Reduction method for dimensionally regulated one-loop N-point Feynman integrals
Abstract
We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D=6, a triangle integral in D=4, and a general two-point integral in D space time dimensions. All the divergences present in the original integral are contained in the general two-point integral and associated coefficients. The problem of vanishing of the kinematic determinants has been solved in an elegant and transparent manner. Being derived with no restrictions regarding the external momenta, the method is completely general and applicable for arbitrary kinematics. In particular, it applies to the integrals in which the set of external momenta contains subsets comprised of two or more collinear momenta, which are unavoidable when calculating one-loop contributions to the hard-scattering amplitude for exclusive hadronic processes at large momentum transfer in PQCD. Further, a tensor decomposition scheme for N-point rank P(\le N) tensor integrals is formulated. Through the tensor decomposition and the scalar reduction presented, the computation of the massless one-loop integrals with an arbitrary number of external lines can be mastered. The iterative structure makes it easy to implement the formalism in an algebraic computer program. The conceptual problems related to the construction of multi-parton one-loop amplitudes in massless field theories are thus solved.Keywords
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