  In this work, we revisit the renormalization group equations (RGEs) of
dimension-seven (dim-7) operators in the Standard Model effective field theory
(SMEFT) resulting from mixing among dim-7 operators themselves by means of the
background field method. Adopting a recently proposed physical basis for dim-7
operators, we achieve the explicit RGEs of all non-redundant dim-7 operators in
the SMEFT for the first time. Together with those originating from the dim-5
and dim-6 operators, these results constitute the complete RGEs of dim-7
operators, and hence can be exploited to study full RG-running effects on some
lepton- or baryon-number-violating processes involving dim-7 operators in the
SMEFT, such as neutrino masses, neutrinoless double beta decay, meson and
nucleon decays. We perform an analysis of the structure and perturbative power
counting of the obtained one-loop anomalous dimension matrix, which is
consistent with a non-renormalization theorem and the naive dimension analysis.
Additionally, a partial check on some results is carried out by means of
different tools and quantum field gauges.
