Test of optimization procedures

A. P. Contogouris; N. Mebarki

doi:10.1103/PhysRevD.39.1464

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Test of optimization procedures

A. P. Contogouris and N. Mebarki

Department of Physics, McGill University, Montreal, Canada

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Phys. Rev. D 39, 1464 – Published 1 March, 1989

DOI: https://doi.org/10.1103/PhysRevD.39.1464

Abstract

On the basis of a recent O( $α_{s}^{3}$ ) calculation by Gorishny, Kataev, and Larin of the ratio &= $σ_{tot (e^{-} e^{+}}$ →hadrons)/σ( $e^{-}$ $e^{+}$ → $μ^{-}$ $μ^{+}$ ) we carry out the following test of two optimization procedures [principle of minimal sensitivity (PMS) and fastest apparent convergence (FAC)]: First, using O( $α_{s}^{2}$ ) calculations, we determine the optimal ${R_{e}^{-} e^{+}}^{(2)}$ ; then, using the O( $α_{s}^{3}$ ) calculation, we determine the optimal ${R_{e}^{-} e^{+}}^{(3)}$ . We form the fractional difference ${(R_{e}^{-} e^{+}}^{(3)}$ ${- R_{e}^{-} e^{+}}^{(2)}$ ) ${/ R_{e}^{-} e^{+}}^{(2)}$ , and compare it with the same quantity in the usual schemes (minimal subtraction and modified minimal subtraction). We find that this difference is largest in the FAC scheme and next to largest in the PMS scheme. Our results cast doubt on the usefulness of optimization.

References (8)

S. Gorishny, A. Kataev, and A. Larin, in Hadron Structure '87, proceedings of the Conference, Smolenice, Czechoslovakia, 1987, edited by D. Krupa (Physics and Applications, Vol. 14) (Physics Institute of EPRC of the Slovak Acadamy of Science, Bratislava, 1988).
W. Celmaster and R. Gonsalves, Phys. Rev. Lett. 44, 560 (1980); Phys. Rev. D 21, 3112 (1980) M. Dine and J. Sapirstein, Phys. Rev. Lett. 43, 668 (1979); K. Chetyrkin, A. Kataev and F. Tkatchov, Phys. Lett. 85B, 227 (1979).
P. Stevenson, Phys. Rev. D 23, 2916 (1981); Phys. Lett. 100B, 61 (1981).
G. Grunberg, Phys. Lett. 95B, 70 (1980); Phys. Rev. D 29, 2315 (1984).
See, e.g., P. Aurenche et al., Nucl. Phys. B286, 553 (1987); , ibid. B297, 661 (1988). For some issues involved in optimization, see A. H. Mueller, Proceedings of Workshop on Hard Hadronic Processes, St. Croix, 1987 (unpublished).
C. J. Maxwell, Phys. Rev. D 28, 2037 (1983).
D. Duke and R. Roberts, Phys. Rep. 120, 275 (1985).
On the basis of Ref. 1, similar conclusions were obtained in a different way by G. Altarelli. See G. Altarelli, presented at the CERN 1987-88 Academic Training Programme (unpublished).

[c1] S. Gorishny, A. Kataev, and A. Larin, in Hadron Structure '87, proceedings of the Conference, Smolenice, Czechoslovakia, 1987, edited by D. Krupa (Physics and Applications, Vol. 14) (Physics Institute of EPRC of the Slovak Acadamy of Science, Bratislava, 1988).

[c2] W. Celmaster and R. Gonsalves, Phys. Rev. Lett. 44, 560 (1980); Phys. Rev. D 21, 3112 (1980) M. Dine and J. Sapirstein, Phys. Rev. Lett. 43, 668 (1979); K. Chetyrkin, A. Kataev and F. Tkatchov, Phys. Lett. 85B, 227 (1979).

[c3] P. Stevenson, Phys. Rev. D 23, 2916 (1981); Phys. Lett. 100B, 61 (1981).

[c4] G. Grunberg, Phys. Lett. 95B, 70 (1980); Phys. Rev. D 29, 2315 (1984).

[c5] See, e.g., P. Aurenche et al., Nucl. Phys. B286, 553 (1987); , ibid. B297, 661 (1988). For some issues involved in optimization, see A. H. Mueller, Proceedings of Workshop on Hard Hadronic Processes, St. Croix, 1987 (unpublished).

[c6] C. J. Maxwell, Phys. Rev. D 28, 2037 (1983).

[c7] D. Duke and R. Roberts, Phys. Rep. 120, 275 (1985).

[c8] On the basis of Ref. 1, similar conclusions were obtained in a different way by G. Altarelli. See G. Altarelli, presented at the CERN 1987-88 Academic Training Programme (unpublished).

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Test of optimization procedures

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