Short distance analysis of weak interactions

We systematically formulate the short distance analysis of weak interactions, and show that in an asymptotically free theory one can calculate the dependence of any weak amplitude on the W boson and heavy quark masses. Our main purpose is to settle some conceptual questions, but we also derive some new quantitative results. For example, we show that in the SU(3) gauge theory with four quark triplets, the two W boson contribution to KL → μμ will differ from the free quark theory estimate by a factor 25(1 − (α(M W /α(m p′) 1 25 )(α(M W )/α(m p′ )) 24 25 . We also show that the amplitudes for K+ → π +e+e− will differ from the free quark theory estimate by a factor of 1.66(α(M W )/α(m p′)) 2 9 − 1.88(α(M W )/α(m p′) −4 9 .