Weak decay constant of neutral pions in a hot and magnetized quark matter

Abstract

The directional weak decay constants of neutral pions are determined at finite temperature T , chemical potential µ 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 (µ)qqπ 0 and the weak decay constant f (µ) π 0 of neutral pions. The temperature dependence of g (µ)qqπ 0 and f (µ) π 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, µ and eB. It is shown that, because of the explicit breaking of the Lorentz invariance by the magnetic field, the directional quark-pion 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 qqπ 0 = g ⊥ qqπ 0 and f π 0 = f ⊥ π 0 . As it turns out, for fixed T, µ and B, g qqπ 0 > g ⊥ qqπ 0and f π 0 < f ⊥ π 0 .

Meson properties in magnetized quark matter

“…There are different regularization approaches, like soft cutoff [15,19], 3-momentum cutoff [16,17] and Pauli-Villars approach [18]. A high order PauliVillars regularization has two advantages.…”

“…For the phase transition from chiral symmetry breaking to its restoration, there are magnetic catalysis effects at the mean field level [4][5][6] and inverse magnetic catalysis effects in lattice QCD simulations [7][8][9] and effective model calculations [10][11][12][13][14]. Considering that pion mesons are the Goldstone modes corresponding to chiral symmetry breaking and dominate the QCD thermodynamics at low temperature, their properties [15][16][17][18][19][20][21][22][23][24][25][26][27] in an external magnetic field are extensively investigated.…”

Anisotropic pressure of deconfined QCD matter in presence of strong magnetic field within one-loop approximation

“…In recent years numerous activities have been in progress such as magnetic catalysis [1][2][3], inverse magnetic catalysis [4][5][6][7][8][9][10][11][12] and chiral magnetic effect [13][14][15] at finite temperature, and the chiral-and color-symmetry broken/restoration phase [16][17][18][19][20]. Also in progress is the study related to the equation of state (EoS) in thermal perturbative QCD (pQCD) models [21,22], holographic models [23,24] and various thermodynamic properties [19,20,25,26], refractive indices and decay constant of hadrons [27][28][29][30][31][32][33][34]; soft photon production from conformal anomaly [35,36] in HIC; modification of dispersion properties in a magnetized hot QED [37,38] and QCD [38][39][40][41] medium; and various transport coefficients [42]…”

Finite temperature QCD four-point function in the presence of a weak magnetic field within the hard thermal loop approximation

“…Several novel properties of hot and dense nuclear matter in the presence of the background magnetic field have been studied over the years, namely, the chiral magnetic effect [4,10,11]; chiral-and color-symmetry broken/restoration phase [12][13][14][15]; magnetic catalysis [16][17][18] and inverse magnetic catalysis [18][19][20][21][22]; bulk properties of Fermi gas [23]; phase structure of QCD [17,[24][25][26][27]; various properties of mesons such as the decay constant, thermal mass, and dispersion relations [28][29][30][31][32]; soft photon production from conformal anomaly in heavy-ion collisions [33,34]; modification of QED dispersion properties [35]; electromagnetic radiation [36]; dilepton production [37][38][39][40][41][42]; transport properties [43,44]; and properties of quarkonia [45][46][47][48].…”