Pion scattering poles and chiral symmetry restoration

D. Fernandez-Fraile, A. Gomez Nicola, E. T. Herruzo

Published 2007-07-10, updated 2007-09-03Version 2

Using unitarized Chiral Perturbation Theory methods, we perform a detailed analysis of the $\pi\pi$ scattering poles $f_0(600)$ and $\rho(770)$ behaviour when medium effects such as temperature or density drive the system towards Chiral Symmetry Restoration. In the analysis of real poles below threshold, we show that it is crucial to extend properly the unitarized amplitudes so that they match the perturbative Adler zeros. Our results do not show threshold enhancement effects at finite temperature in the $f_0(600)$ channel, which remains as a pole of broad nature. We also implement T=0 finite density effects related to chiral symmetry restoration, by varying the pole position with the pion decay constant. Although this approach takes into account only a limited class of contributions, we reproduce the expected finite density restoration behaviour, which drives the poles towards the real axis, producing threshold enhancement and $\pi\pi$ bound states. We compare our results with several model approaches and discuss the experimental consequences, both in Relativistic Heavy Ion Collisions and in $\pi\to \pi\pi$ and $\gamma\to \pi\pi$ reactions in nuclei.