Mirror versus naive assignment in chiral models for the nucleon

Abstract

In the framework of chiral model(s) based on the linear realization of chiral symmetry, we investigate the low-energy phenomenological properties of the nucleon and its chiral partner (identified with either N (1535) or N (1650)) in the naive assignment and compare the results with the ones obtained in the mirror assignment. We find that, within the naive assignment, we are not able to reproduce the experimental value of the isospin-odd scattering length, while the mirror assignment is in good agreement with it for both choices N (1535) and N (1650). The isospin-even scattering length is not yet conclusive in either assignment because it depends crucially on the poorly known scalar mesonic sector. The decay with Γ N(1535)→Nη turns out to be far too small in both the naive and mirror assignments, while Γ N(1650)→Nη is described correctly by both of them. In conclusions, the mirror assignment with N (1650) as the chiral partner of the nucleon is the favored configuration.

Casimir effect for nucleon parity doublets

“…This representation reproduces the Casimir energy for D = 4 and δ = 2, which is shown in Eqs. (15) and (16).…”

Extended Goldberger-Treiman relation in a three-flavor parity doublet model

“…This model includes a chiral invariant mass denoted by m 0 , which implies that the masses of N (939) and N (1535) tend to m 0 when the chiral symmetry is restored and their mass splitting is given by the spontaneous chiral symmetry braking. This structure has been studied by many works [2][3][4][5][6][7][8][9][10][11][12]. One of the key feature of the structure is a relation among the pionic interactions and mass difference between the chiral partners, which is an extended Goldberger-Treiman relation.…”

“…Refs. [6,12]). On the other hand, parity doublet models are applied to study the nuclear matter, where large value of m 0 (e.g.…”

Role of scalar dibaryon andf0(500)in the isovector channel of low-energy neutron-proton scattering

“…For the sake of definiteness, we will use the results of Ref. [24], in which N (1650) is regarded as the chiral partner. On the other hand, in an enlarged mixing scenario [25], N (1535) is favored as the chiral partner of the nucleon.…”

“…[18]. A modern variant is the extended Linear Sigma Model (eLSM), which contains (pseudo)scalar and (axial-)vector mesons and which was successfully applied in the context of meson-meson interactions [19][20][21][22] and also meson-nucleon interactions [23][24][25]. In particular, baryons and their chiral partners are treated in the so-called mirror assignment, in which a chirally invariant mass term is present [26][27][28].…”