Abstract
We study massless one-loop box integrals by treating the number of space-time dimensions D as a negative integer. We consider integrals with up to three kinematic scales ( s, t and either zero or one off-shell legs) and with arbitrary powers of propagators. For box integrals with q kinematic scales (where q=2 or 3) we immediately obtain a representation of the graph in terms of a finite sum of generalised hypergeometric functions with q−1 variables, valid for general D. Because the power each propagator is raised to is treated as a parameter, these general expressions are useful in evaluating certain types of two-loop box integrals which are one-loop insertions to one-loop box graphs. We present general expressions for this particular class of two-loop graphs with one off-shell leg, and give explicit representations in terms of polylogarithms in the on-shell case.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
