Radiative Decay \({{\pi }^{ \pm }} \to {{\ell }^{ \pm }}{{\nu }_{{{{\ell }^{ \pm }}}}}\gamma \) in the Relativistic Quark Model

Abstract

The paper presents a technique for calculating the decay form factors of a pseudoscalar pion, \({{\pi }^{ \pm }} \to {{\ell }^{ \pm }}{{\nu }_{{{{\ell }^{ \pm }}}}}\gamma \), in an approach based on the composite quark model and the point form of Poincare-invariant quantum mechanics (PiQM in what follows). It is shown that consideration of the electromagnetic structure of constituent \(u\) and \(d\) quarks using the virtuality parameter leads to values of the axial \({{F}_{{\text{A}}}}\) and vector \({{F}_{{\text{V}}}}\) form factors that are consistent with current experimental data. Based on the calculation results, a self-consistent model is proposed describing the electroweak decays \({{\pi }^{ \pm }} \to {{\ell }^{ \pm }}{{\nu }_{{{{\ell }^{ \pm }}}}}\) and \({{\pi }^{ \pm }} \to {{\ell }^{ \pm }}{{\nu }_{{{{\ell }^{ \pm }}}}}\gamma \) of a light pseudoscalar pion.