$K \to \pi$ matrix elements of the chromomagnetic operator on the lattice

Understand

We present the results of the first lattice QCD calculation of the $K \to \pi$ matrix elements of the chromomagnetic operator $O_{CM} = g\, \bar s\, \sigma_{\mu\nu} G_{\mu\nu} d$, which appears in the effective Hamiltonian describing $\Delta S = 1$ transitions in and beyond the Standard Model.

• Having dimension 5, the chromomagnetic operator is characterized by a rich pattern of mixing with operators of equal and lower dimensionality.
• The multiplicative renormalization factor as well as the mixing coefficients with the operators of equal dimension have been computed at one loop in perturbation theory.
• The power divergent coefficients controlling the mixing with operators of lower dimension have been determined non-perturbatively, by imposing suitable subtraction conditions.