Padé approximation and glueball mass estimates in 3d and 4d with [formula omitted] colors

D Dudal,M.S Guimaraes,S.P Sorella

doi:10.1016/j.physletb.2014.03.056

D Dudal, M.S Guimaraes + Show 1 more

Open Access

https://doi.org/10.1016/j.physletb.2014.03.056

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Abstract

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 theoretically 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.

Highlights

Confinement is a well accepted phenomenon in pure gauge theories [1], the extraction of the observable degrees of freedom, which ought to be glueballs, is a challenging task
The one standard deviation errors on those are taken from the original papers and shown between parentheses. This observation of c.c. poles is what lies at the heart of the i -particles setup introduced in [48]: the Refined Gribov-Zwanziger (RGZ) gluon propagator can be expressed in terms of a pair of “complex” particles with c.c. masses
Our calculations have relied on the tree level confining gluon RGZ propagators, which encode nonperturbative information on the Gribov horizon and on dimension two condensates

Summary

Introduction

Confinement is a well accepted phenomenon in pure gauge theories [1], the extraction of the observable degrees of freedom, which ought to be glueballs, is a challenging task. The mass parameter λ4 is present because of the restriction to the Gribov region Ω, the others are related to a stabilization of the vacuum by means of d = 2 condensates This tree level analytic form is dictated by the underlying RGZ dynamics. One can even directly attempt to construct numerical estimates for the gluon spectral function based on either the Schwinger-Dyson equations [46] or “inversion” of the lattice data [47], but in none of the aforementioned cases a closed analytical expression can be derived, one is always reduced to fitting the numerical result with some a priori completely free to choose function This is different from the RGZ (loop expansion) approach, where the functional form are closed analytical expressions (albeit with the condensates’ values fixed via the lattice data).

The RGZ gluon propagator

Derivation of the spectral densities at lowest order

Setup of the moment problem

2.18 GeV no data

Applications

Discussion