Περίληψη:
We present in detail two resummation methods emerging from the
application of the Simplified Differential Equations approach to a
canonical basis of master integrals. The first one is a method which
allows for an easy determination of the boundary conditions, since it
finds relations between the boundaries of the basis elements and the
second one indicates how using the x -> 1 limit to the solutions of a
canonical basis, one can obtain the solutions to a canonical basis for
the same problem with one mass less. Both methods utilise the residue
matrices for the letters 0, 1 of the canonical differential
equation. As proof of concept, we apply these methods to a canonical
basis for the three-loop ladder-box with one external mass off-shell,
obtaining subsequently a canonical basis for the massless three-loop
ladder-box as well as its solution.
