Description
The Standard Model effective field theory (SMEFT) is one of the
preferred approaches for studying particle physics in the present
scenario. The dimension-six SMEFT operators are the most relevant ones
and have been studied in various works. The renormalization group
evolution equations of these operators are available in the literature
and facilitate examining the SMEFT on combined experimental information
gathered across different energy scales. But, the dimension-six
operators are not the dominant term for all observables, and some of
these operators are loop-generated when UV theories are matched to the
SMEFT. Also, considering that for relatively low values of the cut-off
scale of the SMEFT, contributions from dimension-eight operators cannot
be neglected.
In this work, we present the renormalization of the bosonic sector of
the dimension-eight operators by tree-level generated dimension-eight
operators in the matching of weakly coupled UV theories to the SMEFT.
These operators appear in the positivity constraints, which determine
the signs of certain combinations of Wilson coefficients based on the
unitarity and analyticity of the S-matrix. These constraints are
remarkably significant as any experimental evidence of a violation of
these constraints would indicate the invalidity of the EFT approach,
such as, for example, the existence of lighter degrees of freedom below
the cut-off scale of the EFT. Also, these restrictions can be taken into
account while defining priors on the fits aiming at constraining the
SMEFT parameter space.
