Pion Phenomenology from the Thermal Soft-Wall Model of Holographic QCD

Abstract

Within the framework of the thermal soft-wall model of AdS/QCD, we investigate phenomenological properties of pions at finite temperature. This includes the electromagnetic (EM) form factor $F_{\pi}(Q^{2}, T)$, the thermal mass $M_{\pi}(T)$, charge radius $r_{\pi}(T)$, the generalized parton distribution (GPD) $H_{\pi}(x, Q^{2}, T)$, the charge density $\rho_{\pi}(b, T)$ of the pion, the pion-nucleon coupling constant $g_{\pi NN}(T)$, and pion-$\Delta$ baryon coupling constant $g_{\pi \Delta \Delta}(T)$ coupling constant at finite temperature. The thermal pion form factor is extrapolated from the zero-temperature case. Subsequently, the GPD is obtained at finite temperature from this form factor. The above-mentioned quantities were analyzed using a thermal dilaton field in the five-dimensional AdS action. Moreover, we determine the theoretical expression for the temperature-dependent pion-nucleon coupling constant, and the pion-$\Delta$ baryon coupling constant using thermal profile functions of the nucleon, $\Delta$ baryon and the pion. Our results show that the values of these quantities decrease with increasing temperature and vanish near the critical temperature $T_c$; except for the pion radius, which diverges at $T_c$. Our results reproduce expected features of low-energy hadron dynamics, thus validating the phenomenological utility of the thermal soft-wall model.