Physics Letters B 735 (2014) 122–126
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Short-range force between two Higgs bosons
Feng Feng
a,b,1
, Yu Jia
c,d,b
, Wen-Long Sang
a,e,∗
a
School of Physical Science and Technology, Southwest University, Chongqing 400700, China
b
Center for High Energy Physics, Peking University, Beijing 100871, China
c
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
d
Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing 100049, China
e
State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
17 December 2013
Received
in revised form 9 June 2014
Accepted
10 June 2014
Available
online 16 June 2014
Editor:
A. Ringwald
The S-wave scattering length and the effective range of the Higgs boson in Standard Model are
studied using effective-field-theory approach. After incorporating the first-order electroweak correction,
the short-range force between two Higgs bosons remains weakly attractive for M
H
= 126 GeV. It is
interesting to find that the force range is about two order-of-magnitude larger than the Compton
wavelength of the Higgs boson, almost comparable with the typical length scale of the strong interaction.
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP
3
.
1. Introduction
The ground-breaking discovery of a new particle with mass
around 126 GeV by the Atlas and CMS Collaborations at CERN
Large Hadron Collider (LHC) in July 2012 [1,2], heralds an excit-
ing
new era of particle physics. Undoubtedly, the top priority in
the coming years is to pin down the detailed property of this
new boson as precisely as possible, e.g., its quantum number, de-
cay
and production patterns [3]. Hopefully, one will finally be able
to determine whether this new boson is the long-sought Brout–
Englert–Higgs
boson of Standard Model (SM)
2
or of some exotic
origin.
The
SM Higgs boson is an elementary scalar particle carrying
J
PC
= 0
++
. An enormous amount of work has been devoted to
exploring the physics involving an individual Higgs boson, while
the respective studies concerning the multi-Higgs-boson dynamics,
such as double- or triple-Higgs productions at LHC experiments,
are still in the infancy stage [3]. Nevertheless, a thorough investi-
gation
of the latter is crucial in unraveling the nature of the Higgs
potential since it directly probes the self-coupling of the Higgs
bosons.
It
is of fundamental curiosity to inquire the short-range force
which two Higgs bosons would experience. A few decades ago,
*
Corresponding author at: School of Physical Science and Technology, Southwest
University, Chongqing 400700, China.
E-mail
address: wlsang@ihep.ac.cn (W.-L. Sang).
1
Current address: School of Science, China University of Mining and Technology,
Beijing 100083, China.
2
For simplicity, hereafter we shall simply call it Higgs boson.
Cahn and Suzuki [5], as well as Rupp [6], studied the inter-
action
between two Higgs bosons by utilizing some nonper-
turbative
methods, only including the Higgs self-coupling. They
claimed that the attraction would become strong enough as M
H
>
1.3TeV to bind them together into a Higgs–Higgs bound state
(Higgsium), albeit highly unstable. Such a large Higgs mass vi-
olates
the perturbative unitarity bound [4]. If the new particle
discovered in LHC is indeed the SM Higgs boson, the Higgsium
seems unlikely to be formed in the first place. This expectation
is supported by the recent lattice simulation of the electroweak
gauge model [7]. Nevertheless, Grinstein and Trott recently sug-
gested
that the possibility for the existence of the light Higgsium
might be still open due to some new physics scenario at TeV
scale [8].
The
model-independent parameters that characterize any short-
range
force are scattering length and effective range. The effective-
field-theory
(EFT) approach provides a systematic framework to
expedite inferring these parameters. The aim of this paper is to
decipher the short-range force experienced by two God particles
following this modern doctrine. In particular, we will investigate
the influence of the W , Z and top quark on the inter-Higgs force.
It will be interesting if our predictions can be confronted by the
future lattice simulation, or even by the double Higgs production
experiments.
2. The Higgs sector in SM
After the spontaneous electroweak symmetry breaking, the
Higgs sector in SM Lagrangian reads (in unitary gauge):
http://dx.doi.org/10.1016/j.physletb.2014.06.024
0370-2693/
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by
SCOAP
3
.