Parity Doubling and SU(2)_L x SU(2)_R Restoration in the Hadron Spectrum

Abstract

We construct the most general nonlinear representation of chiral SU(2)_L x SU(2)_R broken down spontaneously to the isospin SU(2), on a pair of hadrons of same spin and isospin and opposite parity. We show that any such representation is equivalent, through a hadron field transformation, to two irreducible representations on two hadrons of opposite parity with different masses and axial couplings. This implies that chiral symmetry realized in the Nambu-Goldstone mode does not predict the existence of degenerate multiplets of hadrons of opposite parity nor any relations between their couplings or masses.

Comments: 4 pages, 1 figure; v3: Note added to clarify implications for hadrons that do not couple to pions: Chiral symmetry can be realized linearly on such states, leading to parity doubling. To the extent that they are parity doubled, these hadrons must decouple from pions, a striking prediction that can be tested experimentally. This applies to the work of L. Glozman and collaborators