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5
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84931516933
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These questions were originally posed by P. M. Stevenson (private communication to Dr. Gorishny, Dr. Kataev, and Dr. Larin, 1988), before the original Resup+e- calculation was completed.
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10
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84931516934
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edited by, C. Albright, H. Kasper, R. Raja, J. Yoh, World Scientific, Singapore
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(1993)
The Fermilab Meeting, Proceedings of the Annual Meeting of the Division of Particles and Fields of the APS, Batavia, Illinois, 1992
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31
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84931516931
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Two schemes, which for the same μ value are related by a′ = a(1 + v1 a + cdots), have tilde{Λ} parameters which are related by ln( tilde{Λ}′/ tilde{Λ}) = v1/b. This relation is exact, Ref. 19, Ref. 3
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32
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84931516932
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The choice of Λ overlineMS as the free parameter of QCD is an arbitrary choice, but a harmless one since the Λ of any other ``reference scheme'' could be related exactly to Λ overlineMS (see, Ref. 20, above). Thus, this choice affects only how the predictions are parametrized, and not their content. For complications related to flavor thresholds, see Appendix B.
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34
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84931516935
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Some authors use a different definition: tilde{ρ}2 = ρ2 + 1 / 4 c2.
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40
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84931516936
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Fixed point behavior will also be found in RS's which are sufficiently close to the ``optimized'' scheme. This is the case, for instance, in the ``fastest apparent convergence'' (FAC) or ``effective charge'' scheme (the RS in which r1=r2=0). However, this scheme gives an asup * that is 64 % larger than ours, for Nf=2.
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41
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4243375814
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The αs3 corrections to the Bjorken sum rule for polarized electroproduction and to the Gross-Llewellyn Smith sum rule
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The π2 term in r2, Ref. 2, gives a substantial negative contribution to ρ2. Another timelike process, hadronic decay of the Higgs boson, also has a sizable, negative ρ2: see, Ref. 9, and references therein. In a spacelike case, deep inelastic scattering, the third order QCD corrections to the Gross Llewellyn Smith, and Bjorken sum rules give ρ2's that are negative only for Nf ge 4 or 5. [See,] It may be that in this case fixed point behavior will extend to fewer flavors only in higher orders. Alternatively, might be that there is a real difference in behavior between spacelike and timelike processes. Another possibility is that exponentiation of some of the π2 contributions is important. See, e.g., 90B, 295, G. Parisi, Phys. Lett.
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(1980)
Physics Letters B
, vol.259
, pp. 345
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Larin, S.A.1
Vermaseren, J.A.M.2
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43
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0011564712
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It is noteworthy that the fixed point values all lie comfortably below the classical critical value 9 / 8π = 0.358 of
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(1977)
Phys. Lett.
, vol.67 B
, pp. 175
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Mandula, J.1
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44
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84931516948
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Obviously, the procedure may be repeated with different trial values of Λ overlineMS if one seeks to determine the value that gives the best fit to the Resup+e- data.
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58
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84931516950
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Crystal Ball Collaboration, C. Edwards et al., SLAC Report No. SLAC PUB 5160, 1990 (unpublished).
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60
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p. III.7A;
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78
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84931516952
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Sec. 5.
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88
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We thank Dr. R. S. Fletcher for helpful correspondence on this issue.
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89
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84931516954
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Yu. L. Dokshitzer, V. A. Khoze, and S. I. Troyan, Lund Report No. LU TP 92 10 (unpublished).
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90
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84931516955
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V. Khoze, in Proceedings of the XXVIth International Conference on High Energy Physics, Dallas, Texas, 1992, edited by J. Sanford, AIP Conf. Proc. No. 272 (AIP, New York, 1993).
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