Non-perturbative matching of three/four-flavor Wilson coefficients with a position-space procedure
March 30, 2020
August 27, 2020
We construct a strategy to non-perturbatively convert Wilson coefficients in the four-flavor theory to those in the three-flavor theory. This non-perturbative matching is expected to reduce one of the biggest systematic uncertainties in RBC/UKQCD's $K¥to¥pi¥pi$ calculation, where the matching was performed perturbatively at scales below the charm threshold. Since our method uses two-point functions in position space, which are a gauge-invariant and are free from contact terms, it prevents irrelevant mixing with gauge noninvariant operators and operators that vanish by the equations of motion. In this report, we present the strategy and our preliminary results for the non-perturbative matching of the Wilson coefficients that multiply the $¥Delta S=1$ four-quark operators associated with $K¥to¥pi¥pi$ decays.
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