Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A semi-analytic method to compute Feynman integrals applied to four-loop
  corrections to the $\overline{\rm MS}$-pole quark mass relation   We describe a method to numerically compute multi-loop integrals, depending
on one dimensionless parameter $x$ and the dimension $d$, in the whole
kinematic range of $x$. The method is based on differential equations, which,
however, do not require any special form, and series expansions around singular
and regular points. This method provides results well suited for fast numerical
evaluation and sufficiently precise for phenomenological applications. We apply
the approach to four-loop on-shell integrals and compute the coefficient
function of eight colour structures in the relation between the mass of a heavy
quark defined in the $\overline{\rm MS}$ and the on-shell scheme allowing for a
second non-zero quark mass. We also obtain analytic results for these eight
coefficient functions in terms of harmonic polylogarithms and iterated
integrals. This allows for a validation of the numerical accuracy.

29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin