@misc{10481/106491,
year = {2025},
month = {9},
url = {https://hdl.handle.net/10481/106491},
abstract = {The Kaon bag parameter BˆK plays a critical role in constraining the parameters
of the CKM matrix and in probing physics beyond the Standard Model. In this work, we
improve the precision of BˆK to next-to-next-to-leading order (NNLO) and provide world
averages for both 3- and 4-favour theories. In the course of this, as our main technical
development, we carry out the two-loop matching between the RI-(S)MOM and MS schemes.
Our world averages combine all available lattice data, including conversion between the 3-
and 4-favour theories as appropriate. We obtain the result Bˆ
(f=3)
K = 0.7627(60), which
comprises the complete set of 3- and 4-favour lattice results and can be used directly in
phenomenological applications. The error is dominated by lattice uncertainties and missing
higher-order corrections (residual scale dependence). Our averages include a PDG rescaling
factor of 1.28 refecting a mild tension among the lattice inputs after inclusion of NNLO
corrections in the scheme conversion and matching across favour thresholds. Our averages
imply an updated value |ϵK| = 2.171(65)pert.(71)non-pert.(153)param. ×10−3
. We briefy discuss
applications of our results to D-meson mixing.},
organization = {MICIU/AEI/10.13039/501100011033 -  FEDER/UE (grant PID2022-139466NB-C21)},
organization = {Consejería de Universidad, Investigación e Innovación, Gobierno de España and Unión Europea – NextGenerationEU (AST22 6.5 and CNS2022-136024)},
organization = {UK Science and Technology Facilities Council (grant ST/X000796/1)},
publisher = {Springer},
keywords = {CP Violation},
keywords = {Higher-Order Perturbative Calculations},
keywords = {Kaons},
title = {RI-(S)MOM to MS conversion for BK at two-loop order},
doi = {10.1007/JHEP09(2025)011},
author = {Gorbahn, Martin and Jäger, Sebastian and Kvedaraitè, Sandra},
}