  We consider the non-oscillatory explanations of the low energy excess of
events detected by MiniBooNE. We present a systematic search for
phenomenological scenarios based on new physics which can produce the excess.
We define scenarios as series of transitions and processes which connect
interactions of accelerated protons in target with single shower events in the
MiniBooNE detector. The key elements of the scenarios are production and decay
of new light $\mathcal{O}(\text{keV}-100\,\text{MeV})$ particles (fermions
or/and bosons). We find about $20$ scenarios with minimal possible number of
new particles and interaction points. In practice, they are all reduced to few
generic scenarios and in this way we develop the effective theory of the
MiniBooNE excess. We consider tests of the scenarios with near or close
detectors in neutrino experiments T2K ND280, NO$\nu$A, MINER$\nu$A as well as
in NOMAD and PS191. The scenarios immediately connect the MiniBooNE excess and
expected numbers of new physics events in these detectors. We compute the
expected numbers of events as functions of lifetimes and masses of new
particles and confront them with the corresponding experimental bounds. We
indicate scenarios that are excluded or strongly disfavored by one or several
experiments. Given our general approach, this work can also be regarded as the
effective theory of new physics at accelerator based neutrino experiments,
being relevant for future projects such as DUNE.
