Low-energy effective field theory below the electroweak scale: matching at one loop

Understand

We compute the one-loop matching between the Standard Model Effective Field Theory and the low-energy effective field theory below the electroweak scale, where the heavy gauge bosons, the Higgs particle, and the top quark are integrated out.

• The complete set of matching equations is derived including effects up to dimension six in the power counting of both theories.
• We present the results for general flavor structures and include both the $CP$-even and $CP$-odd sectors.
• The matching equations express the masses, gauge couplings, as well as the coefficients of dipole, three-gluon, and four-fermion operators in the low-energy theory in terms of the parameters of the Standard Model Effective Field Theory.