Abstract
Relations between multiple unitarity cuts and coproducts of Feynman inte-grals are extended to allow for internal masses. These masses introduce new branch cuts, whose discontinuities can be derived by placing single propagators on shell and identified as particular entries of the coproduct. First entries of the coproduct are then seen to include mass invariants alone, as well as threshold corrections for external momentum channels. As in the massless case, the original integral can possibly be recovered from its cuts by starting with the known part of the coproduct and imposing integrability contraints. We formulate precise rules for cuts of diagrams, and we gather evidence for the relations to co-products through a detailed study of one-loop triangle integrals with various combinations of external and internal masses.
Highlights
The evaluation of Feynman integrals is a necessary ingredient for the precise determination of physical observables in perturbative quantum field theories
Our observations suggest that the coproduct can always be written in such a form where: (i) the first entries of the coproduct component ∆1,n−1 are either consistent with the thresholds of Mandelstam invariants or are internal masses themselves; (ii) the second entry is the discontinuity across the branch cut associated with the corresponding first entry, as is the case for diagrams with no internal masses [31]
In this paper we have studied the analytic structure of one-loop three-point Feynman integrals with different configurations of internal and external masses
Summary
The evaluation of Feynman integrals is a necessary ingredient for the precise determination of physical observables in perturbative quantum field theories. One of the results of that paper was the establishment of a relation between (multiple) cuts of diagrams and the coproduct of the corresponding Feynman integral. We explain how these cuts can be applied iteratively to reproduce multiple discontinuities. We have checked that the remaining cases do behave in the expected way
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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
