Relations among pionic decays of spin-1 mesons from an SU(4)$\times$U(1) emergent symmetry in QCD

TL;DR

This paper explores an emergent SU(4)×U(1) symmetry in two-flavor QCD, analyzing how it influences the decay properties of spin-1 mesons and deriving relations among their masses and couplings.

Contribution

It introduces a chiral model with hidden local symmetry to connect meson decay properties with an emergent SU(4)×U(1) symmetry in QCD, providing testable predictions.

Findings

Couplings proportional to mass differences of mesons.

Relations among decay widths and meson parameters.

Predictions for decay width ratios compared with future experiments.

Abstract

Motivated by recent results by lattice analysis, we assume that the spin-1 mesons of $\left( \rho, \omega, a_1, \rho', \omega', b_1, f_1, h_1\right)$ make a representation of $\mathbf{16}$ of U(4) emergent symmetry in two-flavor QCD when the chiral symmetry is not broken. We study the decay properties of the spin-1 mesons by using a chiral model with an SU(4)$\times$U(1) hidden local symmetry. We first show that, since the SU(4) symmetry is spontaneously broken together with the chiral symmetry, each coupling of the interaction among one pion and two spin-1 mesons is proportional to the mass difference of the relevant spin-1 mesons similarly to the Goldberger-Treiman relation. In addition, some of one-pion couplings are related with each other by the SU(4) symmetry. We further show that there is a relation among the mass of $\rho'$ meson, the $\rho'\pi\pi$ coupling and the $\rho'$-photon mixing strength as well as the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation for the $\rho$ meson. From the relations, we give numerical predictions such as ratios of the spin-1 meson decay widths, which are compared with future experiments for testing the existence of the U(4) emergent symmetry.