  We develop the consequences of introducing a purely leptonic, lepton number
violating non-standard interaction (NSI) and standard model neutrino mixing
with a fourth, sterile neutrino in the analysis of short-baseline, neutrino
experiments. We focus on the muon decay at rest (DAR) result from the Liquid
Scintillation Neutrino Experiment (LSND) and the Karlsruhe and Rutherford
Medium Energy Neutrino Experiment (KARMEN). We make a comprehensive analysis of
lepton number violating, NSI effective operators and find nine that affect muon
decay relevant to LSND results. Two of these preserve the standard model (SM)
value 3/4 for the Michel rho and delta parameters and, overall, show favorable
agreement with precision data and the electron anti-neutrino signal from LSND
data. We display theoretical models that lead to these two effective operators.
In the model we choose to apply to DAR data, both electron anti-neutrino
appearance from muon anti-neutrino oscillation and electron anti-neutrino
survival after production from NSI decay of the positive muon contribute to the
expected signal. This is a unique feature of our scheme. We find a range of
parameters where both experiments can be accommodated consistently with recent
global, sterile neutrino fits to short baseline data. We comment on
implications of the models for new physics searches at colliders and comment on
further implications of the lepton number violating interactions plus sterile
neutrino-standard model neutrino mixing.
