Understand
The directional weak decay constants of neutral pions are determined at finite temperature T, chemical potential \mu and in the presence of a constant magnetic field B.
- To do this, we first derive the energy dispersion relation of neutral pions from the corresponding effective action of a two-flavor, hot and magnetized Nambu--Jona-Lasinio model.
- Using this dispersion relation, including nontrivial directional refraction indices, we then generalize the PCAC relation of neutral pions and derive the Goldberger-Treiman (GT) as well as the Gell--Mann-Oakes-Renner (GOR) relations consisting of directional quark-pion coupling constant g_{qq\pi^{0}}^{(\mu)} and weak decay constant f_{\pi^{0}}^{(\mu)} of neutral pions.
- The temperature dependence of g_{qq\pi^{0}}^{(\mu)} and f_{\pi^{0}}^{(\mu)}, are then determined for fixed chemical potential and various constant background magnetic fields.