Year: 2025
Type: article
Abstract: A bstract The Kaon bag parameter $$ {\hat{B}}_K $$ B ̂ K 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 $$ {\hat{B}}_K $$ B ̂ K to next-to-next-to-leading order (NNLO) and provide world averages for both 3- and 4-flavour theories. In the course of this, as our main technical development, we carry out the two-loop matching between the RI-(S)MOM and $$ \overline{\textrm{MS}} $$ MS ¯ schemes. Our world averages combine all available lattice data, including conversion between the 3- and 4-flavour theories as appropriate. We obtain the result $$ {\hat{B}}_K^{\left(f=3\right)}=0.7627(60) $$ B ̂ K f = 3 = 0.7627 60 , which comprises the complete set of 3- and 4-flavour 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 reflecting a mild tension among the lattice inputs after inclusion of NNLO corrections in the scheme conversion and matching across flavour thresholds. Our averages imply an updated value | ϵ K | = 2 . 171(65) pert. (71) non-pert. (153) param. × 10 − 3 . We briefly discuss applications of our results to D -meson mixing.
Source: Journal of High Energy Physics
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413897959