Vector and Axial Vector Pion Form Factors

Radiative pion decay $\pi^+\rightarrow e^+\nu\gamma$ (RPD) provides critical input to chiral perturbation theory ($\chi$PT). Aside from the uninteresting ``inner bremsstrahlung'' contribution from QED, the RPD rate contains ``structure dependent'' terms given by $F_V$ and $F_A$, the vector and axial-vector pion form factors, respectively. The two appear in the decay rate in combinations $F_V-F_A$ and $F_V + F_A$, i.e., in the so-called $SD^-$ and $SD^+$ terms, respectively. The latter has been measured to high precision by the PIBETA collaboration.\footnote{M. Bychkov et al, Phys. Rev. Lett., \textbf{103}, 051802 (2009), http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.103.051802} We report on the analysis of new data, measured by the PEN collaboration\footnote{http://pen.phys.virginia.edu} in runs between 2008 and 2010 at the Paul Scherrer Institute, Switzerland. We particularly focus on the possibility of improvement in the determination of the $SD^-$ term. Precise determinations of $F_V$ and $F_A$ test the validity of the CVC hypothesis, provide numerical input for the $l_9+l_{10}$ terms in the $\chi$PT lagrangian, and constrain potential non-$(V-A)$ terms, such as a possible tensor term $F_T$.