Four quark operators for kaon bag parameter with gradient flow

Asobu Suzuki, Yusuke Taniguchi, Hiroshi Suzuki, Kazuyuki Kanaya

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


To study the CP-violation using the K0-K̄0 oscillation, we need the kaon bag parameter which represents QCD corrections in the leading Feynman diagrams. The lattice QCD provides us with the only way to evaluate the kaon bag parameter directly from the first principles of QCD. However, a calculation of relevant four quark operators with theoretically sound Wilson-type lattice quarks had to carry a numerically big burden of extra renormalizations and resolution of extra mixings due to the explicit chiral violation. Recently, the small flow-time expansion (SFtX) method was proposed as a general method based on the gradient flow to correctly calculate any renormalized observables on the lattice, irrespective of the explicit violations of related symmetries on the lattice. To apply the SFtX method, we need matching coefficients, which relate finite operators at small flow times in the gradient flow scheme to renormalized observables in conventional renormalization schemes. In this paper, we calculate the matching coefficients for four quark operators and quark bilinear operators, relevant to the kaon bag parameter.

Original languageEnglish
Article number034508
JournalPhysical Review D
Issue number3
Publication statusPublished - Aug 15 2020

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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