RI-(S)MOM to MS¯ conversion for BK at two-loop order

Gorbahn, M ORCID: 0000-0002-8863-7318, Jäger, S ORCID: 0009-0001-4711-9194 and Kvedaraitė, S ORCID: 0000-0002-0269-9543 (2025) RI-(S)MOM to MS¯ conversion for BK at two-loop order Journal of High Energy Physics, 2025 (9). 11-. ISSN 1126-6708, 1029-8479

PDF JHEP09(2025)011.pdf - Open Access published version Download (954kB) | Preview

Abstract

The Kaon bag parameter B̂K 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 B̂K 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 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 B̂Kf=3=0.762760, 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<inf>K</inf>| = 2.171(65)<inf>pert.</inf>(71)<inf>non-pert.</inf>(153)<inf>param.</inf> × 10⁻³. We briefly discuss applications of our results to D-meson mixing.

Item Type:	Article
Uncontrolled Keywords:	5106 Nuclear and Plasma Physics, 5107 Particle and High Energy Physics, 4902 Mathematical Physics, 49 Mathematical Sciences, 51 Physical Sciences
Divisions:	Faculty of Science & Engineering Faculty of Science & Engineering > School of Physical Sciences Faculty of Science & Engineering > School of Physical Sciences > Mathematical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	27 Nov 2025 08:17
Last Modified:	23 May 2026 10:33
DOI:	10.1007/JHEP09(2025)011
Related Websites:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3195671
Disclaimer:	The University of Liverpool is not responsible for content contained on other websites from links within repository metadata. Please contact us if you notice anything that appears incorrect or inappropriate.