Chiral perturbation theory in a magnetic background — finite-temperature effects

Abstract

We consider chiral perturbation theory for SU (2) at finite temperature T in a constant magnetic background B. We compute the thermal mass of the pions and the pion decay constant to leading order in chiral perturbation theory in the presence of the magnetic field. The magnetic field gives rise to a splitting between M π 0 and M π ± as well as between F π 0 and F π ± . We also calculate the free energy and the quark condensate to next-to-leading order in chiral perturbation theory. Both the pion decay constants and the quark condensate are decreasing slower as a function of temperature as compared to the case with vanishing magnetic field. The latter result suggests that the critical temperature T c for the chiral transition is larger in the presence of a constant magnetic field. The increase of T c as a function of B is in agreement with most model calculations but in disagreement with recent lattice calculations.

Meson properties in magnetized quark matter

“…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.…”

One-loop QCD thermodynamics in a strong homogeneous and static magnetic field

“…(3.20), 22) and the medium contributions containing single (n) and double distribution (n 2 ) functions, respectively, are also separated from eq. (3.20),…”

“…Moreover the magnetic field may be assumed uniform because even though the spatial distribution of the magnetic field is globally inhomogeneous, but in the central region of the overlapping nuclei, the magnetic field in the transverse plane varies very smoothly, which is noticed in the hadron-string simulations [9] for Au-Au collisions at √ s N N = 200 GeV with an impact parameter, b = 10 fm. Therefore, a large number of QCD related phenomena are investigated in the strong and homogeneous magnetic field, such as the chiral magnetic effect related to the generation of electric current parallel to the magnetic field due to the difference in number of right and left-handed quarks [10][11][12], the axial magnetic effect due to the flow of energy by the axial magnetic field [13,14], the chiral vortical effect due to an effective magnetic field in the rotating QGP [15,16], the magnetic catalysis and the inverse magnetic catalysis at finite temperature arising due to the breaking and the restoration of the chiral symmetry [17][18][19][20][21], the thermodynamic properties [22][23][24], the refractive indices and decay constant [25,26] of mesons in a hot magnetized medium, the conformal anomaly and the production of soft photons [27,28] at RHIC and LHC, the dispersion relation in a magnetized thermal QED [29], the synchrotron radiation [30], the dilepton production from both the weakly [31][32][33][34] and the strongly [35] coupled plasma etc.…”

The evolution of meson masses in a strong magnetic field

“…On the theoretical side the main directions of research in this area are the lattice studies [20,21]- [31], [32]- [43], the chiral Lagrangians with MF [44]- [50,51], effective hadron Lagrangians [1,2,[52][53][54][55][56], [57]- [60], and recently developed path integral Hamiltonians (PIH) [62]- [68], and the chiral Lagrangian with quark degrees of freedom [69].…”