New Precise Measurement of the Pion Weak Form Factors in the Pi+ -> e+ nu gamma Decay
We have measured the $π^+\to {\rm e}^+νγ$ branching ratio over a wide region of phase space, based on a total of 65,460 events acquired using the PIBETA detector. Minimum-$χ^2$ fits to the measured $(E_{e^+},E_γ)$ 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 ${\rm e}^{+}ν$ 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_γ> 10 $MeV and $θ_{{\rm e^+}γ} > 40^\circ $ is measured to be $B^{\rm exp}=73.86(54) \times 10^{-8}$. Earlier deviations we reported in the high-$E_γ$/low-$E_{{\rm e}^+}$ 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, $α_E = \rm 2.78(10) \times 10^{-4} fm^3$, and neutral pion lifetime, $τ_{π0} = (8.5 \pm 1.1) \times 10^{-17} $s.