13,825 research outputs found

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

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    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

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    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 a0a_{0} and a2a_{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

    Search for C=+C=+ charmonium and XYZ states in e+eβˆ’β†’Ξ³+He^+e^-\to \gamma+ H at BESIII

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    Within the framework of nonrelativistic quantum chromodynamics, we study the production of C=+C=+ charmonium states HH in e+eβˆ’β†’Ξ³Β +Β He^+e^-\to \gamma~+~H at BESIII with H=Ξ·c(nS)H=\eta_c(nS) (n=1, 2, 3, and 4), Ο‡cJ(nP)\chi_{cJ}(nP) (n=1, 2, and 3), and 1D2(nD)^1D_2(nD) (n=1 and 2). The radiative and relativistic corrections are calculated to next-to-leading order for SS and PP wave states. We then argue that the search for C=+C=+ XYZXYZ states such as X(3872)X(3872), X(3940)X(3940), X(4160)X(4160), and X(4350)X(4350) in e+eβˆ’β†’Ξ³Β +Β He^+e^-\to \gamma~+~H at BESIII may help clarify the nature of these states. BESIII can search XYZXYZ states through two body process e+eβˆ’β†’Ξ³He^+e^-\to \gamma H, where HH decay to J/ΟˆΟ€+Ο€βˆ’J/\psi \pi^+\pi^-, J/ΟˆΟ•J/\psi \phi, or DDΛ‰D \bar D. This result may be useful in identifying the nature of C=+C=+ XYZXYZ states. For completeness, the production of C=+C=+ charmonium in e+eβˆ’β†’Ξ³+Β He^+e^-\to \gamma +~H at B factories is also discussed.Comment: Comments and suggestions are welcome. References are update
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