大型强子对撞机矢量玻色子融合对三线性希格斯耦合的约束及相关的希格斯产生资源-CSDN文库

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JHEP07(2017)083

Published for SISSA by Springer

Received: October 27, 2016

Revised: May 13, 2017

Accepted: June 27, 2017

Published: July 17, 2017

Constraints on the trilinear Higgs coupling from

vector boson fusion and associated Higgs production

at the LHC

Wojciech Bizo´n,

Martin Gorbahn,

Ulrich Haisch

a,c

and Giulia Zanderighi

a,c

Rudolf Peierls Centre for Theoretical Physics, University of Oxford,

OX1 3NP Oxford, U.K.

Department of Mathematical Sciences, University of Liverpool,

L69 7ZL Liverpool, U.K.

CERN, Theoretical Physics Department,

CH-1211 Geneva 23, Switzerland

E-mail: Wojciech.Bizon@physics.ox.ac.uk,

Martin.Gorbahn@liverpool.ac.uk, Ulrich.Haisch@physics.ox.ac.uk,

Giulia.Zanderighi@physics.ox.ac.uk

Abstract: We examine the constraints on the trilinear Higgs coupling λ that originate

from associated (V h) and vector boson fusion (VBF) Higgs production in pp collisions in the

context of the Standard Model eﬀective ﬁeld theory. The 1-loop contributions to pp → V h

and pp → jjh that stem from insertions of the dimension-6 operator O

= −λ



†



are calculated and combined with the O(λ) corrections to the partial decay widths of

the Higgs boson. Employing next-to-next-to-leading order QCD predictions, we analyse

the sensitivity of current and forthcoming measurements of the signal strengths in V h

and VBF Higgs production to changes in λ. We show that future LHC runs may be able

to probe modiﬁcations of λ with a sensitivity similar to the one that is expected to arise

from determinations of double-Higgs production. The sensitivity of diﬀerential V h and

VBF Higgs distributions to a modiﬁed h

coupling is also studied.

Keywords: Eﬀective Field Theories, Higgs Physics, Perturbative QCD

ArXiv ePrint: 1610.05771

Open Access,

 The Authors.

Article funded by SCOAP

https://doi.org/10.1007/JHEP07(2017)083

JHEP07(2017)083

O(0.1 fb) at 14 TeV centre-of-mass energy (

√

s) even the high-luminosity option of the

LHC (HL-LHC) will only be able to set very loose bounds on the Higgs quartic. The

prospect to observe double-Higgs production at the HL-LHC is considerably better be-

cause at 14 TeV the pp → hh production cross section amounts to O(35 fb) [2–9]. Mea-

suring double-Higgs production at the HL-LHC however still remains challenging (see for

instance [10–27]) and as a result even with the full data set of 3 ab

−1

only an O(1) deter-

mination of the trilinear Higgs coupling seems possible under optimistic assumptions.

A second possibility consists in studying the eﬀects that a modiﬁcation of λ has at loop

level in single-Higgs production. In fact, such indirect probes of the h

coupling have been

ﬁrst proposed in the context precision studies of e

−

→ hZ [28, 29] and subsequently

extended to observables accessible at hadronic machines such as the LHC [30, 31]. For

both types of colliders it has been shown that future determination of λ via loop eﬀects

are complementary to the direct HL-LHC determination through pp → hh, since these

probes can provide competitive constraints under the simpliﬁed assumption that new-

physics eﬀects dominantly modify the h

coupling.

This paper is a sequel to the article [30], in which two of us have calculated the O(λ)

corrections to the gg → h and h → γγ processes that arise at the 2-loop level within the

SM eﬀective ﬁeld theory (SMEFT). The discussion in the present paper focuses instead

on associated (V h) and vector boson fusion (VBF) Higgs production. Speciﬁcally, we

compute the 1-loop contributions to the pp → V h and pp → jjh amplitudes that result

from insertions of the eﬀective operator O

= −λ



†



. Combining these contributions

with the O(λ) corrections to the partial decay widths of the Higgs boson, we analyse the

sensitivity of present and future LHC measurements of the V h and VBF Higgs processes

to shifts in the trilinear Higgs interactions. In order to obtain high-precision predictions

for the V h and VBF Higgs cross sections we include QCD corrections up to next-to-next-

to-leading order (NNLO) in our study. We ﬁnd that HL-LHC measurements of the V h

and VBF signal strengths may allow to set bounds on the Wilson coeﬃcient of O

that are

comparable to the limits that are expected to arise from HL-LHC determinations of pp →

hh. By studying diﬀerential distributions it may even be possible to improve the obtained

constraints. We present NNLO predictions for the V h and VBF Higgs distributions that

are most sensitive to the shifts in the trilinear Higgs interactions. Our analysis shows that

measurements of the spectra in V h production provide sensitivity to the relative sign of

the Wilson coeﬃcient of O

. The discriminating power in VBF Higgs production is less

pronounced compared to the V h channels. A similar investigation of the V h and VBF Higgs

processes in an anomalous coupling approach was presented in [31]. Whenever indicated

we will highlight the similarities and diﬀerences between this and our work.

The article at hand is structured in the following way. In section 2 we introduce the

eﬀective interactions relevant for the computations performed in our paper. The results

of our loop calculations of the V V h vertex and the partial decay widths of the Higgs

boson are presented in section 3 and 4, respectively. The computations of the vector boson

mediated Higgs cross sections and distributions are described in section 5 and 6. Our

numerical analysis is presented in section 7. Both LHC Run I and HL-LHC constraints on

the trilinear Higgs coupling are considered. Section 8 contains our conclusions.

– 2 –

JHEP07(2017)083

2 Preliminaries

Physics beyond the SM (BSM) can be described in a model-independent fashion by sup-

plementing the SM Lagrangian L

by eﬀective operators O

of mass dimension six. In

our article, we will consider the following Lagrangian

L = L

k=6,H

¯c

, (2.1)

where

= −λ



†



, O

∂



†



∂



†



, (2.2)

with λ deﬁned as in (1.2) and H denoting the SM Higgs doublet. The dimension-6 operators

introduced in (2.2) modify the trilinear Higgs coupling. Upon canonical normalisation of

the Higgs kinetic term, one ﬁnds

L ⊃ −λc

= −λ



1 + ¯c

−

3¯c



, (2.3)

where the Wilson coeﬃcients ¯c

and ¯c

as well as the trilinear Higgs coupling λ are all

understood to be evaluated at the weak scale hereafter denoted by µ

It is important to realise that the indirect probes of the trilinear Higgs coupling con-

sidered in our work measure c

, i.e. the coeﬃcient multiplying the interaction term −λvh

in the eﬀective Higgs potential after EWSB. Relating the coeﬃcient c

to any underlying

theory, such as for instance the SMEFT, necessarily involves model assumptions. In the

following we will focus our attention on BSM scenarios where the Wilson coeﬃcient ¯c

rep-

resents the only relevant modiﬁcation of the h

vertex. Corrections due to ¯c

are on the

other hand ignored. Such eﬀects will cause a universal shift in all Higgs-boson couplings

at tree level and also induce logarithmically-enhanced contributions to the oblique param-

eters S and T at the 1-loop level [32]. The Wilson coeﬃcient ¯c

can therefore be probed

by means other than V h or VBF Higgs production that are the focal point of the present

work. We also do not consider eﬀects of dimension-8 operators such as −λ¯c



†



Under these model assumptions one obtains the simple relation

= 1 + ¯c

, (2.4)

which allows one to parameterise modiﬁcations of the h

vertex in terms of the Wilson

coeﬃcient ¯c

. In our article we will use this parameterisation, but emphasise that all

formulas and results presented in the following sections can be translated to an anomalous

coupling approach by simply replacing ¯c

with c

− 1. In fact, we have veriﬁed that to

the perturbative order considered here and in [31] the calculations of V h and VBF Higgs

production in the SMEFT and the anomalous coupling framework agree exactly if the

relation (2.4) is taken into account.

The eﬀects of −λ¯c



†



could be easily incorporated in our analysis by shifting the coeﬃcient c

introduced in (2.3) by 2¯c

[30].

– 3 –

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