A five-fold Mellin-Barnes integral for the massless box diagram is reduced to a two-fold triangle integral using analytical regularization and residue calculus, without Barnes lemmas.
On conformal invariant integrals involving spin one-half and spin-one particles
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abstract
We consider the evaluation of D-dimensional conformal invariant integrals which involve spin one-half and spin-one particles. The star-triangle relation for the massless Yukawa theory is derived, and the longitudinal part of the three-point Green function of massless QED is determined to the lowest order in position space. The operator algebraic method of calculating massless Feynman integrals is used for the evaluation.
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A simple way to reduce the number of contours in the multi-fold Mellin-Barnes integrals
A five-fold Mellin-Barnes integral for the massless box diagram is reduced to a two-fold triangle integral using analytical regularization and residue calculus, without Barnes lemmas.