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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 isthe one spin trace formalism. Until now, the two spin trace formalism has beenexclusively used for weak matrix element calculations with staggered fermions.Here, the one spin trace formalism to calculate $ B_K $ with staggered fermionsis explained. It is shown that the one spin trace operators require additionalchiral partner operators in order to keep the continuum chiral behavior. Therenormalization of the one spin trace operators is described and compared withthe two spin trace formalism.Comment: 47 pages, latex, 4 figures are available on reques

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

One spin trace formalism for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">B</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">K</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>

One spin trace formalism forBK