The chromomagnetic operator on the lattice

TL;DR

This paper investigates the lattice computation of the chromomagnetic operator's matrix elements, focusing on operator mixing and perturbative calculations within the twisted mass lattice framework.

Contribution

It provides a detailed one-loop perturbative calculation of mixing coefficients for the chromomagnetic operator on the lattice, addressing operator mixing complexities.

Findings

Calculated mixing coefficients for the chromomagnetic operator

Analyzed operator mixing with lower-dimensional operators

Used twisted mass lattice formulation with improved gluon action

Abstract

We study matrix elements of the "chromomagnetic" operator on the lattice. This operator is contained in the strangeness-changing effective Hamiltonian which describes electroweak effects in the Standard Model and beyond. Having dimension 5, the chromomagnetic operator is characterized by a rich pattern of mixing with other operators of equal and lower dimensionality, including also non gauge invariant quantities; it is thus quite a challenge to extract from lattice simulations a clear signal for the hadronic matrix elements of this operator. We compute all relevant mixing coefficients to one loop in lattice perturbation theory; this necessitates calculating both 2-point (quark-antiquark) and 3-point (gluon-quark-antiquark) Green's functions at nonzero quark masses. We use the twisted mass lattice formulation, with Symanzik improved gluon action. For a comprehensive presentation of our results, along with detailed explanations and a more complete list of references, we refer to our forthcoming publication [1].