Isospin symmetry of $\omega$ meson in the soft-wall model of holographic QCD at finite temperature

Abstract

Coupling constants of $\rho$- and $\omega$- meson-nucleon are related with each other by isospin relation. In present work, it is aimed at studying the violation (if it exists) of isospin symmetry of the $\omega$-meson and to study the temperature dependence of $\omega$-meson-nucleon-delta and $\omega$-meson-delta coupling constants using the soft-wall model of holographic QCD. Firstly, the coupling constants are obtained by applying the profile functions of the vector and fermion fields to the model at a finite temperature. The interaction Lagrangian is written, including the minimum and magnetic interactions of vector and fermion fields which is defined in the bulk of the 5-dimensional AdS space-time. Secondly, the temperature dependence of the coupling constants $g_{\omega N N}(T)$, $g_{\omega \Delta \Delta}(T)$ and $g_{\omega N \Delta}(T)$ has been plotted. Comparing $g_{\omega N N}(T)$ with the coupling constant $g_{\rho NN}(T)$, it obtained that the isospin symmetry of the omega meson is not violated at the finite temperature. It is also observed that the coupling constants of the $\omega$ vector meson with baryons decreases with increasing temperature, and this coupling constant becomes zero near the Hawking phase transition temperature.