Hidden Local Symmetry and Chiral Effective Theory for Vector and Axial-vector Mesons

Abstract

In this paper, we present the full Lagrangian of mesons (pseudoscalars, vectors and axial-vectors) to $O(p^4)$ by using the explicit global chiral symmetry and hidden local symmetry in the chiral limit. In this approach, we see that there are many other terms besides the usual eleven terms given in the literature from hidden local symmetry approach. Of particular, there are some terms in our full results which are important for understanding the vector meson dominance and $\pi -\pi$ scattering and providing consistent predictions on the decay rates of $a_1\to \gamma \pi$ and $a_1\to \rho \pi$ as well as for constructing a consistent effective chiral Lagrangian with chiral perturbation theory. It is likely that the structures of the effective chiral Lagrangian for $O(p^4)$ given in the literature by using hidden local symmetry are incomplete and consequently the resulting couplings are not reliable. It is examined that the more general effective chiral Lagrangian given in present paper can provide more consistent predictions for the low energy phenomenology of $\rho -a_1$ system and result in more consistent descriptions on the low energy behavior of light flavor mesons.

arXiv commentRevTex, 18 pages, to be published in EPJC

References in corpus (3)

• Pion-pion scattering at low energy
• U(2)_{L}\times U(2)_{R} Chiral Theory of Mesons
• Symmetry Principle Preserving and Infinity Free Regularization and renormalization of quantum field theories and the mass gap

Cited by in corpus (4)

• Dropping rho and A_1 Meson Masses at Chiral Phase Transition in the Generalized Hidden Local Symmetry
• Chiral partner structure of heavy baryons from the bound state approach with hidden local symmetry
• Hidden Local Symmetry and Effective Chiral Theory for Vector and Axial-vector Mesons
• Spin Polarisability of the Nucleon in the Heavy Baryon Effective Field Theory