Abstract.
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 \(\alpha_s^3 n_f^2\). 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 \(\alpha_s^3\) contribution.
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References
K.G. Chetyrkin, J.H. Kühn, A. Kwiatkowski, Phys. Rep. 277, 189 (1996)
M. Steinhauser, Phys. Rep. 364, 247 (2002)
K.G. Chetyrkin, J.H. Kühn, M. Steinhauser, Nucl. Phys. B 482, 213 (1996)
K.G. Chetyrkin, R. Harlander, M. Steinhauser, Phys. Rev. D 58, 014012 (1998)
K.G. Chetyrkin, J.H. Kühn, M. Steinhauser, Nucl. Phys. B 505, 40 (1997)
J.H. Kühn, M. Steinhauser, Nucl. Phys. B 619, 588 (2001)
D.J. Broadhurst, Z. Phys. C 54, 599 (1992)
M. Steinhauser, Comput. Phys. Commun. 134, 335 (2001)
K.G. Chetyrkin, F.V. Tkachov, Nucl. Phys. B 192, 159 (1981)
S. Laporta, Int. J. Mod. Phys. A 15, 5087 (2000)
T. van Ritbergen, J.A.M. Vermaseren, S.A. Larin, Phys. Lett. B 400, (1997), 379
M. Czakon, The four-loop QCD beta-function and anomalous dimensions (2004), hep-ph/0411261
Y. Schröder, Nucl. Phys. Proc. Suppl. 116, 402 (2003)
P. Mastrolia, E. Remiddi, Nucl. Phys. Proc. Suppl. 89, 76 (2000)
J.A.M. Vermaseren, New features of FORM (2000), math-ph/0010025
R.H. Lewis, Fermat’s User Guide, http:/www.bway.netlewis/
E. Remiddi, SOLVE, unpublished, available from the author
C. Anastasiou, A. Lazopoulos, JHEP 07, 046 (2004)
S. Laporta, E. Remiddi, Acta Phys. Polon. B 28, 959 (1997)
Y. Schröder, M. Steinhauser, private communication, Y. Schröder, A. Vuorinen, in preparation
S. Laporta, Phys. Lett. B 549, 115 (2002)
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Received: 22 December 2004, Published online: 3 March 2005
K.G. Chetyrkin: On leave from Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, 117312, Russia.
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Chetyrkin, K.G., Kühn, J.H., Mastrolia, P. et al. Heavy quark vacuum polarization: first two moments of the \({\mathcal{O}}(\alpha_s^3 n_f^2)\) contribution. Eur. Phys. J. C 40, 361–366 (2005). https://doi.org/10.1140/epjc/s2005-02151-y
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DOI: https://doi.org/10.1140/epjc/s2005-02151-y