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.
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