SMEFT eects on gravitational wave spectrum from electroweak phase transition Katsuya Hashinoa and Daiki Uedab

2025-05-03 0 0 6.49MB 33 页 10玖币

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SMEFT eﬀects on gravitational wave spectrum from electroweak

phase transition

Katsuya Hashino(a), and Daiki Ueda(b)

(a) Department of Physics, Faculty of Science and Technology, Tokyo University of Science,

Noda, Chiba 278-8510, Japan

(b) Center for High Energy Physics, Peking University, Beijing 100871, China

Abstract

Future gravitational wave observations are potentially sensitive to new physics cor-

rections to the Higgs potential once the ﬁrst-order electroweak phase transition arises.

We study the SMEFT dimension-six operator eﬀects on the Higgs potential, where

three types of eﬀects are taken into account: (i) SMEFT tree level eﬀect on ϕ6oper-

ator, (ii) SMEFT tree level eﬀect on the wave function renormalization of the Higgs

ﬁeld, and (iii) SMEFT top-quark one-loop level eﬀect. The sensitivity of future grav-

itational wave observations to these eﬀects is numerically calculated by performing a

Fisher matrix analysis. We ﬁnd that the future gravitational wave observations can

be sensitive to (ii) and (iii) once the ﬁrst-order electroweak phase transition arises

from (i). The dimension-eight ϕ8operator eﬀects on the ﬁrst-order electroweak phase

transition are also discussed. The sensitivities of the future gravitational wave obser-

vations are also compared with those of future collider experiments.

arXiv:2210.11241v2 [hep-ph] 1 May 2023

Contents

1 Introduction 1

2 Formula 3

3 First-order phase transitions in SMEFT 6

3.1 Higgspotential ................................. 6

3.2 First-order electroweak phase transition . . . . . . . . . . . . . . . . . . . . 7

4 GW spectrum and statistical analysis 11

4.1 GW spectrum from ﬁrst-order phase transition . . . . . . . . . . . . . . . . 11

4.2 Statistical analysis in GW experiments . . . . . . . . . . . . . . . . . . . . 13

5 Numerical results 17

6 Discussion 19

7 Summary 21

A Sensitivity reach of DECIGO at diﬀerent bench mark point of bubble

wall velocity 22

1 Introduction

The CERN large hadron collider (LHC) has discovered the Higgs boson [1,2] and measured

its properties closely resembling the Standard Model (SM). The discovery of the Higgs boson

strengthened the conviction of the SM. However, the shape of the Higgs potential is still

unknown, and determining the nature of the electroweak phase transition would be a major

scientiﬁc goal. In particular, the strongly ﬁrst-order electroweak phase transition (SFO-

EWPT) could provide suitable conditions for achieving the observed baryon asymmetry of

the universe (BAU) [3–5] in the electroweak baryogenesis scenario, but the SFO-EWPT in

the SM only arises for a Higgs mass mh.65 GeV [6–10] well below the measured Higgs

mass 125 GeV [11]. In these circumstances, there is growing attention to new physics (NP)

eﬀects on the Higgs potential from both theoretical and experimental points of view, but

the lack of new particle discoveries at the LHC strengthens the possibility of the NP scale

higher than the electroweak symmetry breaking (EWSB) scale.

This situation motivates the eﬀective ﬁeld theory (EFT) approach to describe the NP

eﬀects. The Standard Model Eﬀective Field Theory (SMEFT) [12–15] is one of the actively

studied EFTs, and information about the NP eﬀects is transferred to higher-dimensional

operators of EFTs consisting of the SM ﬁelds. To generate the SFO-EWPT, a consider-

able amount of literature [16–46] has considered the SMEFT dimension-six ϕ6operator#1.

In the context of the electroweak baryogenesis scenario, the other SMEFT dimension-six

operators [18,25,44–46,48] are also studied. On the experimental grounds, there is grow-

ing interest in the constraints on the SMEFT Wilson coeﬃcients from the current and

past experimental data, and future collider experiments, e.g., high-luminosity LHC [49],

the International Linear Collider (ILC) [50], the Compact LInear Collider (CLIC) [51],

the Future Circular Collider of electrons and positrons (FCC-ee) [52], and the Circular

Electron Positron Collider (CEPC) [53]. Furthermore, the SFO-EWPT predicts stochas-

tic background of gravitational waves (GWs), and its spectrum can be peaked around

the future interferometer experiment band with milli- to deci-Hertz, such as Laser In-

terferometer Space Antenna (LISA) [54], DECi-hertz Interferometer Gravitational wave

Observatory (DECIGO) [55], and Big-Bang Observer (BBO) [56]. Therefore, the sen-

sitivities of future GW observations to the SMEFT ϕ6operator also have been investi-

gated [19,20,27,28,31–33,37,39–41,43,46].

The previous works mainly studied a parameter space to generate a detectable amount

of GWs, but they have not quantiﬁed how precisely the NP eﬀects can be measured once

the GWs are detected. In light of these circumstances, in the previous works of the NP

search by the GW observations [57], the method of Fisher matrix analysis was proposed to

evaluate the expected sensitivities to NP model parameters. This analysis quantiﬁes how

precisely the NP model parameters can be measured by the GWs observations, and it is

clariﬁed that the GW observations potentially have higher sensitivities to small deviations

of the Higgs potential by the NP eﬀects than the future collider experiments such as the

ILC-250. This result naturally leads us to study the sub-dominant SMEFT eﬀects on the

Higgs potential and the sensitivities of the GW observations to them.

In this paper, we study the SMEFT dimension-six operator corrections to the Higgs

potential and the sensitivities of the GW observations to them. We will focus on three

types of the SMEFT dimension-six operator eﬀects: (i) SMEFT tree level eﬀect on ϕ6,

(ii) SMEFT tree level eﬀects on the wave function renormalization of the Higgs ﬁeld, and

(iii) SMEFT one-loop top-quark eﬀects. Type (i) dominates the SMEFT eﬀect on the

Higgs potential and can achieve the SFO-EWPT. Type (ii) is the tree level eﬀects, but

not dominant eﬀects because of the suppression by interference eﬀects with the Higgs self

couplings. Type (iii) arises from the loop diagrams and can not dominate the SMEFT eﬀect,

but it can be a measurable eﬀect because of the large top Yukawa coupling. Therefore, we

focus on a scenario where the SFO-EWPT mainly arises by (i), and the Higgs potential is

#1In Refs. [23,47], the validity of the SMEFT description for the SFO-EWPT is questioned; see Sec. 6.

slightly shifted by (ii) and (iii). We will evaluate the SMEFT eﬀects on the GW spectrum

and perform the Fisher matrix analysis to clarify the expected sensitivities of future GW

observations to (ii) and (iii). Their expected sensitivities to (ii) and (iii) are also discussed

when the SMEFT dimension-eight ϕ8operator is added.

This paper is organized as follows. In Sec. 2, we provide formulae of the SMEFT

dimension-six operator eﬀects on the Higgs potential, and in the following section, we

evaluate the SMEFT eﬀects on the SFO-EWPT. In Sec. 4, we brieﬂy review Refs. [55,57–63]

and summarize formulae of the GW spectrum from the SFO-EWPT and how to evaluate

the sensitivities of future GWs observations to the SMEFT eﬀects, e.g., the Fisher matrix

analysis. In Sec. 5, the results of numerical calculations are collected. In Sec. 6, the

SMEFT dimension-eight operator eﬀects on the SFO-EWPT are discussed. We ﬁnish with

the summary of the paper in Sec. 7.

2 Formula

The information of the NP particles is transferred to higher-dimensional operators of the

SMEFT when the NP scale is higher than the EWSB scale. The SMEFT operators con-

tribute to the Higgs potential and aﬀect the EWPT. In this section, we provide the for-

mulae of the SMEFT dimension-six operator eﬀects on the Higgs potential by taking into

account the SMEFT eﬀects on the wave function renormalization of the Higgs ﬁeld and the

SMEFT top-quark eﬀects. In particular, we newly consider the dimension-six OuH operator

eﬀects. For convenience, we also summarize the OH,OHD, and OHeﬀects as studied in

Refs. [16–24,26,27,29,31–37,39,42–47]. The Lagrangian of the SMEFT is deﬁned as [12]

LSMEFT =LSM +X

CiOi,(2.1)

where the ﬁrst term on the right-hand side is the SM Lagrangian, and the second term

denotes the higher-dimensional operators consisting of the SM ﬁelds. The Lagrangian

of Eq. (2.1) is invariant under the SM gauge symmetry, and all the SM particles, e.g.,

W, Z, H, and t, are dynamical. We consider the SMEFT operators involving Higgs and

top-quarks, which contribute to the Higgs potential since the top Yukawa coupling is large.

For simplicity, we will restrict this study to CP-conserving interactions. The dimension-six

operators relevant to the Higgs potential up to the tree level are

OH= (H†H)(H†H),(2.2)

OHD = (H†DµH)∗(H†DµH),(2.3)

OH= (H†H)3,(2.4)

where the Higgs ﬁeld is written in unitary gauge as √2HT= (0, ϕ) = (0, v +h) with

v= 246 GeV. The dimension-six operators involving the Higgs ﬁelds and top quarks are

listed as follows,

(OuH )ij = (H†H)(¯qiuj˜

H),(2.5)

(O(1)

Hq)ij = (H†i←→

DµH)(¯qiγµqj),(2.6)

(O(3)

Hq)ij = (H†i←→

µH)(¯qiτIγµqj),(2.7)

(OHu)ij = (H†i←→

DµH)(¯uiγµuj),(2.8)

with the derivative

H†←→

µH=H†τIDµH−(DµH)†τIH. (2.9)

Here, qis the SU(2)Lquark doublet, uthe right-handed up-type quark, quark-ﬂavor indices

i, j, an SU(2)Lindex I, and τIthe Pauli matrices.

The Higgs Lagrangian including the SMEFT corrections is deﬁned as

Lϕ=1

2(∂µϕ)2−1

2µ2ϕ2−1

4λϕ4+ ∆LSMEFT,(2.10)

where the ﬁrst, second, and third terms represent the SM renormalizable interactions, and

the last term denotes the SMEFT corrections. We summarize the SMEFT corrections to

the Higgs Lagrangian for each operator as follows:

•OH— Substituting the Higgs ﬁeld √2HT= (0, ϕ) into OHyields the correction at

the tree-level as follows,

∆LSMEFT =1

8CHϕ6.(2.11)

As studied in Ref. [16–24,26,27,29,31–37,39,42–46], the ϕ6operator can give rise

to the SFO-EWPT and is a dominant SMEFT eﬀect on the Higgs Lagrangian. Al-

though, as studied in Refs. [23,47], the SMEFT dimension-six operator descriptions

of the SFO-EWPT are limited, the SMEFT with an additional dimension-eight ϕ8

operator can be UV completed in an extended model with a singlet scalar boson and

describe the SFO-EWPT [47]. The additional dimension-eight operator eﬀects on the

sensitivity reach of the future GW observations are discussed in Sec. 6.

•OHD — As shown in Ref. [47], this operator yields the correction at the tree level to

the Higgs Lagrangian as follows,

∆LSMEFT =1

4CHDϕ2(∂µϕ)2.(2.12)

As discussed in the next section, Eq. (2.12) contributes to the Higgs potential by the

wave function renormalization of ϕ.

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SMEFTeectsongravitationalwavespectrumfromelectroweakphasetransitionKatsuyaHashino(a),andDaikiUeda(b)(a)DepartmentofPhysics,FacultyofScienceandTechnology,TokyoUniversityofScience,Noda,Chiba278-8510,Japan(b)CenterforHighEnergyPhysics,PekingUniversity,Beijing100871,ChinaAbstractFuturegravitationalwave...

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SMEFT eects on gravitational wave spectrum from electroweak phase transition Katsuya Hashinoa and Daiki Uedab

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