Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory

We use the one-loop Chiral Perturbation Theory pion-pion scattering amplitude and dispersion theory in the form of the inverse amplitude method, to study the quark mass dependence of the two lightest resonances of the strong interactions, the f_0(600) (sigma) and the rho-meson. As main results we find that the rho-pion-pion coupling constant is almost quark mass independent and that the rho mass shows a smooth quark mass dependence while that of the sigma shows a strong non-analyticity. These findings are important for studies of the meson spectrum on the lattice.

Note:

4 pages, three figures

12.39.Fe
14.40.Cs
13.75.Lb
pi p: scattering amplitude
dispersion relation
perturbation theory: chiral
rho(770): mass
f0(600): mass
mass dependence
quark: mass

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