our models into CalcHEP [67]. The points have beenchosen so as to be consistent with the employed constraints discussed in Section 3. Thelargest contributions to the charged Higgs production come from the processes involvingwith the top quark with the cross-section ∼ 10−5 pb in CMSSM, while this processes canreach up to σ ∼ 10−3 pb in NMSSM and σ ∼ 10−2 pb in UMSSM. Even though the im-provement in the latter models is quite significant, it is mostly because of the different massscales of the charged Higgs boson. As discussed in the previous section, mH± & 2 TeVis not allowed by the constraints in CMSSM, mH± & 1 TeV in NMSSM and mH± & 500GeV in UMSSM are allowed. However, considering σ(pp → tH±), one should still notethat NMSSM still yields one magnitude larger cross-section (∼ 10−4 pb) in comparison toCMSSM and UMSSM for this production channel, if one considers the similar mass scalesfor the charged Higgs boson (mH± ∼ 2 TeV). Similar discussion holds for σ(pp → tbH±).The other channels can also be seen in Table 2, and as is stated before, they are eithernegligible or a few magnitudes smaller than those involving with top-quark.

Despite such small cross-sections in comparison to, for instance, the SM-like Higgsboson [68], some possible signal processes relevant to the charged Higgs boson becomeobservable with a larger center of mass and luminosity. In addition, as stated before, thecharged Higgs decays are crucial, since it does not exist in the SM, and these decays canalso be distinguishing between models. In this sense, we consider its decays and discuss thechannels in a variety of SUSY models, which may play an important role in detecting thecharged Higgs boson in future collider experiments. Depending on its mass, the chargedHiggs boson can decay into either a pair of SUSY particles or the SM particles. Sincethe current LHC results imply rather a heavy mass spectrum for the squarks and gluinos,it might be possible to realize H± → tb(τ ντ ) processes which yield matter sparticles intheir final states. However, these channels are hardly possible when the SUSY models areconstrained from the GUT scale with the universal boundary conditions. However, it might

18

Observables CMSSM NMSSM UMSSM

mH±(GeV) σ(pb) mH±(GeV) σ(pb) mH±(GeV) σ(pb)

2019 4.5× 10−5 1011 1.0× 10−3 551 1.6× 10−2

pp→ tH± 3001 3.1× 10−6 2055 1.2× 10−4 1015 8.3× 10−4

4002 1.0× 10−7 5849 5.8× 10−9 2061 1.7× 10−5

2019 5.2× 10−6 1011 1.3× 10−4 551 1.0× 10−3

pp→ W∓H± 3001 4.2× 10−7 2055 1.8× 10−5 1015 6.4× 10−5

4002 1.7× 10−8 5849 1.3× 10−9 2061 2.0× 10−6

2019 4.8× 10−8 1011 4.0× 10−4 551 2.7× 10−4

pp→ H∓H± 3001 3.7× 10−10 2055 5.9× 10−6 1015 1.0× 10−5

4002 1.5× 10−12 5849 3.0× 10−18 2061 4.0× 10−8

2019 1.6× 10−8 1011 5.2× 10−6 551 1.3× 10−4

pp→ H01,2,3H

± 3001 9.3× 10−11 2055 1.5× 10−8 1015 4.4× 10−6

4002 2.4× 10−13 5849 1.8× 10−15 2061 1.3× 10−8

2019 1.7× 10−5 1011 4.1× 10−2 551 7.2× 10−3

pp→ tbH± 3001 1.4× 10−6 2055 1.8× 10−2 1015 3.4× 10−4

4002 3.2× 10−8 5849 1.7× 10−9 2061 6.7× 10−7

Table 2: The charged Higgs boson production modes and cross-sections over some bench-mark points (we used the centre of mass energy

√s=14 TeV). The points have been chosen

so as to be consistent with all of the employed constraints discussed in Section 3.

still be possible that the charged Higgs boson can decay into a pair of chargino-neutralino.If SUSY particles are so heavy that the charged Higgs is not kinematically allowed todecay into the SUSY particles, then the SM particles take over and provide dominantdecay channels. Since only the Yukawa couplings to the third family are significant, thefinal states are expected to include either third family quarks or leptons. The dominantdecay channel is realized as H± → tb. Indeed, it is not surprising to realize the dominantchannel as H± → tb in all the cases when the charged Higgs boson is heavy, while, otherdecay channels can also be identified up to considerable percentage in some models. Inthis context, we start presenting our results for the H± → tb process first, then we includeother possible channels in our consideration.

5.1 H± → tb

Figure 9 represents our results for BR(H± → tb) in correlation with mH± in CMSSM(left), NMSSM (middle) and UMSSM (right). As mentioned before, it provides the maindecay channel for the charged Higgs boson in a possible signal, which could be detectedin future collider experiments. When the DM constraints are applied (black points) top ofthe LHC constraints, CMSSM allows this channel only up to 80%, and it leaves a slight

19

Figure 9: The plots in the BR(H± → tb)−mH± plane for CMSSM (left), NMSSM (middle)and UMSSM (right). The color coding is the same as Figure 3.

open window for the other possible decay modes. The constraints also bound this processfrom below as BR(H± → tb) & 70%. Hence, even though CMSSM allows some otherchannels, their branching ratios cannot be larger than 30%. In the case of NMSSM, itis possible to find solutions in which the charged Higgs boson only decays into tb, thereis not any lower bound provided by the constraints. In other words, it is possible torealize BR(H± → tb) ∼ 10%, which means one can identify some other channels as themain channel, which are discussed later. Similar results can be found also in the UMSSMframework. In this context, there is a wide portion in the fundamental parameter space ofNMSSM and UMSSM which distinguishes these models from CMSSM.

5.2 H± → τντ

Figure 10: The plots in the BR(H± → τν) − mH± plane for CMSSM (left), NMSSM(middle) and UMSSM (right). The color coding is the same as Figure 3.

Figure 10 displays our result for the BR(H± → τν) in correlation with mH± in CMSSM(left), NMSSM (middle) and UMSSM (right). The color coding is the same as Figure 3.All three models allow this channel only up to about 20%. This channel is expected tobe dominant when H± → tb is not allowed, i.e. mH± < mt + mb [69]. Even though thereis not a certain constraint through this leptonic decay of the charged Higgs, and it canprovide relatively clearer signal and less uncertainty, it may not display a possible signaland distinguish the models through these leptonic processes.

20

Figure 11: The plots in the BR(H± → χ01χ±1 ) − mH± plane for CMSSM (left), NMSSM

(middle) and UMSSM (right). The color coding is the same as Figure 3.

5.3 H± → χ±i χ0j

Figure 11 shows the results for the BR(H± → χ01χ±1 ) in correlation with mH± in CMSSM

(left), NMSSM (middle) and UMSSM (right). The color coding is the same as Figure 3.Even though it is possible to realize this process up to about 8% (green) in CMSSM, theLHC measurements for the SM-like Higgs boson (blue) bound it as BR(H± → χ0

1χ±1 ) &

2%. However, these solutions do not satisfy the WMAP and Planck bounds on the relicabundance of the LSP neutralino. When one employs the DM constraints (black) it is seenthat BR(H± → χ0

1χ±1 ) . 1%. Hence, a possible signal involving with the H±χ0

1χ±1 process

is hardly realized in the CMSSM framework, while it is open in the NMSSM and UMSSMframeworks up to about 20%− 25% consistently with all the constraints including the DMones. Note that even though the solutions presented in Figure 11 are enough to claim asensible difference from CMSSM, better results for the branching ratios in NMSSM andUMSSM may still be obtained with more thorough statistics.

As discussed in Section 4, the heavier neutralino and chargino mass eigenstates areallowed to participate in H± → χ0

i χ±j . However, the heavier ones continue to decay

into the lighter mass eigenstates, and each decay cascade gives a suppression unless theirbranching ratio is large (BR ∼ 100%). In this context, even though their signal is not asstrong as H± → χ0

1χ±1 , their contributions would be at the order of minor contributions in

comparison to BR(H± → χ0i χ±j ).

In addition to the charginos and neutralinos, the Higgs boson can be allowed to decayinto some other supersymmetric particles, which could be, in principle, a pair of tb or τ ν.As shown in Figure 5, the H± → tb process is not kinematically allowed in CMSSM, whileit is open in NMSSM and UMSSM. However, the large top-quark background significantlysuppresses such processes. On the other hand, the H± → τ ν process is possible in allmodels. Moreover, since it happens through the leptonic processes, the signal could beclear for such decay processes. The minimum and maximum rates for various decay modesof the Charged Higgs boson obtained in the parameter scan are represented in Table 3. Thevalues have been chosen as to be consistent with all the constraints applied. As mentionedbefore, the dominant decay channel, H± → tb, does not leave too much space for theother modes in CMSSM, while it is possible to realize this decay mode as low as a fewpercent, and these models can significantly yield other decay modes such as those withneutralino and chargino, stop and bottom, and/or stau and neutralino, which can be ashigh as about 30% in NMSSM and UMSSM. In addition, the decay processes includingother Higgs bosons can be also available in the latter models. For instance, NMSSM allows

21

Parameters CMSSM NMSSM UMSSM

Min(%) Max(%) Min(%) Max(%) Min(%) Max(%)

BR(H± → χ01χ±1 ) − 0.5 − 20 − 23

BR(H± → χ02χ±1 ) − − − 3 − 1

BR(H± → χ03χ±1 ) − - − 24 − 21

BR(H± → χ04χ±1 ) − - − 26 − 25

BR(H± → χ05χ±1 ) − − − 25 − 19

BR(H± → χ06χ±1 ) − − − − − 8

BR(H± → τ ν) − 13 − 33 − 5

BR(H± → tb) − − − 35 − 8

BR(H± → A01W

±) − − − 43 − −

BR(H± → H02W

±) − − − 16 − 2

BR(H± → ZW±) − − − 3 − 2

BR(H± → tb) 73 83 7 95 8 98

BR(H± → τν) - 16 − 17 − 18

Table 3: Minimum and maximum rates for various decay modes of the Charged Higgsboson obtained in the parameter scan. The values have been chosen so as to be consistentwith all the constraints applied.

the process, H± → A01W

± up to 43%, while the H± → H02W

± process can be also realizedup to 16%. The latter process is also allowed in UMSSM up to about 30%.

6 Conclusion

We perform numerical analyses for the CMSSM, NMSSM and UMSSM to probe the allowedmass ranges for the charged Higgs boson and its possible decay modes as well as showingthe allowed parameter spaces of these models. Since there is no charged scalar in SM, thecharged Higgs boson can signal the new physics as well as being distinguishable among themodels beyond SM. Throughout our analyses, we find that it is possible to realize muchheavier scales (& 10 TeV) in the NMSSM and UMSSM framework. In addition to thecharged Higgs boson, we find mt & 2 TeV in CMSSM, while it can be as light as about1 TeV in NMSSM and 500 GeV in UMSSM. These bounds on the stop mass mostly arisefrom the 125 GeV Higgs boson mass constraint, while this constraint is rather relaxed inNMSSM and UMSSM because of extra contributions from the new sectors in these models.Besides, the sbottom mass cannot be lighter than about 2 TeV in CMSSM and 1 TeV inNMSSM and UMSSM. Such masses for the stop and sbottom exclude H± → tb in CMSSM,while it can still be open in NMSSM and UMSSM. Another pair of supersymmetric particlesrelevant to the charged Higgs boson decay modes is τ and ν, whose masses are boundedas mτ & 500 GeV and mν & 1 TeV. Even though their total mass is close by the chargedHiggs boson mass, there might be a small window which allows H± → τ ν. We also presentthe masses for the chargino and neutralino, since the charged Higgs boson can, in principle,

22

decay into them.While the heavy mass scales in NMSSM and UMSSM open more decay modes for the

charged Higgs boson, its heavy mass might be problematic in its production processes. Welist the possible production channels and their ranges. The production channels, in whichthe charged Higgs boson is produced associated with top-quark, provide the most promisingchannels. Considering the same mass scale (mH± ∼ 2 TeV) in all the models CMSSM andUMSSM predict σ(pp → tH±) ∼ 10−5 pb, while NMSSM prediction is one magnitudelarger (∼ 10−4 pb). Similarly UMSSM prediction fades away as σ(pp → tbH±) ∼ 10−7

pb, which is much lower than the CMSSM prediction (∼ 10−5 pb), while NMSSM yieldsσ(pp→ tbH±) ∼ 10−2 pb. Even though NMSSM predictions come forward in the chargedHiggs prodictions, UMSSM allows lighter charged Higgs mass solutions (mH± ∼ 500 GeV)as well, and such solutions yield much larger production cross-section as σ(pp → tH±) ∼10−2 pb and σ(pp→ tbH±) ∼ 10−3 pb.

Even if these predictions for the charged Higgs boson production are low in comparisonto the SM-like Higgs boson, it can be attainable with larger center of mass energy andluminosity. In addition, its decay modes are completely distinguishable from any neutralscalar, and hence it can manifest itself through some decay processes. The dominant decaymode for the charged Higgs boson in CMSSM is mostly to tb with 70% . BR(H± →tb) . 80%, while it is also possible to realize H± → τν and H± → τ ν up to about20%. On the other hand, the allowed heavy mass scales in NMSSM and UMSSM allowthe modes H± → tb, τ ν, χ±i χ

0j in addition to those realized in the CMSSM framework.

Among these modes, even though tb channel distinguishes these models from CMSSM, thelarge irreducible top-quark background can suppress such processes; thus, it is not easy toprobe the charged Higgs boson through such a decay mode. Nevertheless, despite the clearleptonic background, NMSSM and UMSSM imply similar predictions for the τ ν decaymode to the results from CMSSM. This channel can probe the charged Higgs in futurecollider experiments but it cannot distinguish the mentioned SUSY models. On the otherhand, H± → χ±i χ

0j is excluded by the current experimental constraints in the CMSSM

framework, while it is still possible to include this decay mode in NMSSM and UMSSM.Such decay modes can be probed in the collider experiments through the missing energyand CP-violation measurements. Additionally, the lightest chargino mass in NMSSM andUMSSM is bounded from below as mχ±1

& 1 TeV, which seems testable in near future LHCexperiments through the analyses for the chargino-neutralino production processes.

AcknowledgementThis work were supported by Balikesir University Research Projects Grant No BAP-

2017/142 and BAP-2017/174. The work of L. SELBUZ is supported in part by AnkaraUniversity-BAP under grant number 17B0443004.

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