Physics Letters B 732 (2014) 247–254
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Physics Letters B
www.elsevier.com/locate/physletb
Padé approximation and glueball mass estimates in 3d and 4d
with N
c
=2, 3 colors
D. Dudal
a,∗
, M.S. Guimaraes
b
, S.P. Sorella
b
a
Ghent University, Department of Physics and Astronomy, Krijgslaan 281-S9, 9000 Gent, Belgium
b
Departamento de Física Teórica, Instituto de Física, UERJ — Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013 Maracanã,
Rio de Janeiro, Brazil
article info abstract
Article history:
Received 9 October 2013
Received in revised form 7 February 2014
Accepted 27 March 2014
Available online 2 April 2014
Editor: J.-P. Blaizot
A Padé approximation approach, rooted in an infrared moment technique, is employed to provide mass
estimates for various glueball states in pure gauge theories. The main input in this analysis are theoreti-
cally well-motivated fits to lattice gluon propagator data, which are by now available for both SU
(2) and
SU
(3) in 3 and 4 space–time dimensions. We construct appropriate gauge invariant and Lorentz covariant
operators in the (pseudo)scalar and (pseudo)tensor sector. Our estimates compare reasonably well with
a variety of lattice sources directly aimed at extracting glueball masses.
© 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
Although confinement is a well accepted phenomenon in pure
gauge theories [1], the extraction of the observable degrees of free-
dom, which ought to be glueballs, is a challenging task. Several
theoretical methods
1
have been tested, to name a few: qualitative
studies [2], effective Hamiltonian methods [3–6], AdS/CFT inspired
tools [7,8], lattice simulations [9–12], functional approaches [13,
14], Regge trajectory analyses [15], sum rules analyses [16],etc.
We refer to [17] for a recent review on the subject. Also, from the
experimental side, the status of glueballs is at the best inconclu-
sive as they are hard to detect, partially due to their mixing with
other states, see [18] for more details.
In this current note, we will apply a method developed in [19].
The
main purpose is to benefit from high precision lattice com-
putations of the gluon propagator in certain preferential gauges,
in particular the Landau gauge [20]. As these correlation functions
carry essential nonperturbative information on the gluon dynam-
ics, it seems natural to benefit from these data. As we are inter-
ested in continuum computations, we need functional forms for
e.g. the gluon propagator, as we plan to study the correlation func-
tions of bound state and thus of composite operators. As it will
become clear, we will probe the analyticity properties of the latter
*
Corresponding author.
E-mail addresses: da
vid.dudal@ugent.be (D. Dudal), msguimaraes@uerj.br
(M.S. Guimaraes), sorella@uerj.br (S.P. Sorella).
1
Sometimes with the inclusion of quarks to study the glueball spectrum in QCD
itself.
propagators, which is not an easy task if the input gluon propa-
gator is a complicated function. A recent numerical approach to
derive the spectral density of a (tree level) bound state propagator
given an a priori analytical prescription for the input constituent
propagator can be found in [21,22], thereby confirming the ana-
lytical results of [23]. A far more appealing approach would be to
only use the gluon lattice data, which is however still in its in-
fancy given all the difficulties to extend the lattice data from the
Euclidean region p
2
0 to the complex p
2
plane [24].
We will thus rely on the fits constructed for d
= 4 SU(3) data
in [25] (see also [26,27]) and for d
=3, 4 SU(2) data in [28], which
have the upshot of allowing for a pure analytical study of the cor-
relation functions over the complex plane. It is worth pointing out
that these fits are the result of a well-motivated and consistent
theoretical framework. We remind here that the Landau gauge, as
any covariant gauge fixing, suffers from the Gribov problem: there
exist multiple gauge equivalent field configurations fulfilling the
same gauge condition. An effective action formalism to deal with
the Gribov issue was worked out in a series of papers by Gribov
and Zwanziger [29–32], see also the recent work [33]. Basically, the
domain of integration of the gauge fields in the Euclidean func-
tional integral is further constrained to the first Gribov region
Ω,
whose boundary is the Gribov horizon, where the Faddeev–Popov
operator attains the first vanishing eigenvalue [34]. In recent years,
we included into the original derivation of [29–32], the dynamical
effects of dimension two condensates [35–38], resulting in what is
nowadays called the Refined Gribov–Zwanziger (RGZ) action.
Let us also notice that the relevance of dimension two con-
densat
es for certain nonperturbative effects in gauge theories was
already realized in e.g. [39–43]. The analytic form of the tree level
http://dx.doi.org/10.1016/j.physletb.2014.03.056
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
.