Minimal Nambu-Goldstone Higgs Model in Supersymmetric SU5 Revisited Koichi Hamaguchiab Shihwen Hora Natsumi Nagataa

2025-05-02 0 0 1.36MB 36 页 10玖币

侵权投诉

Minimal Nambu-Goldstone Higgs Model

in Supersymmetric SU(5) Revisited

Koichi Hamaguchia,b∗, Shihwen Hora†, Natsumi Nagataa‡

aDepartment of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113–0033, Japan

bKavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU),

University of Tokyo, Kashiwa 277–8583, Japan

Abstract

We revisit the minimal Nambu-Goldstone (NG) Higgs supersymmetric (SUSY)

SU(5) grand uniﬁed model and study its phenomenological implications. The Higgs

sector of the model possesses a global SU(6) symmetry, which is spontaneously

broken and results in the Higgs doublets of the minimal SUSY Standard Model

(MSSM) as NG chiral superﬁelds. Therefore, the model naturally leads to light

Higgs doublets and solves the doublet-triplet splitting problem. Because of the

SU(6) symmetry, the couplings of the Higgs sector are tightly restricted, and thus

the model is more predictive than the minimal SUSY SU(5). We determine all the

grand-uniﬁed-theory parameters via the matching conditions of the gauge coupling

constants at the uniﬁcation scale and calculate proton lifetime, confronting this with

current experimental bounds. We discuss that this model is incompatible with the

constrained MSSM, whilst it has a large viable parameter space in the high-scale

SUSY scenario. The perturbativity condition on the trilinear coupling of the adjoint

Higgs ﬁeld imposes an upper (lower) limit on the wino (gluino) mass, implying a

hierarchical mass pattern for these gauginos. Future proton-decay searches can

probe a large part of the parameter space, especially if the SUSY-breaking scale is

.100 TeV.

∗E-mail address: hama@hep-th.phys.s.u-tokyo.ac.jp

†E-mail address: shihwen@hep-th.phys.s.u-tokyo.ac.jp

‡E-mail address: natsumi@hep-th.phys.s.u-tokyo.ac.jp

arXiv:2210.09333v1 [hep-ph] 17 Oct 2022

1 Introduction

Uniﬁcation of interactions has been one of the main goals of particle physics. The mini-

mal supersymmetric (SUSY) SU(5) grand uniﬁed theory (GUT) [1,2] oﬀers a desirable

framework to this end, where the three Standard Model (SM) gauge couplings are uniﬁed

with a great accuracy [3–9]. Nevertheless, the minimal SU(5) GUT is known to have a

fatal defect, called the doublet-triplet splitting problem. In SU(5), the Higgs doublets in

the minimal SUSY SM (MSSM) are embedded into 5and 5representations, accompa-

nied with color-triplet components. These color-triplet ﬁelds induce proton decay, and

to evade the limits imposed by proton-decay searches they must have a GUT-scale mass.

On the other hand, the MSSM Higgs doublets need to have a SUSY-scale mass to achieve

a successful electroweak-symmetry breaking. This mass splitting is realized with a huge

amount of ﬁne-tuning in the minimal SU(5), making this model less appealing.

An attractive idea to solve this doublet-triplet splitting problem is that the Higgs boson

is a pseudo-Nambu-Goldstone (pNG) boson associated with the spontaneous breaking of a

global symmetry. Such a scenario in the framework of GUTs was ﬁrst explored in Ref. [10]

and discussed later in Refs. [11–28]. In the model considered in Ref. [10], the 5and 5

Higgs representations, as well as an adjoint Higgs ﬁeld of SU(5), are embedded into an

adjoint representation of an SU(6) global symmetry. The SU(5) GUT gauge group is a

subgroup of this SU(6). The vacuum expectation value (VEV) of this adjoint ﬁeld breaks

both the SU(6) global symmetry and the SU(5) GUT gauge symmetry, giving masses

to the SU(5) gauge bosons and yielding a pair of massless doublet Higgs ﬁelds as NG

multiplets. The color-triplet components of the 5and 5representations remain massive,

i.e., have a GUT-scale mass. The mass term of the doublet Higgs ﬁelds is protected from

quantum corrections thanks to the non-renormalization theorem in SUSY theories, and

is generated through the SUSY-breaking eﬀect. As a result, the MSSM Higgs doublets

acquire a mass around the SUSY-breaking scale, and hence, the doublet-triplet splitting

problem is solved in a natural manner. We refer to this setup as the minimal NG Higgs

SUSY SU(5) GUT model.

In this work, we revisit this model and study its phenomenological implications in

detail. Because of the global SU(6) symmetry in the Higgs sector, the number of free pa-

rameters in this model is smaller than that in the minimal SU(5), allowing us to determine

all of the GUT parameters, such as the SU(5) gauge coupling constant, the trilinear cou-

pling of the adjoint Higgs ﬁeld, λ, the colored Higgs mass, MHC, and the GUT gauge boson

mass, MX, through the matching conditions of the gauge coupling constants at the GUT

scale, αa(QG)(a= 1,2,3), where QGis the uniﬁcation scale deﬁned by α1(QG) = α2(QG).

It is found from the perturbativity condition on λthat α2(QG)&α3(QG)and MHC.MX

are favored. The former inequality restricts the low-energy SUSY mass spectrum since

αa(QG)depend on the masses of the MSSM SUSY particles through the renormalization

group equations (RGEs). In addition, we can predict proton decay rates by determining

MHCand MX. To show the signiﬁcance of these results, we consider two scenarios for the

SUSY mass spectrum: the constrained MSSM (CMSSM) and high-scale SUSY. It is found

that the CMSSM is incompatible with the p→K+¯νbound from the Super-Kamiokande

experiment [29,30], as the SUSY particles are predicted to lie around O(10) TeV in this

case. In the high-scale SUSY scenario, on the other hand, we ﬁnd a large viable parameter

space. We also ﬁnd that the perturbativity condition on λleads to an upper (lower) limit

on the wino (gluino) mass, implying a hierarchical mass pattern for these gauginos. Fu-

ture proton decay searches can test a large part of the viable parameter regions, especially

if the SUSY-breaking scale is .100 TeV.

This paper is organized as follows. In Sec. 2, we review the minimal NG Higgs SUSY

SU(5) GUT model and discuss its symmetry-breaking structure and mass spectrum. In

Sec. 3, we show how to extract the GUT parameters from the GUT-scale matching con-

ditions of the SM gauge coupling constants. We also evaluate the mass parameters for

the MSSM Higgs ﬁelds induced by the SUSY-breaking eﬀect. Then, we show the results

of our analysis for the CMSSM and high-scale SUSY in Sec. 4. Section 5is devoted to

conclusion and discussion. We summarize relevant formulae for the RGE analysis and

proton decay calculation in Appendix Aand B, respectively.

2 Model

The minimal NG Higgs SUSY SU(5) GUT model was ﬁrst proposed in Ref. [10] and

discussed later in Refs. [11,12,14,15,20]. In this setup, the Higgs sector is assumed to

possess a global SU(6) symmetry, and the MSSM Higgs multiplets reside in the adjoint

representation of the SU(6), ˆ

Σ. The SU(5) GUT gauge group is a subgroup of the SU(6),

and hence, this global symmetry is explicitly broken by the gauge interaction. The global

SU(6) symmetry is violated also by the couplings of the Higgs multiplets to the MSSM

matter ﬁelds. The superpotential of this model thus has the structure

W=WHiggs(ˆ

Σ) + WYukawa ,(1)

where WHiggs(ˆ

Σ) respects the global SU(6) symmetry while WYukawa, which includes the

MSSM matter chiral superﬁelds, does not. The SU(6)-symmetric part is

WHiggs(ˆ

Σ) = 1

3λTrˆ

Σ3+1

2MTrˆ

Σ2.(2)

We decompose ˆ

Σin terms of SU(5) representations as

Σ = 

−5S/√60 ¯

H/√2

H/√2S1l5/√60 + Σ

,(3)

where 1l5is the 5×5identity matrix and Σ≡ΣATAwith TAthe SU(5) generators.1

WHiggs(ˆ

Σ) is then expressed with these component ﬁelds as

WHiggs(ˆ

Σ) = 1

3λTr(Σ3) + 1

2λ¯

HΣH+1

2MTr(Σ2) + 1

2M¯

−1

3√15λS3−1

√15λS ¯

HH +1

√60λSTr(Σ2) + 1

4MS2.(4)

The terms in the ﬁrst line appear also in the minimal SUSY SU(5) [1,2], where the

coeﬃcients of these terms are independent. On the contrary, there are relations among

1We normalize these generators as Tr(TATB) = δAB /2.

the coeﬃcients in the present scenario, which play an important role in the following

discussion.

The adjoint Higgs ˆ

Σis assumed to have a VEV of the form

hˆ

Σi=ˆ

V·diag(1,1,1,1,−2,−2) ,(5)

where ˆ

V=M/λ.2This VEV spontaneously breaks the global SU(6) symmetry into

SU(4) ⊗SU(2) ⊗U(1); the SU(5) gauge symmetry, which corresponds to the second

to ﬁfth rows/columns, is broken into the SM gauge group, SU(3)C⊗SU(2)L⊗U(1)Y.

The SU(3)Cgauge group is inside the SU(4) global group. The symmetry breaking of

SU(6) →SU(4) ⊗SU(2) ⊗U(1) yields 35 −(15 + 3 + 1) = 16 NG bosons, among which

12 are absorbed by the massive gauge bosons corresponding to the broken generators of

SU(5) →SU(3)C⊗SU(2)L⊗U(1)Y. The rest four NG bosons, together with their SUSY

partner ﬁelds, appear as physical NG chiral superﬁelds—they are dubbed as the Mixed-

type superﬁelds in Ref. [31]. As we see below, these four massless chiral superﬁelds can

be identiﬁed as the MSSM Higgs superﬁelds.

We now calculate the mass spectrum of the component ﬁelds:







H+







,¯







HC1

HC2

HC3

H−

−H0







,(8)

Σ = 

Σ8Σ(3,2)

Σ(3∗,2) Σ3

+1

2√15 

21l30

0−31l2

Σ24 .(9)

The adjoint Higgs ﬁelds Σ8and Σ3have the identical mass

MΣ≡MΣ8=MΣ3=3

2λˆ

V . (10)

The components Σ(3,2) and Σ(3∗,2) are massless NG ﬁelds and absorbed by the SU(5) gauge

ﬁelds to be massive. The component Σ24 mixes with the SU(5) singlet ﬁeld S, whose mass

eigenvalues are found to be 3λˆ

V /2and λˆ

V /2. The color triplet Higgs ﬁelds HCand ¯

acquire a mass of

MHC=3

2λˆ

V , (11)

2This VEV can be decomposed as follows:

hˆ

Σi=3

5ˆ

V·diag(0,2,2,2,−3,−3) + 1

5ˆ

V·diag(5,−1,−1,−1,−1,−1) .(6)

The ﬁrst term breaks the SU(5) gauge group. It then follows that

hΣi=3

5ˆ

V·diag(2,2,2,−3,−3) ,hSi=−r12

5ˆ

V . (7)

which is equal to the adjoint Higgs mass. The MSSM Higgs mass is, on the other hand,

computed as

MH=1

2M−λ

√15 −s12

5ˆ

V!+λ

5(−3) ˆ

V= 0 ,(12)

verifying the expectation that Huand Hdare the NG chiral superﬁelds. We see that the

doublet-triplet mass splitting is naturally realized in this setup. Finally, the mass of the

SU(5) gauge bosons is found to be

MX= 3√2g5ˆ

V , (13)

with g5the SU(5) gauge coupling constant.

Notice that even though the SU(6) global symmetry is explicitly broken by the gauge

interactions and WYukawa,Huand Hdremain massless in the SUSY limit because of the

non-renormalization property of superpotential; in particular, radiative corrections to the

Kähler potential, which give multiplicative wave-function renormalization factors to the

component ﬁelds, do not generate a mass for Huand Hd(see, e.g., Ref. [11]).

Next, we consider the eﬀect of SUSY breaking. We here assume that the SUSY-

breaking eﬀect is mediated to the Higgs sector such that the global SU(6) symmetry is

respected. The soft SUSY-breaking terms in the Higgs sector, then, have the form

Lsoft =− 1

3AλλTrˆ

Σ3+1

2BMMTrˆ

Σ2+ h.c.!−2m2

ΣTr(ˆ

Σ†ˆ

Σ) ,(14)

where we use the same symbols for the scalar components of the Higgs ﬁelds. In terms of

the SU(5) representations, these soft terms are expressed as

Lsoft =−"1

3λAλTr(Σ3) + 1

2λAλ¯

HΣH−1

3√15λAλS3−1

√15λAλS¯

√60λAλSTr(Σ2) + 1

2BMMTr(Σ2) + 1

2BMM¯

HH +1

4BMMS2+ h.c.#

−m2

Σh|S|2+H†H+¯

H†¯

H+ 2Tr(Σ†Σ)i.(15)

In the presence of the soft SUSY-breaking terms, the VEV of ˆ

Σshifts from the one in

Eq. (5) [32]. The F-term is also induced in hˆ

Σi. We ﬁnd

hˆ

Σi=ˆ

V+ ∆ ˆ

V+Fˆ

Σθ2·diag(1,1,1,1,−2,−2) ,(16)

with

∆ˆ

V=2

λ(Aλ−BM)−4

λ2ˆ

VA2

λ−3AλBM+ 2B2

M+m2

Σ+O(M3

SUSY/M2

GUT),(17)

Fˆ

Σ= (Aλ−BM)ˆ

V+2

λAλBM−B2

M−m2

Σ+O(M3

SUSY/MGUT),(18)

where MGUT and MSUSY are the GUT and SUSY-breaking scales, and we take all of

the parameters to be real just for simplicity. As we see in the next section, these terms

generate the mass terms for the MSSM Higgs ﬁelds.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

MinimalNambu-GoldstoneHiggsModelinSupersymmetricSU(5)RevisitedKoichiHamaguchia;b*,ShihwenHora,NatsumiNagataaaDepartmentofPhysics,UniversityofTokyo,Bunkyo-ku,Tokyo1130033,JapanbKavliInstituteforthePhysicsandMathematicsoftheUniverse(KavliIPMU),UniversityofTokyo,Kashiwa2778583,JapanAbstractWerevisi...

展开>> 收起<<

Minimal Nambu-Goldstone Higgs Model in Supersymmetric SU5 Revisited Koichi Hamaguchiab Shihwen Hora Natsumi Nagataa.pdf

共36页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Minimal Nambu-Goldstone Higgs Model in Supersymmetric SU5 Revisited Koichi Hamaguchiab Shihwen Hora Natsumi Nagataa

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: