A new resummation scheme in scalar field theories

A new resummation scheme in scalar field theories is proposed by combining parquet resummation techniques and flow equations, which is characterized by a hierarchy structure of the Bethe--Salpeter (BS) equations. The new resummation scheme greatly improves on the approximations for the BS kernel. Resummation of the BS kernel in the $t$ and $u$ channels to infinite order is equivalent to truncate the effective action to infinite order. Our approximation approaches ensure that the theory can be renormalized, which is very important for numerical calculations. Two-point function can also be obtained from the four-point one through flow evolution equations resulting from the functional renormalization group. BS equations of different hierarchies and the flow evolution equation for the propagator constitute a closed self-consistent system, which can be solved completely.Comment: 12 pages, 4 figures. v2: title changed, one figure added, final version in Eur. Phys. J.

Four-fermion interactions and the chiral symmetry breaking in an external magnetic field

We investigate the chiral symmetry and its spontaneous breaking at finite temperature and in an external magnetic field with four-fermion interactions of different channels. Quantum and thermal fluctuations are included within the functional renormalization group approach, and properties of the set of flow equations for different couplings, such as its fixed points, are discussed. It is found that external parameters, e.g. the temperature and the external magnetic field and so on, do not change the structure of the renormalization group flows for the couplings. The flow strength is found to be significantly dependent on the route and direction in the plane of couplings of different channels. Therefore, the critical temperature for the chiral phase transition shows a pronounced dependence on the direction as well. Given fixed initial ultraviolet couplings, the critical temperature increases with the increasing magnetic field, viz., the magnetic catalysis is observed with initial couplings fixed.Comment: 8 pages, 4 figure

Mesonic excitations and pi--pi scattering lengths at finite temperature in the two-flavor Polyakov--Nambu--Jona-Lasinio model

The mesonic excitations and s-wave pi--pi scattering lengths at finite temperature are studied in the two-flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model. The masses of pi-meson and sigma-meson, pion-decay constant, the pion-quark coupling strength, and the scattering lengths $a_{0}$ and $a_{2}$ at finite temperature are calculated in the PNJL model with two forms of Polyakov-loop effective potential. The obtained results are almost independent of the choice of the effective potentials. The calculated results in the PNJL model are also compared with those in the conventional Nambu--Jona-Lasinio model and indicate that the effect of color confinement screens the effect of temperature below the critical one in the PNJL model. Furthermore, the Goldberger-Treiman relation and the Gell-Mann--Oakes--Renner relation are extended to the case at finite temperature in the PNJL model.Comment: 25 pages, 8 figure