Muon decay: Measurement of the energy spectrum of theνeas a novel precision test for the standard model

The energy distribution of the ${\nu }_{\mathit{e}}$ from the decay of unpolarized ${\mathrm{\mu }}^{+}$ has been calculated on the basis of the most general four-fermion interaction. It depends on a parameter called ω which equals zero in the standard-model. It is shown that the recent measurement of the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${\nu }_{\mathit{e}}$,${\mathit{e}}^{\mathrm{-}}$ ${)}^{12}$Ng.s. with ${\nu }_{\mathit{e}}$ from ${\mathrm{\mu }}^{+}$ decay at rest not only yields the absorption cross section, but also independently determines ω with a precision of Δω=0.026 for 100 measured events. This corresponds to ‖${\mathit{g}}_{\mathit{L}\mathit{L}}^{\mathit{S}}$‖≤0.37, where ${\mathit{g}}_{\mathit{L}\mathit{L}}^{\mathit{S}}$ describes a scalar interaction with left-handed μ and e and right-handed neutrinos.