New Precise Measurement of the Pion Weak Form Factors in ${\pi }^{+}\to e^{+}\nu \gamma$ Decay

We have measured the ${\pi }^{+}\to e^{+}\nu \gamma$ branching ratio over a wide region of phase space, based on a total of 65 460 events acquired using the PIBETA detector. Minimum-${\chi }^2$ fits to the measured ($E_{e^{+}}$, $E_{\gamma }$) 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 $e^{+}\nu$ pair invariant mass squared, parametrized as $F_V(q^2)=F_V(0)(1+a{q}^2)$. The branching ratio for the kinematic region $E_{\gamma }>10\mathrm{MeV}$ and ${\theta }_{e^{+}\gamma }>40°$ is measured to be $B^{\mathrm{expt}}=73.86(54)\times {10}^{-8}$. Earlier deviations we reported in the high-$E_{\gamma }$–low-$E_{e^{+}}$ kinematic region are resolved without a tensor term. We also derive new values for the pion polarizability ${\alpha }_E=2.78(10)\times {10}^{-4}{\mathrm{fm}}^3$ and neutral pion lifetime ${\tau }_{\pi 0}=(8.5\pm 1.1)\times {10}^{-17}\mathrm{s}$.

Figure 1

Data points: Background-subtracted ${\pi }^{+}\to e^{+}\nu \gamma$ distribution of the kinematic variable $\lambda \equiv (2E_e/m_{\pi }){sin}^2({\theta }_{e\gamma }/2)$ for regions I and II (top panel) and of the photon energy for regions I and III (bottom panel). Solid lines: Results of GEANT3 calculations for the best-fit values of $F_V$, $F_A$, and $a$.

Figure 2

Contour plot of loci of constant ${\chi }^2$ for the minimum value ${\chi }_0^2$ plus 1, 2, and 4 units, respectively, in the $F_A\mathrm{\text{−}}{F}_V$ parameter plane, keeping the parameter $a=0.041$. The range of the CVC prediction $F_V=0.0259(9)$ is indicated.