One Spin Trace Formalism for $B_K$

Abstract

It has been known for some time that there are two methods to calculate $B_K$ with staggered fermions: one is the two spin trace formalism and the other is the one spin trace formalism. Until now, the two spin trace formalism has been exclusively used for weak matrix element calculations with staggered fermions. Here, the one spin trace formalism to calculate $B_K$ with staggered fermions is explained. It is shown that the one spin trace operators require additional chiral partner operators in order to keep the continuum chiral behavior. The renormalization of the one spin trace operators is described and compared with the two spin trace formalism.

47 pages, latex, 4 figures are available on request

References in corpus (5)

• On the Viability of Lattice Perturbation Theory
• Perturbative Corrections for Staggered Fermion Bilinears
• Perturbative Corrections for Staggered Four-Fermion Operators
• Perturbative renormalization factors for bilinear and four-quark operators for Kogut-Susskind fermions on the lattice
• Quark Mass Renormalization on the Lattice with Staggered Fermions

Cited by in corpus (9)

• One-loop matching coefficients for improved staggered bilinears
• Perturbative matching of staggered four-fermion operators with hypercubic fat links
• Perturbative improvement of staggered fermions using fat links
• Perturbative Matching of the staggered four-fermion operators for e'/e
• One-loop matching factors for staggered bilinear operators with improved gauge actions
• One-loop matching of Delta S=2 four-quark operators with improved staggered fermions
• Chiral symmetry and taste symmetry from the eigenvalue spectrum of staggered Dirac operators
• Penguin diagrams for improved staggered fermions
• Miscellanies of $K^0-{\bar{K}}^0$ mixing and $B_K$