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

Abstract

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.

Final version to appear in Phys. Rev. Lett. References added and typos corrected. 4 pages, three figures

References in corpus (5)

• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• The Inverse Amplitude Method and Adler Zeros
• Infrared regularization for spin-1 fields
• Pion scattering poles and chiral symmetry restoration
• Pattern of Light Scalar Mesons

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