Pion and sigma meson properties in a relativistic quark model

A variety of strong and electroweak interaction properties of the pion and the 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 Mσ = 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 π0 → γγ and σ → γγ 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 σ we determine the width of the electromagnetic σ → γγ transition and discuss the strong decay σ → ππ. In a final step we compute the nonleptonic decays D → σπ and B → σπ 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. PACS: 12.39.Ki, 13.25.Ft, 13.40.Gp, 13.40.Hq, 14.40.Lb