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Paper IPM / Particles / 13103  


Abstract:  
The directional weak decay constants of neutral pions are determined at finite temperature T, chemical potential 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 twoflavor, hot and magnetized NambuJonaLasinio model. Using this dispersion relation, including nontrivial directional refraction indices, we then generalize the PCAC relation of neutral pions and derive the GoldbergerTreiman (GT) as well as the GellMannOakesRenner (GOR) relations consisting of directional quarkpion coupling constant g_qq^0^() and weak decay constant f_^0^() of neutral pions. The temperature dependence of g_qq^0^() and f_^0^(), are then determined for fixed chemical potential and various constant background magnetic fields. The GT and GOR relations are also verified at finite T, and eB. It is shown that, because of the explicit breaking of the Lorentz invariance by the magnetic field, the directional quarkpion coupling and decay constants of neutral pions in the longitudinal and transverse directions with respect to the direction of the external magnetic field are different, i.e. g_qq^0^\  g_qq^0^ and f_^0^\  f_^0^. As it turns out, for fixed T, and B, g_qq^0^\  > g_qq^0^ and f_^0^\  < f_^0^.
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