  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.
