Pion and sigma meson properties in a relativistic quark model

Abstract

A variety of strong and electroweak interaction properties of the pion and the light scalar sigma meson are computed in a relativistic quark model. Under the assumption that the resulting coupling of these mesons to the constituent quarks is identical, the sigma meson mass is determined as M_sigma=385.4 MeV. We discuss in detail the gauging of the non-local meson-quark interaction and calculate the electromagnetic form factor of the pion and the form factors of the pi(0) -> gamma gamma and sigma -> gamma gamma processes. We obtain explicit expressions for the relevant form factors and evaluate the leading and next-to-leading orders for large Euclidean photon virtualities. Turning to the decay properties of the sigma we determine the width of the electromagnetic sigma -> gamma gamma transition and discuss the strong decay sigma -> pi pi. In a final step we compute the nonleptonic decays D -> sigma pi and B -> sigma pi relevant for the possible observation of the sigma meson. All our results are compared to available experimental data and to results of other theoretical studies.