Heavy Quark Vacuum Polarization Function at O(alpha**2(s)) O(alpha**3(s))

Jul, 2008
17 pages
Published in:
  • Nucl.Phys.B 813 (2009) 349-369
e-Print:
Report number:
  • MPP-2008-83

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Abstract: (Elsevier)
We determine the full mass and q 2 dependence of the heavy quark vacuum polarization function Π ( q 2 ) and its contribution to the total e + e − cross section at O ( α s 2 ) and O ( α s 3 ) in perturbative QCD. We use known results for the expansions of Π ( q 2 ) at high energies, in the threshold region and around q 2 = 0 , conformal mapping and the Padé approximation method. From our results for Π ( q 2 ) we determine numerically at O ( α s 3 ) the previously unknown non-logarithmic contributions in the high-energy expansion at order ( m 2 / q 2 ) i for i = 0 , 1 and the coefficients in the expansion around q 2 = 0 at order q 2 n with n ⩾ 2 . We also determine at O ( α s 2 ) the previously unknown O ( v 0 ) constant term in the expansion of Π ( q 2 ) in the threshold region, where v is the quark velocity. Our method allows for a quantitative estimate of uncertainties and can be systematically improved once more information in the three kinematic regions becomes available by future multi-loop computations. For the contributions to the total e + e − cross section at O ( α s 2 ) we confirm results obtained earlier by Chetyrkin, Kühn and Steinhauser.
  • quark: vacuum polarization
  • heavy quark
  • quantum chromodynamics: perturbation theory
  • electron positron: interaction
  • vacuum polarization
  • mass dependence
  • momentum transfer dependence
  • total cross section
  • transformation: conformal
  • Pade approximation