New Precise Measurement of the Pion Weak Form Factors in the Pi+ -> e+ nu gamma Decay

Abstract

We have measured the $\ddot{I}{€}^{+}\to {\mathrm{e}}^{+}\hat{I}½{\hat{I}}^3$ branching ratio over a wide region of phase space, based on a total of 65,460 events acquired using the PIBETA detector. Minimum-$\ddot{I}{‡}^2$ fits to the measured $(E_{e^{+}},E_{\hat{I}}^3)$ energy distributions result in the weak form factor value of $F_A=0.0119(1)$ with a fixed value of $F_V=0.0259$. An unconstrained fit yields $F_V=0.0258(17)$ and $F_A=0.0117(17)$. In addition, we have measured $a=0.10(6)$ for the dependence of $F_V$ on $q^2$, the ${\mathrm{e}}^{+}\hat{I}½$ pair invariant mass squared, parametrized as $F_V(q^2)=F_V(0)(1+a\cdot q^2)$. The branching ratio for the kinematic region $E_{\hat{I}}^3>10$MeV and $\hat{I}{¸}_{{\mathrm{e}}^{+}{\hat{I}}^3}>40^{\circ }$ is measured to be $B^{\exp }=73.86(54)\times 10^{-8}$. Earlier deviations we reported in the high-$E_{\hat{I}}^3$/low-$E_{{\mathrm{e}}^{+}}$ kinematic region are resolved, and we find full compatibility with CVC and standard $V$$-$$A$ calculations without a tensor term. We also derive new values for the pion polarizability, $\hat{I}{\pm }_E=2.78(10)\times 10^{-4}\mathrm{f}{\mathrm{m}}^3$, and neutral pion lifetime, $\ddot{I}{„}_{\ddot{I}€0}=(8.5\pm 1.1)\times 10^{-17}$s.

4 pages, 2 PDF figures