Determination of the Axial-Vector Form Factor in the Radiative Decay of the Pion

The branching ratio for the decay $\pi \to e\nu \gamma$ has been measured in a counter experiment in which the $e^{+}$ was detected in a magnetic spectrometer and the $\gamma$ ray in a lead-glass hodoscope. From the measured branching ratio we determine $\gamma$, the ratio of the axial-vector form factor to the vector form factor. The latter is computed by using conserved-vector-current theory and ${\tau }_{{\pi }^0}$, the ${\pi }^0$ lifetime. Adopting a best value 0.86×${10}^{-16\mathrm{}}$ sec, we obtain $\gamma =0.15\mathrm{}\pm 0.11$ or $\gamma =-2.07\mathrm{}\pm 0.11$. A comparison between the measured values of $\gamma$ and various theories is made.