Chiral physics in the magnetic field with quark confinement contribution

Abstract

The standard chiral perturbation theory is known to predict much weaker effects in magnetic field, than found in numerical lattice data. To overcome this disagreement we are using the effective chiral confinement Lagrangian, $L_{ECCL}$, containing both chiral and quark degrees of freedom, in the presence of external magnetic field. Without magnetic fields $L_{ECCL}$ reduces to the ordinary chiral Lagrangian $L_{EC L}$, yielding in the lowest order $O(\partial_\mu \varphi)^2$ all known relations, and providing explicit numerical coefficients in the higher $O(p^4, p^6)$ orders. The inclusion of the magnetic field in $L_{ECCL}$ strongly modifies ECL results for chiral condensates, coupling constants $f_\pi, f_K$ and masses of chiral mesons. The resulting behavior contains the only parameter -- the string tension $\sigma$, is roughly proportional to $O\left( \frac{eB}{\sigma}\right)$ and agrees very well with lattice data. These results show that the magnetic field acts not only on the chiral degrees of freedom $(\varphi_\pi)$, but also on quarks in the quark-chiral Lagrangian, which produce much stronger effect.