  Large neutrino event numbers in future experiments measuring coherent elastic
neutrino nucleus scattering allow precision measurements of standard and new
physics. We analyze the current and prospective limits of a light scalar
particle coupling to neutrinos and quarks, using COHERENT and CONUS as
examples. Both lepton number conserving and violating interactions are
considered. It is shown that current (future) experiments can probe for scalar
masses of a few MeV couplings down to the level of $10^{-4}$ $(10^{-6})$.
Scalars with masses around the neutrino energy allow to determine their mass
via a characteristic spectrum shape distortion. Our present and future limits
are compared with constraints from supernova evolution, Big Bang
nucleosynthesis and neutrinoless double beta decay. We also outline UV-complete
underlying models that include a light scalar with coupling to quarks for both
lepton number violating and conserving coupling to neutrinos.
