Abstract
We compute the renormalisation factors (Z-matrices) of the ΔF = 2 four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We work with n f = 2+1 flavours of Domain-Wall fermions whose chiral-flavour properties are essential to maintain a continuum-like mixing pattern. We introduce new RI-SMOM renormalisation schemes, which we argue are better behaved compared to the commonly-used corresponding RI-MOM one. We find that, once converted to \( \overline{\mathrm{MS}} \), the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute the BSM neutral kaon mixing matrix elements in the companion paper [1]. We argue that the renormalisation procedure is responsible for the discrepancies observed by different collaborations, we will investigate and elucidate the origin of these differences throughout this work.
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The RBC/UKQCD collaboration., Boyle, P.A., Garron, N. et al. Neutral kaon mixing beyond the Standard Model with n f = 2 + 1 chiral fermions. Part 2: non perturbative renormalisation of the ΔF = 2 four-quark operators. J. High Energ. Phys. 2017, 54 (2017). https://doi.org/10.1007/JHEP10(2017)054
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DOI: https://doi.org/10.1007/JHEP10(2017)054