m_pi and N_c dependence of resonances from Unitarized Chiral Perturbation Theory

Abstract

We review our studies on the rho and sigma resonances properties derived from the Inverse Amplitude Method. In particular, we study the leading $1/N_c$ behavior of the resonances masses and widths and their evolution with changing $m_{\pi }$. The $1/N_c$ expansion gives a clear definition of $\bar{q}q$ states, which is neatly satisfied by the $\rho$ but not by the sigma, showing that its dominant component is not $\bar{q}q$. The $m_{\pi }$ dependence of the resonance properties is relevant to connect with lattice studies. We show that our predictions compare well with some lattice results and we find that the rho-pi-pi coupling constant is $m_{\pi }$ independent, in contrast with the sigma-pi-pi$coupling,thatshowsastrong$m_\pi$ dependence.

Comments: Invited talk at the 12th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU2010), May 31-June 4, 2010, Williamsburg, Virginia. Added references