Search for two body muon decay signals

Lepton family number violation is tested by searching for ${\ensuremath{\mu}}^{+}\ensuremath{\rightarrow}{e}^{+}{X}^{0}$ decays among the $5.8\ifmmode\times\else\texttimes\fi{}{10}^{8}$ positive muon decay events analyzed by the TWIST collaboration. Limits are set on the production of both massless and massive ${X}^{0}$ bosons. The large angular acceptance of this experiment allows limits to be placed on anisotropic ${\ensuremath{\mu}}^{+}\ensuremath{\rightarrow}{e}^{+}{X}^{0}$ decays, which can arise from interactions violating both lepton flavor and parity conservation. Branching ratio limits of order ${10}^{\ensuremath{-}5}$ are obtained for bosons with masses of $13--80\text{ }\text{ }\mathrm{MeV}/{\mathrm{c}}^{2}$ and with different decay asymmetries. For bosons with masses less than $13\text{ }\text{ }\mathrm{MeV}/{\mathrm{c}}^{2}$ the asymmetry dependence is much stronger and the 90% limit on the branching ratio varies up to $5.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. This is the first study that explicitly evaluates the limits for anisotropic two body muon decays.