Effective Field Theory for Leptoquarks

Leptoquarks enter in several extensions of the Standard Model as possible solutions to a number of observed anomalies. We work within the soft-collinear effective theory framework to present a detailed analysis of the decay rates of the three leptoquarks that appear the most in literature, the scalars $S_1$ and $S_3$ and the vector $U_1^{\mu}$. Using renormalization group methods we resum the large logarithms arising from the evolution of the Wilson coefficients between the New Physics scale and the electroweak scale. We also derive the tree-level matching relations for the Wilson coefficients in the effective theory for some specific leptoquark models.