The speed of cool soft pions

Abstract

The speed of cool pions in the chiral limit is analytically computed at low temperature within the imaginary time formalism to two loop order. This evaluation shows a logarithmic dependence in the temperature where the scale within the logarithm is very large compared to the pion decay constant. 11.10.Wx, 12.39.Fe, 14.40.Aq Typeset using REVTEX wtpvabam@lg.ehu.es 1 The dynamics of pions in a thermal bath has been studied intensively in the last few years [1–6] because its absorptive and dispersive properties can determine the termalization processes ocurring in the aftermath of high-energy nuclear collisions. In the limit of exact chiral symmetry, pions are true Goldstone bosons and as such, they travel at speed of light in the vacuum. At non zero temperature, however, relativistic invariance is lost, the thermal bath providing a priviliged rest frame and pions travel at less than the speed of light. Accordingly, the pion dispersion relation as a function of momentum must be modified. In chiral perturbation theory to leading order in low temperature, this modification first shows up at two loops, ∼ T /F 4 π , but in a linear σ model the effect already appears at one loop order, ∼ T /F 2 π m 2 σ [5]. Only very recently [6], the speed of thermal pions has been explicitly computed. This has been obtained from the axial current two-point correlator in the real time formalism within chiral perturbation theory. There, some integrals had to be numerically computed due to its complexity. The final result shows a logarithmic dependence in the temperature, v = 1− T 4 27F 4 π log ( Λ T )

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Cite this paper

@inproceedings{Basagoiti1998TheSO, title={The speed of cool soft pions}, author={M . A . Valle Basagoiti}, year={1998} }