Differential equations for loop integrals without squared propagators

Abstract

We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two-and three-loop diagrams. For these diagrams, the differential equations can thus be computed using "unitarity-compatible" integration-by-parts reductions, which simplify the reduction problem by avoiding integrals with higher-power propagators.

Two-loop leading-color helicity amplitudes for three-photon production at the LHC

“…A number of gauge theories are being studied, starting from string and supersymmetric theories [1][2][3][4][5][6][7][8][9][10][11][12][13], to gravity [14][15][16], to Yang-Mills [17,18], to QED [19] and QCD [20][21][22][23][24][25][26][27][28][29][30][31][32] and ultimately to the full Standard Model [33][34][35][36][37][38][39][40][41][42]. Research on generic methods for solving multi-loop integrals is also ongoing [43][44][45][46][47][48][49][50]…”

Triangle diagram, distance geometry and Symmetries of Feynman Integrals

“…SFI novelties include the definitions of the group and its orbits, as well as the reduction to a line integral. Other recent approaches to the evaluation of Feynman Integrals include a direct solution [9], avoiding squared propagators [10], Intersection theory [11] and a development of loop-tree duality [12].…”