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

4th International Hadron Physics Conference

Constantinou, M.^1 ; Costa, M.^1 ; Frezzotti, R.^2 ; Lubicz, V.^3 ; Martinelli, G.^4 ; Meloni, D.^3 ; Panagopoulos, H.^1 ; Simula, S.^3

Department of Physics, University of Cyprus, Nicosia

CY-1678, Cyprus^1

Dipartimento di Fisica, Università di Roma Tor Vergata, INFN, Rome

I-00133, Italy^2

Dipartimento di Fisica, Università Roma Tre, INFN, Rome

I-00146, Italy^3

SISSA, Trieste

I-34136, Italy^4

关键词: Effective Hamiltonian;    Lattice formulation;    Lattice perturbation;    Lattice simulation;    Mixing coefficient;    Nonperturbative;    Renormalization;    The standard model;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/562/1/012002/pdf
DOI  :  10.1088/1742-6596/562/1/012002

来源: IOP

【 摘 要 】

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. 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.