Density resummation of perturbation series in a pion gas to leading order in chiral perturbation theory

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dc.creatorKrivoruchenko, M. I.
dc.creatorFuchs, C.
dc.creatorMartemyanov, B. V.
dc.creatorFaessler, Amand
dc.date2005-05-10
dc.date2006-10-26
dc.date.accessioned2026-07-07T11:04:45Z
dc.date.available2026-07-07T11:04:45Z
dc.descriptionThe mean field (MF) approximation for the pion matter, being equivalent to the leading ChPT order, involves no dynamical loops and, if self-consistent, produces finite renormalizations only. The weight factor of the Haar measure of the pion fields, entering the path integral, generates an effective Lagrangian $δ\mathcal{L}_{H}$ which is generally singular in the continuum limit. There exists one parameterization of the pion fields only, for which the weight factor is equal to unity and $δ\mathcal{L}_{H}=0$, respectively. This unique parameterization ensures selfconsistency of the MF approximation. We use it to calculate thermal Green functions of the pion gas in the MF approximation as a power series over the temperature. The Borel transforms of thermal averages of a function $\mathcal{J}(χ^αχ^α)$ of the pion fields $χ^α$ with respect to the scalar pion density are found to be $\frac{2}{\sqrtπ}\mathcal{J}(4t)$. The perturbation series over the scalar pion density for basic characteristics of the pion matter such as the pion propagator, the pion optical potential, the scalar quark condensate $<{\bar{q}}q>$, the in-medium pion decay constant ${\tilde{F}}$, and the equation of state of pion matter appear to be asymptotic ones. These series are summed up using the contour-improved Borel resummation method. The quark scalar condensate decreases smoothly until $T_{max}\simeq 310$ MeV. The temperature $T_{max}$ is the maximum temperature admissible for thermalized non-linear sigma model at zero pion chemical potentials. The estimate of $T_{max}$ is above the chemical freeze-out temperature $T\simeq 170$ MeV at RHIC and above the phase transition to two-flavor quark matter $T_{c} \simeq 175$ MeV, predicted by lattice gauge theories.
dc.descriptionReplaced with revised and extended version. Results are compared to lattice gauge theories. 16 pages REVTeX, 13 eps figures
dc.identifierhttps://arxiv.org/abs/hep-ph/0505083
dc.identifierhttp://arxiv.org/abs/hep-ph/0505083
dc.identifierPhys.Rev.D74:125019,2006
dc.identifierdoi:10.1103/PhysRevD.74.125019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/188998
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectHigh Energy Physics - Lattice
dc.subjectNuclear Theory
dc.titleDensity resummation of perturbation series in a pion gas to leading order in chiral perturbation theory
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