N_c and m_pi dependence of rho and sigma mesons from unitarized Chiral Perturbation Theory

We review our work on the rho and sigma resonances 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 quark-antiquark states, which is neatly satisfied by the rho but not by the sigma, showing that its dominant component is not quark-antiquark. 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, that shows a strong m_pi dependence.Comment: To appear in the Proceedings of the Chiral10 Workshop, June 21-24 2010. Valencia, Spai

Moving frames for cotangent bundles

Cartan's moving frames method is a standard tool in riemannian geometry. We set up the machinery for applying moving frames to cotangent bundles and its sub-bundles defined by non-holonomic constraints.Comment: 13 pages, to appear in Rep. Math. Phy