LHC单希格斯产额探针：揭示希格斯自耦合的新途径

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本文主要探讨了利用大型强子对撞机(LHC)单次希格斯玻色子(Higgs boson)的生产来探测希格斯自耦合的新方法。传统的测量手段通常关注希格斯对的总截面和微分分布，然而，作者提出了一种创新策略，即通过分析那些受到异常三线性希格斯自耦合影响的电弱环路效应，来间接测量这种重要的希格斯粒子特性。研究者首先详细计算了各种希格斯产生机制，包括 gluon-gluon fusion (ggF), vector-boson fusion (VBF), weak boson associated production (WH, ZH), top-quark相关过程 (ttH, HttbarH)，以及希格斯的衰变模式，如γγ(光子对), WW* / ZZ*→4 fermions (四重轻子), bb(底夸克对)和ττ(τ子对)。他们在8 TeV LHC实验数据上进行参数拟合，以估算出对三线性自耦合的敏感度。结果表明，这种方法能够提供与直接测量希格斯对生产相媲美的自耦合限制，而且在当前和未来的LHC运行中将有更大的提升潜力。这不仅拓展了我们在理解基本粒子相互作用方面的研究范围，也为希格斯物理的研究提供了新的洞察途径，特别是在探索标准模型之外的潜在新物理时。本文的贡献在于提出了一个新颖的手段来测试希格斯自耦合，这对于深化对希格斯粒子性质的理解，以及可能的理论突破具有重要意义。通过这种方法，物理学家能够在不依赖于精确测量希格斯对事件的情况下，进一步探索宇宙的基本结构和规律。

JHEP12(2016)080

same eﬀect for all processes, without any dependence on the kinematics. Denoting as M

a generic amplitude for single Higgs production or a Higgs decay width, the correction to

M induced by the λ

-dependent diagram of ﬁgure 1 can be written as

(δM)



− 1



, Z

1 − κ

δZ

, (2.2)

where M

is the lowest-order amplitude and

δZ

= −

√

2 π



2π

√

− 1



. (2.3)

In order to extend the range of convergence of the perturbative expansion to large

values of κ

, the one-loop contribution in Z

has been resummed. In so doing, terms of

O((κ

α)

) which are expected to be the dominant higher-order corrections at large κ

are

correctly accounted for.

In addition to the λ

universal term above, amplitudes depend linearly on λ

dif-

ferently for each process and kinematics. Let M

be the Born amplitude corresponding

to a given process (production or decay). At the level of cross section or decay width,

the linear dependence on λ

originates from the interference of the Born amplitude M

and the virtual EW amplitude M

, besides the wave function renormalisation constant.

The amplitude M

involves one-loop diagrams when the process at LO is described by

tree-level diagrams, like, e.g., vector boson fusion production, while it involves two-loop

diagrams when the LO contribution is given by one-loop diagrams, like, e.g., gluon-gluon-

fusion production. The λ

-linearly-dependent contributions in M

, which we denote as

, can be obtained for any process by evaluating in the SM the diagrams that contain

one trilinear Higgs coupling (M

) and then rescaling them by a factor κ

. In order

to correctly identify M

(the contributions related to the H

interaction) in the M

amplitude in the SM, it is convenient to choose a speciﬁc gauge, namely the unitary gauge.

In a renormalisable R

gauge, λ

-dependent diagrams are due not only to the interaction

among three physical Higgs ﬁelds but also to the interaction among one physical Higgs and

two unphysical scalars, making the identiﬁcation less straightforward.

Once all the contributions from M

and Z

are taken into account, denoting as Σ

a generic cross section for single Higgs production or a Higgs decay width, the corrections

induced by an anomalous trilinear coupling modify the LO prediction (Σ

) according to

NLO

= Z

(1 + κ

) , (2.4)

where the coeﬃcient C

, which originates from M

, depends on the process and the

kinematical observable considered, while Z

is universal, see eq. (2.2). Here and in the

following the LO contribution is understood as including QCD corrections so that the labels

LO and NLO refer to EW corrections. We remind that among all terms contributing to

the complete EW corrections we consider only the part relevant for our discussion, i.e., the

one related to the Higgs trilinear interaction. The Σ

NLO

in the SM can be obtained from

eq. (2.4) setting κ

= 1 and expanding the Z

factor, or

NLO

= Σ

(1 + C

+ δZ

) . (2.5)

– 5 –

JHEP12(2016)080

Thus, the relative corrections induced by an anomalous trilinear Higgs self-coupling can be

expressed as

δΣ

≡

NLO

− Σ

NLO

= Z

− (1 + δZ

) + (Z

− 1)C

, (2.6)

which, neglecting O(κ

) terms in the r.h.s, can be compactly written as

δΣ

= (κ

− 1)C

+ (κ

− 1)C

, (2.7)

with

δZ

(1 − κ

δZ

)

. (2.8)

Before describing the method and results of the calculation of the C

coeﬃcients, we

scrutinise the theoretical robustness of eq. (2.6) and its range of validity. Our aim is to

employ eq. (2.6) to evaluate the LHC sensitivity on λ

without making “a priori” any

assumptions on the value of the parameter κ

. We will, however, demand as a consistency

constraint that, for large values of κ

, λ

-dependent terms from O(α

) corrections with

j > 1 do not overwhelm the eﬀects from the C

coeﬃcients. In order to take into account

all the O((κ

α)

) contributions and perform a resummation of the κ

δZ

terms in Z

need to impose that κ

δZ

. 1, i.e., |κ

| . 25. The corresponding parametric uncertainty

in Σ

NLO

is therefore given by O((κ

)) terms that can be sizeable for large values of

. The size of such missing terms can be estimated by calculating the diﬀerence between

δΣ

computed using eq. (2.6) and eq. (2.7), or equivalently δ(Σ

NLO

/Σ

) ' κ

δZ

Requiring this uncertainty to be . 10% and assuming as an order of magnitude of the

two-loop contribution C

δZ

∼ 10

−5

, we ﬁnd |κ

| . 20, which we take as the range of

validity of our perturbative calculation.

At variance with the SM, where the Higgs self coupling and the Higgs mass are related,

in our setup they are two independent parameters. This in general spoils the renormalis-

ability of the model and makes its parameters sensitive to the UV scales. However, one

knows a priori that the λ

-dependent O(α) corrections to Σ in eq. (2.6) are ﬁnite. The

reason is twofold:

i) the LO result does not depend on λ

and therefore no renormalisation of λ

at NLO

is either needed nor possible.

ii) All the counterterms needed at NLO do not contain divergent contributions propor-

tional to the trilinear coupling.

This last point can be understood as follows: the only counterterm that contains

divergent contributions proportional to λ

is the Higgs mass counterterm. However, the

dependence in Σ

is all of kinematical origin. Therefore, when the NLO corrections

are calculated, no renormalisation of m

is needed.

The arguments above are suﬃcient for all the processes except for H → γγ, which

deserves a dedicated discussion. In a R

gauge the LO dependence of Γ(H → γγ) upon

is not purely kinematical, but it also comes from diagrams containing unphysical

– 6 –

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