Isospin breaking in nuclear physics: The Nolen-Schiffer effect

Using the QCD sum rules we calculate the neutron-proton mass difference at zero density as a function of the difference in bare quark massm_d—m_u. We confirm results of Hatsuda, Høgaasen and Prakash that the largest term results from the difference in up and down quark condensates, the explicitC(m_d—m_u) entering with the opposite sign. The quark condensates are then extended to finite density to estimate the Nolen-Schiffer effect. The neutron-proton mass difference is extremely density dependent, going to zero at roughly nuclear matter density.The Ioffe formula for the nucleon mass is interpreted as a derivation, within the QCD sum rule approach, of the Nambu-Jona-Lasinio formula. This clarifies theN_c counting and furthermore provides an alternative interpretation of the Borel mass.