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Register a new userHidden Local Symmetry and Effective Chiral Theory for Vector and Axial-vector Mesons
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Bing An Li
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The Lagrangian of pseudoscalar, vector, and axial-vector mesons is determined by the explicit global chiral symmetry and hidden local chiral symmetry. There are fourteen interacting terms up to the dimension-four of covariant derivatives rather than the usual eleven interacting terms given in literature from hidden local symmetry approach. There are only two independent parameters. The three new terms are important in phenomenology.
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A previous formal derivation of the effective chiral Lagrangian for low-lying pseudoscalar mesons from first-principles QCD without approximations [Wang et al., Phys. Rev. D61, (2000) 54011] is generalized to further include scalar, vector, and axial-vector mesons. In the large Nc limit and with an Abelian approximation, we show that the properties of the newly added mesons in our formalism are determined by the corresponding underlying fundamental homogeneous Bethe--Salpeter equation in the ladder approximation, which yields the equations of motion for the scalar, vector, and axial-vector meson fields at the level of an effective chiral Lagrangian. The masses appearing in the equations of motion of the meson fields are those determined by the corresponding Bethe--Salpeter equation.
The magnetic and quadrupole moments of the vector and axial-vector mesons containing heavy quark are estimated within the light cone sum rules method. Our predictions on magnetic moments for the vector mesons are compared with the results obtained by other approaches.
The in-medium behavior of ground-state $qbar{q}$ mesons, where $q in {u,d,s,c}$, in vector and axial-vector channels is studied based on the spectral analysis for mesonic correlators at finite temperature and zero chemical potential. We first compute the correlators by solving the quark gap equations and the inhomogeneous Bethe-Salpeter equations in the rainbow-ladder approximation. Using a phenomenological ansatz, the spectral functions are extracted by fitting the correlators. By analyzing the evolution of the spectral functions with the temperature, we obtain the dissociation temperatures of mesons and discuss their relations to the critical temperature of the chiral symmetry restoration. The results show a pattern of the flavor dependence of the thermal dissociation of the mesons.
The structure of the scalar mesons has been a subject of debate for many decades. In this work we look for $bar{q}q$ states among the physical resonances using an extended Linear Sigma Model that contains scalar, pseudoscalar, vector, and axial-vector mesons both in the non-strange and strange sectors. We perform global fits of meson masses, decay widths and amplitudes in order to ascertain whether the scalar $bar{q}q$ states are below or above 1 GeV. We find the scalar states above 1 GeV to be preferred as $bar{q}q$ states.
In this work the neutral meson properties have been investigated in the presence of thermo-magnetic background using two-flavor Nambu--Jona-Lasinio model. Mass, spectral function and dispersion relations are obtained in the scalar ($sigma$) and pseudo-scalar ($pi^0$) channels as well as in the vector ($rho^0$) and axial vector ($a^0_1$) channels. The general Lorentz structures for the vector and axial-vector meson polarization functions have been considered in detail. The ultra-violet divergences appearing in this work have been regularized using a mixed regularization technique where the gamma functions arising in dimensional regularization are replaced with incomplete gamma functions as usually done in the proper time regularization procedure. The meson spectral functions obtained in the presence of a magnetic field possess nontrivial oscillatory structure. Similar to the scalar and pseudo-scalar channel, the spectral functions for each of the modes of $rho^0$ are observed to overlap with the corresponding modes of its chiral partner $a_1^0$ mesons in the chiral symmetry restored phase. We observe discontinuities in the masses of all the mesonic excitations for a non-zero external magnetic field.
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