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

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Abstract

We propose a Penguin-Box Expansion (PBE) for flavour-changing neutral-current (FCNC) processes. The basic elements of this expansion are universal mt-dependent functions resulting from various box and penguin diagrams common to many FCNC processes. The mt-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, KL → μμ, KL → π0 e+e- and the ratio ε{lunate}′ ε{lunate}. We find simple analytic formulae for all these decays which exhibit the dependence on mt and other parameters of the standard model. We point out that due to the decrease of sin δ with increasing mt, the branching ratios for CP-violating semi-leptonic decays exhibit, in contrast to CP-conserving decays, a much weaker dependence on mt than expected on the basis of the box and penguin diagram functions alone. New insight suppression of ε{lunate}′ ε{lunate} for large mt 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}mt {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. © 1991.

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Buchalla, G., Buras, A. J., & Harlander, M. K. (1991). Penguin-box expansion: Flavour-changing neutral-current processes and a heavy top quark. Nuclear Physics, Section B, 349(1), 1–47. https://doi.org/10.1016/0550-3213(91)90186-2

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