A class of Bessel function integrals with application in particle physics

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Abstract
Many problems in particle physics and field theory require the evaluation of integrals of the form l1,(l2),(l3)(p1,p2,p3)=4p1p2p3/ pi integral 0infinity r2j(l1)(p1r)j(l2)(p2r)j(l3)(p3r)dr. Our investigation arose in connection with a new method of partial wave mass renormalization of the electron self-energy in quantum electrodynamics (QED) where these integrals play a crucial role. Previous studies appear not to have led to expressions which are readily computable. We derive an explicit formula for the general case and a recursive method of construction which allows us to generate all cases of practical interest to high precision. Our algorithms are highly efficient on scalar computers and readily vectorize on suitable machines.