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The heavy-quark contribution to the polarisation function $\Pi$ at higher perturbative orders is presently only known approximately.
A. O. G. Källén and A. Sabry, Fourth order vacuum polarization , Kong. Dan. Vid. Sel. Mat. Fys. Med. 29
1955
Earlier work this paper cites.
Academic Press, Inc., 1970
G. A. Baker Jr. and J. L. Gammel, The Padé Approximant in Theoretical Physics , vol. 71 of Mathematics in Science and Engineering , ch. 1, pp. 1–38 · 1970
Earlier work this paper cites.
V. A. Novikov, L. B. Okun, M. A. Shifman, A. I. Vainshtein, M. B. Voloshin and V. I. Zakharov, Sum Rules for Charmonium and Charmed Mesons Decay Rates in Quantum Chromodynamics , Phys. Rev. Lett. 38
1977
Earlier work this paper cites.
V. A. Novikov, L. B. Okun, M. A. Shifman, A. I. Vainshtein, M. B. Voloshin and V. I. Zakharov, Charmonium and Gluons: Basic Experimental Facts and Theoretical Introduction , Phys. Rept. 41
1978
Earlier work this paper cites.
J. R. Dormand and P. J. Prince, A family of embedded Runge-Kutta formulae , Journal of Computational and Applied Mathematics 6
1980
Earlier work this paper cites.
R. Tarrach, The Pole Mass in Perturbative QCD , Nucl. Phys. B183
1981
Earlier work this paper cites.
K. G. Chetyrkin and F. V. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops , Nucl. Phys. B192
1981
Earlier work this paper cites.
O. V. Tarasov, Anomalous dimensions of quark masses in three loop approximation , JINR-P2-82-900, 1982
1982
Earlier work this paper cites.
N. Gray, D. J. Broadhurst, W. Grafe and K. Schilcher, Three Loop Relation of Quark MS ¯ \overline{\rm MS} and Pole Masses , Z. Phys. C48
1990
Earlier work this paper cites.
A. V. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation , Phys. Lett. B254
1991
Earlier work this paper cites.
P. Nogueira, Automatic feynman graph generation , J. Comput. Phys. 105
1993
Earlier work this paper cites.
A. H. Hoang, J. H. Kühn and T. Teubner, Radiation of light fermions in heavy fermion production , Nucl. Phys. B452
1995
Earlier work this paper cites.
K. G. Chetyrkin, J. H. Kühn and M. Steinhauser, Heavy Quark Vacuum Polarisation to Three Loops , Phys. Lett. B371
1996
Earlier work this paper cites.
K. Chetyrkin, J. H. Kühn and M. Steinhauser, Three loop polarization function and 𝒪 ( α s 2 ) {\cal O}(\alpha_{s}^{2}) corrections to the production of heavy quarks , Nucl.Phys. B482
1996
Earlier work this paper cites.
E. Remiddi, Differential equations for Feynman graph amplitudes , Nuovo Cim. A110
1997
Earlier work this paper cites.
K. G. Chetyrkin, Quark mass anomalous dimension to 𝒪 ( α s 4 ) {\cal O}(\alpha_{s}^{4}) , Phys. Lett. B404
1997
Earlier work this paper cites.
J. A. M. Vermaseren, S. A. Larin and T. van Ritbergen, The four loop quark mass anomalous dimension and the invariant quark mass , Phys. Lett. B405
1997
Earlier work this paper cites.
K. G. Chetyrkin and M. Steinhauser, Short distance mass of a heavy quark at order α s 3 \alpha_{s}^{3} , Phys. Rev. Lett. 83
1999
Earlier work this paper cites.
T. van Ritbergen, A. N. Schellekens and J. A. M. Vermaseren, Group theory factors for Feynman diagrams , Int. J. Mod. Phys. A14
1999
Earlier work this paper cites.
K. G. Chetyrkin and M. Steinhauser, The Relation between the MS ¯ \overline{\rm MS} and the on-shell quark mass at order α s 3 \alpha_{s}^{3} , Nucl. Phys. B573
2000
Earlier work this paper cites.
K. Melnikov and T. v. Ritbergen, The three loop relation between the MS ¯ \overline{\text{MS}} and the pole quark masses , Phys.Lett. B482
2000
Earlier work this paper cites.
A. H. Hoang et al., Top - anti-top pair production close to threshold: Synopsis of recent NNLO results , Eur. Phys. J.direct 2
2000
Earlier work this paper cites.
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations , Int.J.Mod.Phys. A15
2000
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions , Nucl. Phys. B580
2000
Cited alongside, same era.
C. W. Bauer, A. Frink and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language , J. Symb. Comput. 33
2002
Cited alongside, same era.
S. Laporta, High precision ϵ \epsilon expansions of massive four loop vacuum bubbles , Phys.Lett. B549
2002
Cited alongside, same era.
Y. Schröder and A. Vuorinen, High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles , JHEP 0506
2005
Cited alongside, same era.
K. Chetyrkin, J. H. Kühn, P. Mastrolia and C. Sturm, Heavy-quark vacuum polarization: First two moments of the 𝒪 ( α s 3 n f 2 ) {\cal O}(\alpha_{s}^{3}n_{f}^{2}) contribution , Eur.Phys.J. C40
2005
Cited alongside, same era.
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Y. Schröder and M. Steinhauser, Four-loop singlet contribution to the electroweak ρ \rho parameter , Phys.Lett. B622
2005
Cited alongside, same era.
R. Boughezal, M. Czakon and T. Schutzmeier, Four-Loop Tadpoles: Applications in QCD , Nucl.Phys.Proc.Suppl. 160
2006
Cited alongside, same era.
K. G. Chetyrkin, J. H. Kühn and C. Sturm, Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD , Eur. Phys. J. C48
2006
Cited alongside, same era.
R. Boughezal, M. Czakon and T. Schutzmeier, Charm and bottom quark masses from perturbative QCD , Phys. Rev. D74
2006
Cited alongside, same era.
K. Chetyrkin, M. Faisst, C. Sturm and M. Tentyukov, ϵ \epsilon -finite basis of master integrals for the integration-by-parts method , Nucl.Phys. B742
2006
Cited alongside, same era.
Y. Schröder and M. Steinhauser, Four-loop decoupling relations for the strong coupling , JHEP 0601
2006
Cited alongside, same era.
B. A. Kniehl and A. V. Kotikov, Calculating four-loop tadpoles with one non-zero mass , Phys.Lett. B638
2006
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