Long-distance contribution to εK from lattice QCD

Bai, Ziyuan; Christ, Norman H.; Karpie, Joseph M.; Sachrajda, Christopher T.; Soni, Amarjit; Wang, Bigeng

doi:10.1103/physrevd.109.054501

Title: Long-distance contribution to ε K from lattice QCD

Journal Article · 04 March 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.109.054501 · OSTI ID:2318614

Bai, Ziyuan ^[1];

^[2];

^[1]; Sachrajda, Christopher T. ^[3]; Soni, Amarjit ^[4];

^[5]

Columbia Univ., New York, NY (United States)
Columbia Univ., New York, NY (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Univ. of Southampton (United Kingdom)
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Columbia Univ., New York, NY (United States); Univ. of Kentucky, Lexington, KY (United States)

A lattice QCD approach to the calculation of the long-distance contributions to ϵ_K is presented. This parameter describes indirect CP violation in K → ππ decay. While the short-distance contribution to ϵ_K can be accurately calculated in terms of standard model parameters and a single hadronic matrix element, B_K, there is a long-distance part which is estimated to be approximately 5% of the total and is more difficult to determine. A method for determining this small but phenomenologically important contribution to ϵ_K using lattice QCD is proposed and a complete exploratory calculation of the contribution is presented. This exploratory calculation uses an unphysical light quark mass corresponding to a 339 MeV pion mass and an unphysical charm quark mass of 968 MeV, expressed in the $$\overline{MS}$$ scheme at 2 GeV. This calculation demonstrates that future work should be able to determine this long-distance contribution from first principles with a controlled error of 10% or less.

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Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States); Columbia Univ., New York, NY (United States)

Sponsoring Organization:: USDOE; Science and Technology Facilities Council (STFC)

Grant/Contract Number:: 32SC0011941; SC0011941; AC05-06OR23177; SC0012704; SC001704; ST/T000775/1

OSTI ID:: 2318614

Alternate ID(s):: OSTI ID: 2324573

Report Number(s):: JLAB-THY-23-3937; DOE/OR/23177-7226; TRN: US2409720

Journal Information:: Physical Review. D., Vol. 109, Issue 5; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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