Penguin-box expansion: Flavour-changing neutral-current processes and a heavy top quark

We propose a Penguin-Box Expansion (PBE) for flavour-changing neutral-current (FCNC) processes. The basic elements of this expansion are universal m_t-dependent functions resulting from various box and penguin diagrams common to many FCNC processes. The m_t-independent coefficients of these functions can be calculated by using renormalization group techniques. Of particular interest is a manifestly gauge independent formulation of PBE. We illustrate these ideas by discussing the semi-leptonic decays K → πνν, K_L → μμ, K_L → π⁰ e⁺e^- and the ratio ε{lunate}′ ε{lunate}. We find simple analytic formulae for all these decays which exhibit the dependence on m_t and other parameters of the standard model. We point out that due to the decrease of sin δ with increasing m_t, the branching ratios for CP-violating semi-leptonic decays exhibit, in contrast to CP-conserving decays, a much weaker dependence on m_t than expected on the basis of the box and penguin diagram functions alone. New insight suppression of ε{lunate}′ ε{lunate} for large m_t is obtained. Analyzing the relevant hadronic matrix elements beyond the 1 N approach, we find that for 100 GeV {slanted equal to or less-than}m_t {slanted equal to or less-than} 300 GeV, the values -25 × 10^-3 {slanted equal to or less-than} ε{lunate}′ ε{lunate} {slanted equal to or less-than}3.2 × 10^-3 are possible. The structure of PBE beyond the leading logarithmic approximation is presented.