Magnetic Catalysis in the Higher-Order Quark Sigma Model
  The effect of the higher-order mesonic interactions is investigated on the chiral symmetry breaking in the presence of an external magnetic field. The effective of higher-order mesonic potential is employed and is numerically solved in the mean-field approximation. The chiral symmetry breaking increases with increasing magnetic field. Two sets of free parameterization are investigated on the magnetic catalysis. A comparison is discussed with the original sigma model and other studies. The obtained results are included that the higher-order mesonic interactions play an important role in the magnetic catalysis. 
M. Abu-Shady
hep-ph