TheK/πratio from condensed Polyakov loops

Abstract

We perform a field-theoretical computation of hadron production in large systems at the QCD confinement phase transition associated with restoration of the Z(3) global symmetry. This occurs from the decay of a condensate for the Polyakov loop. From the effective potential for the Polyakov loop, its mass just below the confinement temperature Tc is in between the vacuum masses of the pion and that of the kaon. Therefore, due to phase-space restrictions the number of produced kaons is roughly an order of magnitude smaller than that of produced pions, in agreement with recent results from collisions of gold ions at the BNL-RHIC. From its mass, we estimate that the Polyakov loop condensate is characterized by a (spatial) correlation scale of 1/m ℓ ≃ 1/2 fm. For systems of deconfined matter of about that size, the free energy may not be dominated by a condensate for the Polyakov loop, and so the process of hadronization may be qualitatively different as compared to large systems. In that vein, experimental data on hadron abundance ratios, for example K/π, in high-multiplicity pp events at high energies should be very interesting.

Deconfinement in matrix models about the Gross-Witten point

“…We conclude by discussing the relationship of our results to the Polyakov loop model [22,23,24,25,26,27,28,29,30,31,32]. In this model, the pressure is assumed to be a potential for ℓ times T 4 .…”

“…In order to fit the pressure away from T d , however, it is necessary to assume that the variation of m 2 is not simply linear in the temperature. As shown in [27], by temperatures of ≈ 3T d , the pressure is nearly a constant times T 4 ; this requires that m 2 is nearly constant with respect to temperature. As noted above, when the value of the loop is near one, and given the uncertainties in the lattice data, we cannot exclude such a change in the relationship between m 2 and the temperature.…”

“…In the expression of (27), λ only appears in the loop potential and in the constraint. Thus before doing the matrix integral, we can extremize with respect to λ.…”

“…II with the most general effective Lagrangian, including all terms up to two spatial derivatives. At first sight, matrix models of loops appear to be an inelegant type of nonlinear sigma model [22,23,24,25,26,27,28,29,30,31,32,33,34]. This is not a matter of choice, but is dictated by the physics.…”

Partial deconfinement in color superconductivity

“…At zero density importance sampling lattice simulations are able to provide vital information about the nature of the temperature driven phase transition for 2 and 3 colors Yang-Mills theories with and without matter fields (see [12] for a review). Different models [13,14,15,16,17,18,19,20,21,22,23,24,25,26] are used in literature to tackle/study the features of this phase transition from a theoretical stand point. Some models compute non zero temperature corrections for the glueball Lagrangian with or without elementary gluon degrees of freedom (the latter added to describe the deconfined side of the phase transition).…”