In-medium Pion and Partial Restoration of Chiral Symmetry

TL;DR

This paper derives a model-independent sum rule linking the in-medium quark condensate, pion decay constant, and wave-function renormalization, showing that pion-nucleus interaction data imply partial chiral symmetry restoration in nuclear matter.

Contribution

It introduces a new sum rule relating in-medium QCD parameters and connects experimental pion-nucleus scattering data to chiral symmetry restoration.

Findings

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

In-medium pion properties can be inferred without knowing the in-medium pion mass.

The sum rule applies at all densities, providing a fundamental link between QCD and nuclear physics.

Abstract

The partial restoration of chiral symmetry in nuclear medium is investigated in a model independent way by exploiting operator relations in QCD. An exact sum rule is derived for the quark condensate valid for all density. This sum rule is simplified at low density to a new relation with the in-medium quark condensate <bar{q}q>*, in-medium pion decay constant F_{pi}^t and in-medium pion wave-function renormalization Z_{pi}*. Calculating Z_{pi}*at low density from the iso-scalar pion-nucleon scattering data and relating F_{pi}^t to the isovector pion-nucleus scattering length b_1^*, it is concluded that the enhanced repulsion of the s-wave isovector pion-nucleus interaction observed in the deeply bound pionic atoms directly implies the reduction of the in-medium quark condensate. The knowledge of the in-medium pion mass m_{pi}* is not necessary to reach this conclusion.