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 $(\rho,a_1)$ and $(K^*,K_1)$, become degenerate to values between 500 and 600 MeV in the chiral symmetry restored vacuum, while parity partners $(\omega,f_1)$ 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.
Highlights
Understanding the generation of the masses of hadrons that are larger than several hundred MeV starting from the current quark masses of less than 10 MeV is one of the fundamental problems in QCD [1,2]
It was found that the chiral symmetric part of the four-quark condensate is as large as the chiral symmetry breaking part and that the magnitude of the chiral symmetry breaking part follows that obtained from using the vacuum saturation hypothesis [17]. This explains why in the previous QCD sum rules, the four-quark operators were multiplied by a κ factor larger than 1 after vacuum saturation hypothesis to correctly obtain the hadron mass from the sum rule analysis [20,21]
We further provide explicit forms for the chiral symmetric and breaking quark operators appearing in the meson and baryon sum rules and show relevant relations based on Fiertz transformations
Summary
Understanding the generation of the masses of hadrons that are larger than several hundred MeV starting from the current quark masses of less than 10 MeV is one of the fundamental problems in QCD [1,2]. It was found that the chiral symmetric part of the four-quark condensate is as large as the chiral symmetry breaking part and that the magnitude of the chiral symmetry breaking part follows that obtained from using the vacuum saturation hypothesis [17] This explains why in the previous QCD sum rules, the four-quark operators were multiplied by a κ factor larger than 1 after vacuum saturation hypothesis to correctly obtain the hadron mass from the sum rule analysis [20,21]. We further provide explicit forms for the chiral symmetric and breaking quark operators appearing in the meson and baryon sum rules and show relevant relations based on Fiertz transformations
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