Study of the O(N) linear sigma model at finite temperature using the 2PPI expansion

TL;DR

This paper introduces a new 2PPI expansion method for the O(N) linear sigma model at finite temperature, summing specific graphs to all orders, ensuring renormalization and Goldstone's theorem, and improving upon the Hartree approximation.

Contribution

The paper develops a renormalizable 2PPI expansion for the O(N) model at finite temperature that sums seagull and bubble graphs to all orders, satisfying Goldstone's theorem.

Findings

The expansion can be renormalized with standard counterterms.

Goldstone's theorem holds at each order of the expansion.

Sigma meson self-energy can be exactly calculated at one loop 2PPI order.

Abstract

We show that a new expansion which sums seagull and bubble graphs to all orders, can be applied to the O(N) linear sigma model at finite temperature. We prove that this expansion can be renormalised with the usual counterterms in a mass independent scheme and that Goldstone's theorem is satisfied at each order. At the one loop order of this expansion, the Hartree result for the effective potential (daisy and superdaisy graphs) is recovered. We show that at one loop 2PPI order, the self energy of the sigma meson can be calculated exactly and that diagrams are summed beyond the Hartree approximation.