The mass splitting among the isospin multiplets of light vector mesons

TL;DR

This paper uses chiral perturbation theory and coupled channel methods to calculate isospin mass splittings of light vector mesons, providing insights into the long-standing K* mass difference puzzle.

Contribution

It presents a full one-loop ChPT calculation including isospin breaking effects to analyze vector meson mass splittings, especially K*.

Findings

Mass difference between rho^\pm and rho^0 is very small.

Mass difference between charged and neutral K* can reach about 2.91 MeV.

Results help clarify the K* mass splitting puzzle.

Abstract

By including the strong isospin symmetry breaking effects and the electromagnetic contributions between the pseudoscalar mesons, we calculate the phase shifts of the $P$-wave $\pi\pi$ and $K\pi$ scattering up to $\mathcal{O}(p^4)$ in the framework of the SU(3) chiral perturbation theory (ChPT) and coupled channel inverse amplitude method. We re-fit the low energy constants with the present meson-meson scattering data and derive the mass differences for the charged and neutral iso-multiplets of $\rho$ and $K^{*}$. Our results show that the mass difference between $\rho^\pm$ and $\rho^0$ is very small while the mass difference between the charged and neutral $K^*$ can reach a relatively large value of $m_{K^{*0}}-m_{K^{*+}}= 2.91^{+1.43}_{-1.41}$ MeV. This full one-loop ChPT calculation would shed some light towards a better understanding of the long-standing puzzle about the $K^*$ mass splitting.