K -> pi matrix elements of the chromagnetic operator on the lattice

TL;DR

This paper reports the first lattice QCD calculation of K to pi matrix elements of the chromomagnetic operator, providing key non-perturbative data relevant for understanding Delta S=1 transitions in and beyond the Standard Model.

Contribution

It introduces a novel lattice QCD computation of the chromomagnetic operator matrix elements, including non-perturbative renormalization and mixing coefficients, for the first time.

Findings

Preliminary B_{CMO} value of 0.29(11) obtained.

Computed mixing coefficients and renormalization factors.

Results suggest a lower B_{CMO} than phenomenological estimates.

Abstract

We present preliminary results of the first lattice QCD calculation of the K -> pi matrix elements of the chromomagnetic operator O_{CM}=g sbar sigma_{munu} G_{munu} 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 computed non-perturbatively, by imposing suitable subtraction conditions. The numerical simulations have been carried out using the gauge field configurations produced by the European Twisted Mass Collaboration with N_f=2+1+1 dynamical quarks at three values of the lattice spacing. Our preliminary result for the B-parameter of the chromomagnetic operator is B_{CMO}=0.29(11), which can be compared with the estimate B_{CMO}~1-4 currently used in phenomenological analyses.