arXiv:hep-lat/9906023v2 2 Jul 1999
Screening Masses in SU(2) Pure Gauge Theory
The Mehta Research Institute,
Chhatnag Road, Jhusi, Allahabad 211019, India.
Department of Theoretical Physics,
Tata Institute of Fundamental Research,
Homi Bhabha Road, Mumbai 400005, India.
We perform a systematic scaling study of screening masses in pure
gauge SU(2) theory at temperatures above the phase transition tem-
perature. The major finite volume effect is seen to be spatial decon-
finement. We extract the screening masses in the infinite volume and
zero lattice spacing limit. We find that these physical results can be
deduced from runs on rather coarse lattices. Dimensional reduction is
clearly seen in the spectrum.
In a recent paper  we examined the spectrum of screening masses at
finite temperature in four dimensional SU(2) and SU(3) pure gauge theories.
Our primary result was that dimensional reduction could be seen in the
(gauge invariant) spectrum of the spatial transfer matrix of the theory. In
addition, we had shown that the specific details of the spectrum precluded
any attempt to understand it perturbatively. In this paper we present a
complete set of non-perturbative constraints on the effective dimensionally
reduced theory [2, 3, 4] at a temperature (T) above the phase transition
temperature (Tc) for the SU(2) case in the zero-lattice spacing and infinite
The study of screening masses is interesting for two reasons. First, they
are crucial to phenomenology because they determine whether the fireball
obtained in a relativistic heavy-ion collision is large enough for thermody-
namics. Second, the problem of understanding screening masses impinges
on several long-standing problems concerning the infrared behaviour of the
T > Tcphysics of non-Abelian gauge theories.
It is known that electric polarisations of gluons get a mass in perturbation
theory, whereas magnetic polarisations do not. Long ago, Linde pointed out
 that T > 0 perturbation theory breaks down at a finite order due to
this insufficient screening of the infrared in non-Abelian theories. The most
straightforward way to cure this infrared divergence would be if the magnetic
polarisations also get a mass non-perturbatively. There have been recent
attempts to measure such a mass in gauge-fixed lattice computations .
It was found long back that the solution could be more complicated
and intimately related to the dynamics of dimensionally reduced theories.
Jackiw and Templeton analysed perturbative expansions in massless and
super-renormalisable three dimensional theories  and found that subtle
non-perturbative effects screen the infrared singularities in such theories. In
a companion paper, Applequist and Pisarski discussed the possibility that
such effects might, among other things, also give rise to magnetic masses
. In fact the recent suggestion of Arnold and Yaffe that non-perturbative
terms and logarithms of the gauge coupling may be important in an expan-
sion of the Debye screening mass in powers of the coupling  may be seen
as an example of such non-perturbative effects. The generation of the other
screening masses are also non-perturbative. We discuss these issues further
after presenting our main results.
In this paper we report our measurements of the screening masses in the
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