Eur. Phys. J. C (2016) 76:22
DOI 10.1140/epjc/s10052-015-3866-y
Regular Article - Theoretical Physics
Infrared-improved soft-wall AdS/QCD model for mesons
Ling-Xiao Cui
1,2,3,4,a
, Zhen Fang
1,2,3,4,b
, Yue-Liang Wu
1,2,3,4,c
1
State Key Laboratory of Theoretical Physics (SKLTP), Beijing, People’s Republic of China
2
Kavli Institute for Theoretical Physics China (KITPC), Beijing, People’s Republic of China
3
Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
4
University of Chinese Academy of Sciences (UCAS), Beijing, People’s Republic of China
Received: 24 September 2015 / Accepted: 22 December 2015 / Published online: 19 January 2016
© The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract We construct and investigate an infrared-
improved soft-wall AdS/QCD model for mesons. Both lin-
ear confinement and chiral symmetry breaking of low energy
QCD are well characterized in such an infrared-improved
soft-wall AdS/QCD model. The model enables us to obtain
a more consistent numerical prediction for the mass spectra
of resonance scalar, pseudoscalar, vector, and axial-vector
mesons. In particular, the predicted mass for the lightest
ground state scalar meson shows good agreement with the
experimental data. The model also provides a remarkable
check for the Gell-Mann–Oakes–Renner relation and a sen-
sible result for the space-like pion form factor.
1 Introduction
The property of asymptotic freedom of quantum chromo-
dynamics (QCD) [1,2] at short distances or high energies
enables us to make perturbative treatment successfully on
QCD at ultraviolet (UV) region. At low energies, the QCD
perturbative method is no longer applicable due to strong
interactions at infrared (IR) region. So far we are still unable
to solve from first principles the low energy dynamics of
QCD, while the chiral symmetry breaking and linear con-
finement are known to be two important features of non-
perturbative QCD at the low energies. Many theoretical
approaches have been developed to describe these two inter-
esting properties of non-perturbative QCD. Such as the lat-
tice QCD and effective quantum field theories. One often
adopts effective quantum field theories to describe the low
energy dynamics of QCD based on the approximate global
chiral symmetry and dynamical chiral symmetry breaking
[3]. It has been shown explicitly in Ref. [4] how to derive the
a
e-mail: clxyx@itp.ac.cn
b
e-mail: fangzhen@itp.ac.cn
c
e-mail: ylwu@itp.ac.cn
spontaneous chiral symmetry breaking via the dynamically
generated effective Higgs-like potential and obtain a consis-
tent prediction for the mass spectra of the lowest lying nonet
pseudoscalar and scalar mesons, where the scalars can be
regarded as the composite Higgs-like bosons. While it is not
manifest in such a chiral effective field theory to make pre-
dictions for the mass spectra of high resonance meson states.
The idea of large N
c
expansion [5] and holographic
QCD which has been explicitly realized via the anti-de Sit-
ter/conformal field theory correspondence (AdS/CFT) [6–
8] supply a new point of view for solving the challenging
problem of strong interaction of QCD at low energies. The
AdS/CFT establishes the duality between the weakly cou-
pled supergravity in AdS
5
and the strongly coupled N = 4
super Yang–Mills gauge theory, which makes the calcula-
tions in strongly coupled theory feasible [9]. The so-called
top-down and bottom-up approaches are two complementary
methods in the way of pursuing the gravity/gauge duality of
QCD. The former starts from some brane configurations in
string theory to reproduce some basic features of QCD [11–
13]. The latter, which is known as AdS/QCD, consists of
bulk fields in a curved space to reproduce some experimen-
tal phenomena in QCD [14–17,22–24]. It was also noticed
in Ref. [25–28] that there exists a correspondence of matrix
elements obtained in AdS/CFT with the corresponding for-
mula by using the light-front representation. In this paper we
will focus on the bottom-up approach.
There are the so-called hard-wall and soft-wall AdS/QCD
models. The hard-wall AdS/QCD model was developed in
[14,15]. The pattern of chiral symmetry breaking can be
realized in the hard-wall AdS/QCD models; however, the
mass spectra for the excited mesons cannot match up with
the experimental data well. In the simple soft-wall AdS/QCD
model [16], a dilaton background field with quadratic growth
in the deep infrared (IR) region has been introduced to
show the Regge behavior for the higher excited vector
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