Baryon fields withUL(3)×UR(3)chiral symmetry. V. Pion-nucleon and kaon-nucleon

V. Dmitrašinović¹,

Hua-Xing Chen²

Abstract

We have previously calculated the pion-nucleon ΣπN term in the chiral mixing approach with u, d flavors only, and found the lower bound ΣπN ≥ 1 + 16 3 sin 2 θ 3 2 m 0 u + m 0 d where m 0 u , m 0 d are the current quark masses, and θ is the mixing angle of the [( 1 2 , 0) ⊕ (0, 1 2 )] and the [(1, 1 2 ) ⊕ ( 1 2 , 1)] chiral multiplets. This mixing angle can be calculated as sin 2 θ = 3 8 g (0)A + g(3) A, where gA , gA , are the flavor-singlet and the isovector axial couplings. With presently accepted values of current quark masses, this leads to ΣπN ≥ 58.0 ± 4.5 +11.4 −6.5 MeV, which is in agreement with the values extracted from experiments, and substantially higher than most previous two-flavour calculations. The causes of this enhancement are: 1) the large, ( 16 3 ≃ 5.3), purely SUL(2) × SUR(2) algebraic factor; 2) the admixture of the [(1, 12 ) ⊕ ( 1 2 , 1)] chiral multiplet component in the nucleon, whose presence has been known for some time, but that had not been properly taken into account, yet. We have now extended these calculations of ΣπN to three light flavours, i.e., to SUL(3) × SUR(3) multiplet mixing. Phenomenology of chiral SUL(3) × SUR(3) multiplet mixing demands the presence of three chiral SUL(3) × SUR(3) multiplets, viz. [(6, 3) ⊕ (3, 6)], [(3, 3) ⊕ ( 3, 3)] and [( 3, 3) ⊕ (3, 3)], in order to successfully reproduce the baryons' flavor-octet and flavor-singlet axial currents, as well as the baryon anomalous magnetic moments. Here we use these previously obtained results, together with known constraints on the explicit chiral symmetry breaking in baryons to calculate the ΣπN term, but find little, or no change of ΣπN from the above successful two-flavor result. The physical significance of these results lies in the fact that they show no need for q 4 q components, and in particular, no need for an ss component in the nucleon, in order to explain the large "observed" ΣπN value. We also predict the experimentally unknown kaon-nucleon sigma term ΣKN .

Decay properties of $$P_c$$ states through the Fierz rearrangement

“…We also need light baryon fields, which have been systematically studied in Refs. [66][67][68][88][89][90][91][92]. We briefly summarize the results here.…”

The pion-nucleon σ term from pionic atoms

“…Studies of pionic atoms [27,28,29,30,31,32,33,34,35,36] and low-energy pion-nucleus scattering [37,38] confirmed that the πN isovector s-wave interaction term is indeed renormalized in agreement with Eq. (5). It is this in-medium renormalization that brings in σ πN to the interpretation of pionic-atom data.…”

“…A wide spectrum of evaluated σ πN values, from about 20 to 80 MeV, was compiled by Sainio back in 2002 [1]. Recent evaluations roughly fall into two classes: (i) pion-nucleon low-energy phenomenology, using πN s-wave scattering lengths derived precisely from pionic hydrogen and deuterium, results in calculated values of σ πN ∼ (50 − 60) MeV [2,3,4,5,6], the most recent of which is 58±5 MeV, whereas (ii) recent lattice QCD calculations reach values of σ πN ∼ (30 − 50) MeV [7,8,9,10,11,12], the most recent of which is 26±7 MeV. However, when augmented by chiral perturbation expansions such lattice calculations may lead also to values of about 50 MeV, see e.g.…”

Casimir effect for nucleon parity doublets

“…It should be noted that finite-volume effects for the nucleon masses in a box could be estimated within the framework of the chiral perturbation theory (ChPT) with arXiv:1812.10964v2 [hep-ph] 18 Mar 2019 baryons [61-68], 1 which have been devoted to compare results with artificial volume effects from lattice QCD simulations. We emphasize that our purpose in this work is to investigate the properties of the nucleon parity doublets in a finite box, in which the finite-volume effects for σ mean fields will be essential.…”