In-medium pion and partial restoration of chiral symmetry

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 〈q¯q〉∗/〈q¯q〉=(Fπt/Fπ)Zπ∗1/2 with the in-medium quark condensate 〈q¯q〉∗, in-medium pion decay constant Fπt and in-medium pion wave-function renormalization Zπ∗. Calculating Zπ∗ at low density from the isoscalar pion–nucleon scattering data and relating Fπt to the isovector pion–nucleus scattering length b1∗, 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 mπ∗ is not necessary to reach this conclusion.