Renormalization and mixing in lattice QCD: The case of the chromomagnetic operator

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 StandardModel 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. We also provide a nonperturbative method to compute mixing with lower dimensional operators; we use this method in numerical simulations, and extract the mixing with the 3-dimensional scalar density, finding good agreement with one-loop results.