A search for two body muon decay signals
  Lepton family number violation is tested by searching for $\mu^+\to e^+X^0$ decays among the 5.8$\times 10^8$ 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 $\mu^+\to e^+X^0$ decays, which can arise from interactions violating both lepton flavor and parity conservation. Branching ratio limits of order $10^{-5}$ are obtained for bosons with masses of 13 - 80 MeV/c$^2$ and with different decay asymmetries. For bosons with masses less than 13 MeV/c$^{2}$ the asymmetry dependence is much stronger and the 90% limit on the branching ratio varies up to $5.8 \times 10^{-5}$. This is the first study that explicitly evaluates the limits for anisotropic two body muon decays. 
R. Bayes, J. Bueno, Yu. I. Davydov, P. Depommier, W. Faszer, M. C.   Fujiwara, C. A. Gagliardi, A. Gaponenko, D. R. Gill, A....
hep-ex