Chiral Perturbation to One Loop Including the $ρ$ Meson

Details Chiral Perturbation to One Loop Including the $ρ$ Meson Chiral Perturbation to One Loop Including the $ρ$ Meson

1993-06-07

arxiv.org/abs/hep-ph/9306237v1

Phys.Lett. B316 (1993) 534-541

Physics

High Energy Physics

High Energy Physics - Phenomenology

14pages, KEK-TH-349/KEK preprint 92-169

Scientific paper

10.1016/0370-2693(93)91040-T

We formulate the chiral perturbation theory at the one loop level in the effective lagrangian including the $\rho$ meson as a dynamical gauge boson of a hidden local symmetry(HLS). The size of radiative correction to the phenomenological parameter $a$ of HLS is estimated to be about $10$\%. The complete list of ${\cal O}(E^4)$ terms is given and the one loop counter terms are determined explicitly in the $N$ flavor model. We also obtain matching conditions to the conventional chiral perturbation of Gasser and Leutwyler in the chiral limit in a renormalization scale independent manner. We find that Gasser--Leutwyler's estimates for $L_{9,10}$ are saturated by $\rho$ and its one loop contributions without introducing non-minimal couplings of $\pi$-$\rho$ system, suggesting the absence of the tree level $a_1$ meson contributions.

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