Physics Letters B 742 (2015) 358–362
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
A divergence-free method to extract observables from correlation
functions
Si-xue Qin
Institute for Theoretical Physics, Goethe University, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received
24 November 2014
Received
in revised form 29 January 2015
Accepted
3 February 2015
Available
online 9 February 2015
Editor: A.
Ringwald
Keywords:
Hadron
spectroscopy
Quark–gluon
plasma
Transport
properties
Electrical
conductivity
Spectral
functions
Dyson–Schwinger
equations
Bethe–Salpeter
equation
Nonperturbative
methods
Correlation functions provide information on the properties of mesons in vacuum and of hot nuclear
matter. In this work, we present a new method to derive a well-defined spectral representation for
correlation functions. Combining this method with the quark gap equation and the inhomogeneous
Bethe–Salpeter equation in the rainbow-ladder approximation, we calculate in-vacuum masses of light
mesons and the electrical conductivity of the quark–gluon plasma. The analysis can be extended to other
observables of strong-interaction systems.
© 2015 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Hadrons contribute to most of the visible matter in our real
world and are undoubtedly an embodiment of dynamical chiral
symmetry breaking (DCSB) and confinement. Current and future
hadron physics facilities are focusing on hadron spectroscopy in
order to shed light on the mysteries of quantum chromodynamics
(QCD). On the other hand, it is believed that the Relativistic Heavy
Ion Collider (RHIC) and the Large Hadron Collider (LHC) are able
to create the quark–gluon plasma (QGP) state of the early Universe
through a “mini-big bang”. This provides us with the possibility
to study quark–gluon dynamics directly and to enrich our under-
standing
of the QCD phase diagram. The transport coefficients of
the QGP, which directly reflect details of the quark–gluon interac-
tion,
are highly interesting from both experimental and theoretical
viewpoints.
A
unified description for physics in the two areas has been a
central goal and great challenge for decades. Lattice QCD which is
based on Monte Carlo simulations of quantum fields on finite dis-
crete
spacetime lattices has achieved numerous significant results,
however, it also has its own limitations [1,2]. Thus, relativistically
covariant formalisms of continuum quantum field theory (QFT) are
E-mail address: sixueqin@th.physik.uni-frankfurt.de.
still desirable. Among them, the Dyson–Schwinger equation (DSE)
approach [3–5] is a framework that includes both DCSB and con-
finement
[6]. Remarkably, at zero temperature, T = 0, a single DSE
interaction kernel preserving the one-loop renormalization group
behavior of QCD has been able to provide a unified description
of the pion’s electromagnetic form factor [7], its valence-quark
distribution amplitude [8], and numerous other quantities [9,10].
Therefore, it is of great significance to extend the DSE approach to
further quantitative studies of hadron and QGP physics.
In
the DSE framework, hadrons, i.e., color-singlet bound states
of quarks, are described by the Bethe–Salpeter equation (BSE) or
the Faddeev equation. Solving these equations requires the quark
propagator, i.e., the solution of the gap equation, on the complex
momentum plane. The analytical structure of the quark propagator
strongly depends on the specified truncation scheme and interac-
tion
model. This may lead to technical difficulties in the study of
light-quark hadrons with masses above 1GeV and meson bound-
states
composed of one heavy and one light valence-quark. Those
aspects of these problems connected with continuation into the
complex plane can be solved using the perturbation theory inte-
gral
technique [11,12], as illustrated in Ref. [7], whereas, as high-
lighted
elsewhere [13], resolving the difficulties associated with
heavy-light mesons requires bound-state kernels which are more
sophisticated than that obtained in the simplest DSE truncation. At
nonzero temperature, T = 0, Matsubara frequencies are introduced
http://dx.doi.org/10.1016/j.physletb.2015.02.009
0370-2693/
© 2015 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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