  We constrain general Dirac neutrino interactions based on the Standard Model
Effective Field Theory framework extended with right-handed neutrinos $N$
(SMNEFT) using deep inelastic and coherent elastic neutrino scattering, nuclear
beta decay, and meson decay data, and high energy electron-proton and
proton-proton collider data. We compute the one-loop anomalous dimensions of
the low-energy effective field theory (LEFT) below the electroweak scale and of
SMNEFT above the electroweak scale. The tree-level matching between LEFT and
SMNEFT is performed at the electroweak scale. Currently, the most stringent
limits on scalar and tensor interactions arise from pseudoscalar meson decays
and the LHC measurements at the per mille level. In the future, the upcoming
High-Luminosity LHC (HL-LHC) has the potential to reach the $10^{-4}$ level and
LHeC can play an important role under certain theoretical assumptions.
