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Motivated by recent results by lattice analysis, we assume that the spin-1mesons of $\left( \rho, \omega, a_1, \rho', \omega', b_1, f_1, h_1\right)$ makea representation of $\mathbf{16}$ of U(4) emergent symmetry in two-flavor QCDwhen the chiral symmetry is not broken. We study the decay properties of thespin-1 mesons by using a chiral model with an SU(4)$\times$U(1) hidden localsymmetry. We first show that, since the SU(4) symmetry is spontaneously brokentogether with the chiral symmetry, each coupling of the interaction among onepion and two spin-1 mesons is proportional to the mass difference of therelevant spin-1 mesons similarly to the Goldberger-Treiman relation. Inaddition, 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 aswell as the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation for the $\rho$meson. From the relations, we give numerical predictions such as ratios of thespin-1 meson decay widths, which are compared with future experiments fortesting the existence of the U(4) emergent symmetry.

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