Investigating Higgs self-interaction through di-Higgs plus jet production Kangyu Chai1 2Jiang-Hao Yu3 4 5 6 7yand Hao Zhang1 2 5z 1Theoretical Physics Division Institute of High Energy Physics

2025-05-03 0 0 621.18KB 9 页 10玖币

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Investigating Higgs self-interaction through di-Higgs plus jet production

Kangyu Chai,1, 2, ∗Jiang-Hao Yu,3, 4, 5, 6, 7, †and Hao Zhang1, 2, 5, ‡

1Theoretical Physics Division, Institute of High Energy Physics,

Chinese Academy of Sciences, Beijing 100049, China

2School of Physics, University of Chinese Academy of Science, Beijing 100049, China

3CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,

Chinese Academy of Sciences, Beijing 100190, China

4School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

5Center for High Energy Physics, Peking University, Beijing 100871, China

6School of Fundamental Physics and Mathematical Sciences,

Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China

7International Centre for Theoretical Physics Asia-Paciﬁc, Beijing/Hangzhou, China

(Dated: October 28, 2022)

The Higgs self coupling measurement is quite essential for determining the shape of the Higgs

potential and nature of the Higgs boson. We propose the di-Higgs plus jet ﬁnal states at hadron

colliders to increase the discovery sensitivity of the Higgs self coupling at the low invariant mass

region. Our simulation indicates that the allowed region of the Higgs self coupling would be further

narrowed from [−1.5,6.7] from the most recent ATLAS report down to [0.5,1.7]. Furthermore, we

ﬁnd negative Higgs self couplings would be disfavored beyond 2σconﬁdence level at a future 100 TeV

collider with the help of this signal.

I. INTRODUCTION

The discovery of the Higgs boson in 2012 [1, 2]

represents one milestone of modern particle physics.

It provides the evidence that the observed Higgs

boson is the one predicted by the Standard Model

(SM). While the SM parameters have essentially been

measured to a very high precision level, the Higgs

self couplings, important for electroweak symmetry

breaking and understanding its connection to other

fundamental questions like electroweak baryogenesis [3],

have not been measured directly yet. More importantly,

depending on the nature of the Higgs boson, such

as fundamental, pseudo-Goldstone, pseudo-Dilaton, or

partially composite, the shape of the Higgs potential

could be quite diﬀerent from the SM one [4]. Indeed,

a wide range of new physics (NP) models beyond

the SM predict modiﬁed Higgs potentials that lead

to O(1) corrections to the Higgs self couplings, the

Coleman-Weinberg [5–7] and the tadpole-induced [8, 9]

Higgs scenarios for example. Therefore, a precision

measurement of the Higgs self couplings would provide

an important benchmark for model identiﬁcation and

deepen our understanding on electroweak symmetry

breaking (EWSB).

Experimentally, the Higgs self couplings could be

measured directly from Higgs pair production or Higgs

associated production. Due to their lower cross sections

for the latter, in this work, we focus speciﬁcally on

the former that is dominated by gluon-gluon fusion

∗Electronic address: chaikangyu@ihep.ac.cn

†Electronic address: jhyu@itp.ac.cn

‡Electronic address: zhanghao@ihep.ac.cn

(ggF) at hadron colliders that has been studied in detail

earlier [10–12].1However, due to a strong cancellation

near the kinematical threshold, the cross sections for

Higgs pair production is highly suppressed – At a 13 TeV

pp collider, the ggF cross section for the Higgs pair

production is calculated at next-to-next-to leading order

in ﬁnite top-quark mass approximation, and the result

is 31.02+2.2%

−5.0%(scale)+4%

−18%(mtop)±3.0%(αs+ PDF) fb [17–

20]. Here, “scale” stands for the uncertainty from ﬁnite

order quantum chromodynamics calculation, “mtop” that

from the top-quark mass scheme [20, 21], and “αs+PDF”

that from the strong coupling constant and the parton

distribution functions. As a consequence, the Higgs self

couplings are only very loosely bounded [22], let alone

their precision determination.

Nevertheless, it is worth pointing out that current

experimental searches mainly focus on the high di-Higgs

invariant mass region, while it is perhaps universally

recognized that the it is the low mass region that is most

sensitive to NP. This motivates the study of Higgs self

couplings in the low mass region in this work. To increase

the signiﬁcance of the di-Higgs signal in this region, we

consider instead Higgs pair production through ggF with

an extra hard jet in the ﬁnal state, i.e., pp →hh+jet+X,

with Xany other particles in the ﬁnal state that we

are not interested in. Similar to the pure di-Higgs

production channel, we consider the bbγγ decay channel

of the Higgs pair for its cleanness and the unambiguity

in reconstructing the two Higgs particles.

1Lepton colliders could also measure Higgs self couplings directly,

see, for example, Refs. [13–16]. We focus on hadron colliders in

this work given the foreseen high-luminosity/energy era of the

Large Hadron Collider (LHC) in the near future.

arXiv:2210.14929v1 [hep-ph] 26 Oct 2022

The rest of the paper is organized as follows: In

section II, we set up the framework used in this work,

and brieﬂy summarize previous searches in di-Higgs

production. We then detail our strategy for pp →

hh+jet+Xsearches in section III. Results from detector-

level simulation for this channel are then presented in

section IV, and we conclude in section V.

II. HIGGS NATURE DETERMINATION VIA

HIGGS SELF INTERACTIONS

In the eﬀective ﬁeld theory (EFT) framework, new

physics eﬀect in the Higgs sector could be described using

Higgs EFT (HEFT) and standard model EFT (SMEFT)

in the broken and unbroken phase of electroweak

symmetry, respectively. Although SMEFT is the

most popular EFT scenario, its validity relies on the

assumptions that new physics should decouple at low

energy scale. On the other hand, the HEFT would

describe the Higgs potential in the broken phase and thus

describe the nature of the Higgs and the Higgs couplings

in a more general way.

In the HEFT scenario [23–30], the electroweak gauge

symmetry is broken down to the U(1)em and the global

SU (2)L×SU (2)R/SU (2)Vsymmetry in the Higgs sector

is non-linearly realized. Treating the Higgs boson has an

electroweak singlet, the HEFT Lagrangian at the leading

order reads

L=v2

4Tr DµU†DµU1+2ah

v+bh2

v2+···+ (1)

2(∂µh)2−1

2m2

hh2−κλm2

2vh3−κhm2

8v2h4+···

which parametrize the Higgs potential in the polynomial

form and does not depends on the decoupling behavior.

Depending on the nature of the Higgs boson, the

Higgs potential could be diﬀerent from the SM form as

parameterized by κλ,h.

In the SMEFT scenario [31–41], the Higgs potential

can be expressed as

Vh⊃ −µ2H†H+λH†H2+c6

Λ2λH†H3+··· (2)

where Λ is the UV cutoﬀ, c6is some dimensionless

Wilson coeﬃcient, and “···” represents some higher

dimensional operators of the SMEFT. The triple and

quartic Higgs couplings can then be easily matched to

above parameters after electroweak symmetry breaking

upon substituting Hfor (0, v +h)T/√2, leading to [4]

Vh⊃1

22λv2+3c6λv4

Λ2h2+λv 1 + 5c6v2

2Λ2h3

4λ1 + 15c6v2

2Λ2h4+···

where we have applied the minimization condition µ2=

λv2+ 3c6λv4/(4Λ2) to obtain the expression above and

TABLE I: Higgs self couplings κλand κhin diﬀerent

cases. Here, “MCH5+5” means the minimal composite

Higgs model [42, 43], “CTH8+1 ” the composite twin Higgs

model [44–46], and “CW” the Coleman-Weinberg Higgs

scenario [5–7]. The ﬁrst (second) subscript of the model name

represents the fundamental representation of the left-(right-

)handed top quark under the global symmetry, which is SO(5)

and SO(8) for “MCH5+5” and “CTH8+1”, respectively. In the

CW Higgs scenario, numbers in parentheses are results up to

the two-loop order from Refs.[5, 6].

Higgs self couplings κλκh

SM 1 1

SMEFT (with O6) 1 + c6v2

Λ21 + 6c6v2

Λ2

MCH5+5 1−3

2ξ1−25

3ξ

CTH8+1 1−3

2ξ1−25

3ξ

CW Higgs (doublet) 5

3(1.75) 11

3(4.43)

CW Higgs (singlets) 5

3(1.91) 11

3(4.10)

Tadpole-induced Higgs '0'0

discarded terms that are not interested for the study in

this work. Matching between the HEFT and the SMEFT

operators, the Higgs mass and the κ’s are deﬁned as, up

to O(1/Λ2),

h≡2λv2+3c6λv4

Λ2, κλ≡1 + c6v2

Λ2, κh≡1 + 6c6v2

Λ2.(3)

Note that one reproduces SM tree-level results upon

setting c6= 0. We comment on that (H†H)2(H†H) and

(H†DµH)∗(H†DµH) would also contribute to shifting the

Higgs mass and the Higgs self couplings from the kinetic

Lagrangian, we leave out these operators in our analysis since

they are highly constrained by electroweak precision physics

and/or hV V (V=W±, Z) couplings [4].

Depending on the nature of the Higgs boson, the Higgs

boson could be fundamental, pseudo-Goldstone, pseudo-

Dilaton, or partially composite due to strong dynamics

condensation [4]. For a fundamental Higgs boson, such as

the SM Higgs boson and its scalar/gauge extensions, and

supersymmetric models, the form of the Higgs potential

is polynomial on the Higgs doublet. In this case, there

usually exist additional scalars mixed with the SM Higgs

boson, thus modifying the SM Higgs self couplings with some

enhancement. In contrast, if the Higgs boson is pseudo-

Goldstone due to the vacuum misalignment, the curvature of

the Higgs ﬁeld would cause the Higgs couplings to be always

smaller than their SM values. On the other hand, if the Higgs

boson is a pseudo-dilaton, the Higgs potential would be of

purely the Coleman-Weinberg type and thus the Higgs self-

couplings would be larger than the SM ones. Finally, if the

symmetry breaking is partially induced by condensation, it is

possible to have the tadpole-induced symmetry breaking and

thus the Higgs self couplings are nearly zero. We summarize

the Higgs self couplings in diﬀerent scenarios discussed above

in Table I.

Therefore, measuring the Higgs self couplings could

possibly unveil the pattern of EWSB, which in turn helps

determine the nature of the Higgs boson. In this context,

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InvestigatingHiggsself-interactionthroughdi-HiggsplusjetproductionKangyuChai,1,2,Jiang-HaoYu,3,4,5,6,7,yandHaoZhang1,2,5,z1TheoreticalPhysicsDivision,InstituteofHighEnergyPhysics,ChineseAcademyofSciences,Beijing100049,China2SchoolofPhysics,UniversityofChineseAcademyofScience,Beijing100049,China3CAS...

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Investigating Higgs self-interaction through di-Higgs plus jet production Kangyu Chai1 2Jiang-Hao Yu3 4 5 6 7yand Hao Zhang1 2 5z 1Theoretical Physics Division Institute of High Energy Physics

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