Perturbative and non-perturbative renormalization results of the Chromomagnetic Operator on the Lattice

Understand

The Chromomagnetic operator (CMO) mixes with a large number of operators under renormalization.

• We identify which operators can mix with the CMO, at the quantum level.
• Even in dimensional regularization (DR), which has the simplest mixing pattern, the CMO mixes with a total of 9 other operators, forming a basis of dimension-five, Lorentz scalar operators with the same flavor content as the CMO.
• Among them, there are also gauge noninvariant operators; these are BRST invariant and vanish by the equations of motion, as required by renormalization theory.