Measurement of the Energy Spectrum ofνefrom Muon Decay and Implications for the Lorentz Structure of the Weak Interaction

The KARMEN experiment uses the reaction ${}_{}{}^{12}{}_{}{}^{}C({\nu }_e,e^{-}{)}^{12}{\mathrm{N}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$ to measure the energy distribution of ${\nu }_e$ emitted in muon decay at rest ${\mu }^{+}\to e^{+}+{\nu }_e+{\overline{\nu }}_{\mu }$. The ${\nu }_e$ analog ${\omega }_L$ of the famous Michel parameter $\rho$ has been derived from a maximum-likelihood analysis of events near the kinematic end point, $E_{\max }=52.8\mathrm{MeV}$. The result, ${\omega }_L=({2.7}_{-3.3\mathrm{}}^{+3.8\mathrm{}}\pm 3.1)\times {10}^{-2\mathrm{}}$, is in good agreement with the standard model prediction ${\omega }_L=0\mathrm{}$. We deduce a 90% confidence upper limit of ${\omega }_L\le 0.113$, which corresponds to a limit of $|g_{\mathrm{RL}}^S{+2g}_{\mathrm{RL}}^T|\le 0.78$ on the interference term between scalar and tensor coupling constants.