Measurement of the Branching Ratio for the DecayK+→e++νe

Abstract

The branching ratio for the $K_{e2\mathrm{}}$ decay, $K^{+}\to e^{+}+{\nu }_e$, has been measured relative to the branching ratio for the $K_{\mu 2}$ decay, $K^{+}\to {\mu }^{+}+{\nu }_{\mu }$. The measurement was made at the Rutherford High Energy Laboratory using spark-chamber techniques. Positive kaons from a 700-MeV/c separated beam stopped and decayed in the beryllium plates of a small spark chamber. Charged decay products were momentum-analyzed with a spectrometer system consisting of a bending magnet and four sonic spark chambers. Electrons were identified by a threshold gas Čerenkov counter and by their range in a lead-aluminum spark chamber. Ten events were obtained in the $K_{e2\mathrm{}}$ region of the electron momentum spectrum. We estimate a background of 0.34 events in this region caused by the $K_{\mu 2}$ decay mode. We obtained a value for the ratio $R_K=\frac{\Gamma \left({K_{e2\mathrm{}}}^{+}\right)}{\Gamma \left({K_{\mu 2}}^{+}\right)}=\left({{1.9}_{-0.5\mathrm{}}}^{+0.7\mathrm{}}\right)\times {10}^{-5\mathrm{}}$. This is in good agreement with the prediction of the $V-A$ weak-interaction theory assuming muon-electron universality: $R_K=2.10\mathrm{}\times {10}^{-5\mathrm{}}$. The predicted value includes a radiative correction of - 18.5% resulting from virtual-photon processes. From our measurement of $R_K$ we obtained an upper limit on the amount of pseudoscalar coupling contributing to the $K_{e2\mathrm{}}$ decay. We find $\frac{\left|f^P\right|}{\left|f^A\right|}<2.2\mathrm{}\times {10}^{-3\mathrm{}}$, where $f^P$ and $\frac{f^A}{m_K}$ are the pseudoscalar and axial-vector coupling constants.