Glueball mass estimate from finite temperature SU(2) lattice studies

Abstract

Finite temperature Monte Carlo simulations of the SU (2) Yang-Mills system on the lattice are used to obtain an estimate of the mass m G of the lowest gluonium state. Taking gluon matter in the hadronic regime, below the deconfinement transition, to follow the usual string or bag model pattern, we find from the temperature dependence of the energy density and of the specific heat that m G = (1.7 ± 0.5)x/~, where o is the string tension.Monte Carlo studies of the SU(2) Yang-Mills system on the lattice at finite physical temperature T have revealed a deconfinement transition [1][2][3] at the critical temperature T c ~ 0.5 x,~, where the system changes from gluonium matter to gluon gas; here a denotes the strong tension. Above Tc, at sufficiently high temperatures, this gluon gas attains the (parameter-free) Stefan-Boltzmann limit of an ideal massless boson gas [3]. Below Tc, the behaviour of the system is less well understood; but if we believe that it also provides there a reasonable approximation to the real quark-ghion world, then we expect gluonium matter to exhibit the same basic features as hadron matter.The description of hadrons as bound states of quarks leads to a resonance spectrum, starting with a lowest state of mass m 0. In the continuum, both bag for an ideal gas of resonances, or its derivatives, become singular at the temperature T c = 1/b; above Tc, the integral (2) is no longer defined. If we identify this critical behaviour with the deconfinement transition of the SU(2) lattice problem at T c = 0.5 x/o, then the approach to deconfinement is governed by the lowest gluonium mass m 0 = m o as scale. Comparing the form predicted by eq. (1) with that obtained from the Monte Carlo simulation of the SU(2) Yang-Mills system thus gives an estimate of the glueball mass m G . We note that this approach -using the resonance 332 0 031-9163/81/0000-0000/$ 02.50

QCD phase transition at finite temperature in the dual Ginzburg-Landau theory

“…Thus, the DGL theory suggests a proportional relation between the scalar glueball mass and the square root of the string tension at least near T C . It is worth mentioning that Engels et al [14] obtained a similar relation, m GB (T ) = (1.7 ± 0.5) k(T ), for the lowest scalar glueball at finite temperatures from the thermodynamical study on the SU(2) lattice gauge theory. Eqs.…”

“…We have considered the temperature dependence of the QCD- In particular, the glueball mass reduction at high temperatures would be an important ingredient in the QCD phase transition. In the pure gauge, there are only glueball excitations with the large masses ( > ∼ 1GeV) at low temperatures [2,14], and therefore it seems unnatural that the QCD phase transition takes place at a small critical temperature, T C ≃ 0.2GeV. This problem would be explained by the large reduction of the glueball mass near the critical temperature as is demonstrated in this paper.…”

SU(N) gauge theory couplings on asymmetric lattices

“…During the past year much progress has been made in extracting physically interesting quantities out of Monte Carlo simulations of non-abelian gauge theories on the lattice [1][2][3][4][5][6][7][8][9]. In order to assign absolute values to dimensional quantities like the string tension [1][2][3], glueball mass [3][4][5] or the critical temperature of the gluon gas [6][7][8][9], it is necessary to know the connection between the lattice and continuum scale parameters AL/AMoM [10,11].…”

“…In order to assign absolute values to dimensional quantities like the string tension [1][2][3], glueball mass [3][4][5] or the critical temperature of the gluon gas [6][7][8][9], it is necessary to know the connection between the lattice and continuum scale parameters AL/AMoM [10,11]. This ratio has by now been calculated for different lattice actions [12], including also the contribution of fermions [13] on a four-dimensional euclidean lattice.…”

Finite size effects in euclidean lattice thermodynamics for non-interacting bose and fermi systems

“…It is so far the only approach which allows a unified treatment over the entire temperature range, from the ideal gas at high temperature [1] through the deconfinement transition [1][2][3] into the non-perturbative phase [4]. It was noted in these studies, as well as in corresponding ones for the confinement problem, where the Monte Carlo approach to QCD was first introduced [5], that already for rather small lattices the results become roughly independent of lattice size.…”