Abstract
We develop a systematic procedure for computing maximal unitarity cuts of multiloop Feynman integrals in arbitrary dimension. Our approach is based on the Baikov representation in which the structure of the cuts is particularly simple. We examine several planar and nonplanar integral topologies and demonstrate that the maximal cut inherits IBPs and dimension shift identities satisfied by the uncut integral. Furthermore, for the examples we calculated, we find that the maximal cut functions from different allowed regions, form the Wronskian matrix of the differential equations on the maximal cut.
Highlights
Amplitudes has been achieved, either via the unitarity method [1, 2] and its refinements [3, 4], or by the Ossola, Papadopoulos and Pittau (OPP) approach [5, 6] at the level of the integrand
We develop a systematic procedure for computing maximal unitarity cuts of multiloop Feynman integrals in arbitrary dimension
We provide nontrivial evidence that these m maximal cut functions form the Wronskian matrix associated with the differential equation satisfied by the master integrals on the maximal cut
Summary
We are interested in L-loop Feynman integrals with n external momenta and k propagators, Ia1,...ak,ak+1,...an ≡. For the case with some ai > 1, 1 ≤ i ≤ k, derivates of the Baikov polynomial are needed to get the residue This form can be used to derive integration-by-parts (IBP) identities [54, 55] and differential equations [52] on the maximal cut, and to identify master integrals [56, 57], by using Morse theory, tangent vectors and syzygy computations. For each fixed j, I1,...1,ak+1,...an (mj.)c.’s satisfy (the same form of) dimension shift identities and differential equations on the maximal cut The integrals over these subregions may not be independent. For the examples we considered in this paper, we find that d = nMI, the number of master integrals on the maximal cut.
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