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

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.