Journal
NUCLEAR PHYSICS B
Volume 813, Issue 3, Pages 349-369Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.nuclphysb.2008.12.005
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Funding
- MPI
- EU [MRTN-CT-2006-035482]
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We determine the full mass and q(2) dependence of the heavy quark vacuum polarization function Pi(q(2)) and its contribution to the total e(+)e(-) cross section at O(alpha(2)(s)) and O(alpha(3)(s)) in perturbative QCD. We use known results for the expansions of Pi(q(2)) at high energies, in the threshold region and around q(2) = 0, conformal mapping and the Pade approximation method. From our results for Pi(q(2)) we determine numerically at O(alpha(3)(s)) the previously unknown non-logarithmic contributions ill the high-energy expansion at older (m(2)/q(2))(i) for i = 0, 1 and the coefficients in the expansion around q(2) = 0 at order q(2n) with n >= 2. We also determine at O(alpha(2)(s)) the previously unknown O(nu(0)) constant term in the expansion of Pi(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 ill the three kinematic regions becomes available by future multi-loop computations. For the contributions to the total e(+)e(-) cross section at O(alpha(2)(s)) we confirm results obtained earlier by Chetyrkin, Kuhn and Steinhauser, (C) 2008 Elsevier B.V. All rights reserved.
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