Kaon mixing beyond the standard model with physical masses

Boyle, P. A.; Erben, F.; Flynn, J. M.; Garron, N.; Kettle, J.; Mukherjee, R.; Tsang, J. T.

doi:10.1103/PhysRevD.110.034501

Title: Kaon mixing beyond the standard model with physical masses

Journal Article · 01 August 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.034501 · OSTI ID:2426408

Boyle, P. A.;

;

; Kettle, J.;

;

We present nonperturbative results for beyond the standard model kaon mixing matrix elements in the isospin symmetric limit ( $m_{u} = m_{d}$ ) of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with $N_{f} = 2 + 1$ flavors of dynamical domain wall fermions. For the first time, these quantities are simulated directly at the physical pion mass $m_{π} \sim 139 MeV$ for two different lattice spacings. We include data at three lattice spacings in the range $a = 0.11 - 0.07 fm$ and with pion masses ranging from the physical value up to 450 MeV. Compared to our earlier work, we have added both direct calculations at physical quark masses and a third lattice spacing making the removal of discretization effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalize the lattice operators nonperturbatively using RI-SMOM off-shell schemes. These schemes eliminate the need to model and subtract nonperturbative pion poles that arises in the RI-MOM scheme and, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the $\bar{MS}$ scheme at 3 GeV are $B_{K} \equiv B_{1} = 0.5240 (17) (54)$ , $B_{2} = 0.4794 (25) (35)$ , $B_{3} = 0.746 (13) (17)$ , $B_{4} = 0.897 (02) (10)$ and $B_{5} = 0.6882 (78) (94)$ , where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to $\bar{MS}$ . Published by the American Physical Society 2024

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0012704

OSTI ID:: 2426408

Report Number(s):: BNL--226145-2024-JAAM; 034501

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 3 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Dual QCD Insight into BSM Hadronic Matrix Elements for $K^0$--$\bar K^0$ Mixing from Lattice QCD Buras, A. J.; Gérard, J. -M. Acta Physica Polonica B, Vol. 50, Issue 2 https://doi.org/10.5506/APhysPolB.50.121	journal	January 2019