We present the results of the first lattice QCD calculation of the K→π matrix elements of the chromomagnetic operator OCM=gsσμνGμνd, which appears in the effective Hamiltonian describing ΔS=1 transitions in and beyond the standard model. Having dimension five, 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 nonperturbatively, 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 Nf=2+1+1 dynamical quarks at three values of the lattice spacing. Our result for the B parameter of the chromomagnetic operator at the physical pion and kaon point is BCMOKπ=0.273(69), while in the SU(3) chiral limit we obtain BCMO=0.076(23). Our findings are significantly smaller than the model-dependent estimate BCMO∼1-4, currently used in phenomenological analyses, and improve the uncertainty on this important phenomenological quantity.
Constantinou, M., Costa, M., Frezzotti, R., Lubicz, V., Martinelli, G., Meloni, D., et al. (2018). K →π matrix elements of the chromomagnetic operator on the lattice. PHYSICAL REVIEW D, 97(7), 074501 [10.1103/PhysRevD.97.074501].