What does a change in the quark condensate say about restoration of chiral symmetry in matter?

Abstract

The contribution of nucleons to the quark condensate in nuclear matter includes a piece of first order in $m_{\pi }$, arising from the contribution of low-momentum virtual pions to the $\pi N$ sigma commutator. Chiral symmetry requires that no term of this order appears in the $NN$ interaction. The mass of a nucleon in matter thus cannot depend in any simple way on the quark condensate alone. More generally, pieces of the quark condensate that arise from low-momentum pions should not be associated with partial restoration of chiral symmetry.

9 pages (RevTeX). Definition of effective mass changed; numerical value of leading nonanalytic term corrected, along with various misprints

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