Pion and sigma meson properties in a relativistic quark model

A variety of strong and electroweak interaction properties of a pion and a light scalar σ 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 σ meson mass is determined as M_σ=385.4MeV. We discuss in detail the gauging of the nonlocal meson-quark interaction and calculate the electromagnetic form factor of the pion and the form factors of the π⁰→γγ and →σγγ 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 σ, we determine the width of the electromagnetic →σγγ transition and discuss the strong decay →σππ. In a final step we compute the nonleptonic decays →Dσπ and →Bσπ relevant for the possible observation of the σ meson. All our results are compared to available experimental data and to results of other theoretical studies.