Penguin-like Diagrams from the Standard Model

TL;DR

This paper provides an exact calculation of penguin diagram vertices in the Standard Model, focusing on higher-order electroweak processes involving flavor changes and their implications for flavor-changing phenomena.

Contribution

It introduces a precise computation of penguin diagram vertices in the tHooft-Feynman gauge, including renormalization and relations among vertex functions, advancing understanding of rare flavor-changing processes.

Findings

Derived explicit expressions for gluon-photon penguin vertex form factors.

Established relations among penguin diagram vertex functions via Ward-Takahashi identity.

Estimated contributions of penguin diagrams to flavor-changing processes.

Abstract

The Standard Model is highly successful in describing the interactions of leptons and quarks. There are, however, rare processes that involve higher order effects in electroweak interactions. One specific class of processes is the penguin-like diagram. Such class of diagrams involves the neutral change of quark flavours accompanied by the emission of a gluon (gluon penguin), a photon (photon penguin), a gluon and a photon (gluon-photon penguin), a Z-boson (Z penguin), or a Higgs-boson (Higgs penguin). Such diagrams do not arise at the tree level in the Standard Model. They are, however, induced by one-loop effects. In this paper, we present an exact calculation of the penguin diagram vertices in the tHooft-Feynman gauge. Renormalization of the vertex is effected by a prescription by Chia and Chong which gives an expression for the counter term identical to that obtained by employing Ward-Takahashi identity. The on-shell vertex functions for the penguin diagram vertices are obtained. The various penguin diagram vertex functions are related to one another via Ward-Takahashi identity. From these, a set of relations is obtained connecting the vertex form factors of various penguin diagrams. Explicit expressions for the gluon-photon penguin vertex form factors are obtained, and their contributions to the flavor changing processes estimated.