Parity doublets in the baryon spectrum

Abstract

Physics of the low-lying and high-lying hadrons in the light flavor sector is reviewed. While the low-lying hadrons are strongly affected by both U(1) A and spontaneous SU(2) L × SU(2) R breakings, in the high-lying hadrons these symmetries are restored. A manifestation is a persistence of the chiral multiplet structure in both baryon and meson spectra. A fundamental origin of this phenomenon is that effects of quantum fluctuations of both quark and gluon fields must vanish at large n or J and a semiclassical description becomes adequate. A relation between the chiral symmetry restoration and the string picture of excited hadrons is discussed.

The operator product expansion does not imply parity doubling of hadrons

“…where we used Eq. (7). Clearly, our model wants m 2 P to be larger than m 2 S , which is not inconsistent with what is known about the lowest lying resonances in the scalar and pseudo-scalar channels.…”

“…This means that asymptotically the pseudo-scalar states lie precisely halfway two successive scalar states. 7 In this sense, chiral symmetry is maximally broken by all meson resonances in the 't Hooft model, unlike what is claimed in Refs. [6,7].…”

“…7 In this sense, chiral symmetry is maximally broken by all meson resonances in the 't Hooft model, unlike what is claimed in Refs. [6,7]. 7 A larger value would imply that parity pairs have been misidentified.…”

“…7 In this sense, chiral symmetry is maximally broken by all meson resonances in the 't Hooft model, unlike what is claimed in Refs. [6,7].…”

“…Obviously, we want ρ(n) to be dimensionless, but we do not want ρ(n) to go to zero for large n trivially. Therefore, the denominator is taken to be the smallest possible quantity with dimension of mass made out of the masses with "resonance number" approximately equal to n. "Chiral symmetry restoration" for a particular spin and isospin takes place if ρ(n) goes to zero for large n. Another measure of "chiral symmetry restoration" considered in the literature [6,7] is the "chiral asymmetry"…”