Modified dilepton production rate from charged pion-pair annihilation in the inhomogeneous chiral condensed phase

TL;DR

This paper studies how inhomogeneous chiral condensates affect dilepton production from charged pion pairs, revealing an enhanced rate near twice the pion mass due to modified dispersion relations.

Contribution

It introduces a model for dilepton production in an inhomogeneous chiral phase using modified pion dispersion relations derived from a dual chiral density wave.

Findings

Dilepton production rate is steeper in the inhomogeneous phase.

Enhanced production rate near twice the pion mass.

Anisotropic, quadratic dispersion relations for Nambu-Goldstone modes.

Abstract

We investigate the dilepton production rates from annihilation processes of charged pion pairs with modified pion dispersion relations in the inhomogeneous chiral condensed phase. We assume a dual chiral density wave as an inhomogeneous chiral condensate, and obtain the dispersion relations of the Nambu-Goldstone modes in the inhomogeneous chiral condensed phase. We use a low energy effective Lagrangian based on the O(4) symmetry which is expanded by the order parameter up to the sixth order. The obtained dispersion relations are anisotropic and quadratic for the momentum. We evaluate the electron-positron production rates by charged pion-pair annihilations as functions of an invariant mass using the obtained dispersion relations. Basically, the production rate in the inhomogeneous chiral condensed phase has a steeper overall slope with respect to an invariant mass than that in the homogeneous chiral condensed phase. Therefore, the production rate may be enhanced when the invariant mass is around twice the pion mass.