Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential Equations for Two-Loop Four-Point Functions   At variance with fully inclusive quantities, which have been computed already
at the two- or three-loop level, most exclusive observables are still known
only at one-loop, as further progress was hampered so far by the greater
computational problems encountered in the study of multi-leg amplitudes beyond
one loop. We show in this paper how the use of tools already employed in
inclusive calculations can be suitably extended to the computation of loop
integrals appearing in the virtual corrections to exclusive observables, namely
two-loop four-point functions with massless propagators and up to one off-shell
leg. We find that multi-leg integrals, in addition to integration-by-parts
identities, obey also identities resulting from Lorentz-invariance. The
combined set of these identities can be used to reduce the large number of
integrals appearing in an actual calculation to a small number of master
integrals. We then write down explicitly the differential equations in the
external invariants fulfilled by these master integrals, and point out that the
equations can be used as an efficient method of evaluating the master integrals
themselves. We outline strategies for the solution of the differential
equations, and demonstrate the application of the method on several examples.

5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics