Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heavy-quark vacuum polarization: first two moments of the O(alphas^3
  nf^2) contribution   The vacuum polarization due to a virtual heavy quark pair and specifically
the coefficients of its Taylor expansion in the external momentum are closely
related to moments of the cross section for quark-antiquark pair production in
electron-positron annihilation. Relating measurement and theoretically
calculated Taylor coefficients, an accurate value for charm- and bottom-quark
mass can be derived, once corrections from perturbative QCD are sufficiently
well under control. Up to three-loop order these have been evaluated
previously. We now present a subset of four-loop contributions to the lowest
two moments, namely those from diagrams which involve two internal loops from
massive and massless fermions coupled to virtual gluons, hence of order
alphas^3 nf^2. The calculation demonstrates the applicability of Laporta's
algorithm to four-loop vacuum diagrams with both massive and massless
propagators and should be considered a first step towards the full evaluation
of the order alphas^3 contribution.

20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics