Light masses in short distance penguin loops

Penguin diagrams for decays such as b --> (s,d)gamma involve virtual loops of u or other light quarks. Logarithms of the virtual quark mass could, in principle, influence the phenomenological analysis of the decay. It is thus important to study these logarithms to all orders in QCD perturbation theory. In this paper we show that, at arbitrary order, the matrix elements of operators in the effective hamiltonian contributing to b --> s gamma are finite for the limit of m(u) --> 0 in penguin loops.