In-medium Pions and Partial Restoration of Chiral Symmetry: a model-independent analysis

TL;DR

This paper derives a model-independent relation connecting the in-medium quark condensate to pion properties in nuclear matter, showing that pion-nucleus interactions imply partial chiral symmetry restoration without needing in-medium pion mass data.

Contribution

It introduces a novel, model-independent formula linking the in-medium quark condensate to pion decay constant and wave function renormalization, based on QCD operator relations.

Findings

Enhanced pion-nucleus repulsion indicates reduced quark condensate in medium.

The in-medium quark condensate can be inferred without knowing the in-medium pion mass.

The analysis supports partial restoration of chiral symmetry in nuclear matter.

Abstract

Exploiting operator relations in QCD, we derive a novel and model-independent formula relating the in-medium quark condensate <bar-q q>* to the decay constant F*_t and the wave function renormalization constant Z* of the pion in the nuclear medium. Evaluating Z* at low density from the iso-scalar pion-nucleon scattering data, it is concluded that the enhanced repulsion of the s-wave isovector pion-nucleusinteraction observed in the deeply bound pionic atoms implies directly the reduction of the in-medium quark condensate. The knowlege of the in-medium pion mass is not necessary to reach this conclusion.