Resummation Study on Decay $\rho \to \pi \pi$ in $U(2{)}_L\times U(2{)}_R$ Chiral Theory of Mesons

Abstract

We improve $O(p^4)$ calculation in $U(2{)}_L\times U(2{)}_R$ chiral theory of mesons by resummation calculation for vector mesons physics and restudy decay $\rho \to \pi \pi$. A complete and compact expression for $f_{\rho \pi \pi }(p^2)$ (up to $O(p^{\infty })$) is obtained, from which an important non-perturbative conclusion is given based on convergence and unitarity consideration.

5 pages, 2 figures