The masses of hadrons in the chiral symmetry restored vacuum

Abstract

We calculate the masses of the vector and axial-vector mesons as well as the nucleon and the delta resonance in the chiral symmetry restored vacuum. This is accomplished by separating the quark operators appearing in the QCD sum rules for these hadrons into the chiral symmetric and symmetry breaking parts depending on the contributions of the fermion zero modes. We then extract the vacuum expectation values of all the separated parts of the quark operators using the QCD sum rule relations for these hadrons with their vacuum masses and widths. By taking the chiral symmetry breaking parts to be zero while keeping the symmetric operators to their vacuum values, we obtain the chiral symmetric part of the hadron masses. We find that the masses of chiral partners, such as the $(ρ,a_1)$ and $(K^*,K_1)$, become degenerate to values between 500 and 600 MeV in the chiral symmetry restored vacuum, while parity partners $(ω,f_1)$ that are chiral partners only in the limit where the disconnected diagrams are neglected remain non-degenerate with masses $(655,1060)$ MeV, respectively. The masses of the nucleon and the Delta are also found to reduce to about 500 and 600 MeV, respectively, in the chiral symmetric vacuum. This shows that while chiral symmetry breaking is responsible for the mass difference between chiral partner, both the meson and baryon retain non-trivial fraction of their masses in the chiral symmetry restored vacuum.