Estimating perturbative coefficients in quantum field theory using Padé approximants

Mark A. Samuel; G. Li; Eric Steinfelds

doi:10.1103/PhysRevD.48.869

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Estimating perturbative coefficients in quantum field theory using Padé approximants

Mark A. Samuel, G. Li, and Eric Steinfelds

Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078

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Phys. Rev. D 48, 869 – Published 15 July, 1993

DOI: https://doi.org/10.1103/PhysRevD.48.869

Abstract

We show how one can accelerate the convergence of a perturbation series by using Padé approximants. We use the first few coefficients of each perturbation series to predict the next term. We first check our method for known results and then predict the value of, as yet, unknown terms. Our results for $a_{μ} - a_{e}$ , $a_{e}$ , $a_{μ}$ , $R_{τ}$ , and the QCD $β$ function are remarkably good.

References (10)

G. B. West, Phys. Rev. Lett. 67, 1388 (1991)
D. T. Barclay and C. J. Maxwell, Phys. Rev. Lett. 69, 3417 (1992) A. Duncan and R. Willey (unpublished) Mark A. Samuel and Eric Steinfelds (unpublished)
G. B. West (unpublished)
T. Kinoshita and W. J. Marciano, in Quantum Electrodynamics, edited by T. Kinoshita (World Scientific, Singapore, 1990), p. 419 M. A. Samuel and G. Li, Phys. Rev. D 44, 3935 (1991)
T. Kinoshita, B. Nizic, and Y. Okamoto, Phys. Rev. D 41, 593 (1990)
T. Kinosita, in Quantum Electrodynamics [[4]], p. 218
M. A. Samuel and L. R. Surguladze, Phys. Rev. D 44, 1602 (1991) S. G. Gorishny, A. L. Kataev, and S. A. Larin, Phys. Lett. B 259, 144 (1991)
O. V. Tarasov, A. A. Vladimirov, and A. Yu. Zharkov, Phys. Lett. 93B, 429 (1980)
M. Luban and H. Chew, Phys. Rev. D 31, 2643 (1985)
J. Fleischer, M. Pindor, P. A. Raczka, and R. Raczka, "Approximate Four-Loop Analysis of the $R (e^{+} e^{-})$ Ratio in QCD," Bielefeld Report No. BI-TP 05/89, 1989 (unpublished)

[c1] G. B. West, Phys. Rev. Lett. 67, 1388 (1991)

[c2] D. T. Barclay and C. J. Maxwell, Phys. Rev. Lett. 69, 3417 (1992) A. Duncan and R. Willey (unpublished) Mark A. Samuel and Eric Steinfelds (unpublished)

[c3] G. B. West (unpublished)

[c4] T. Kinoshita and W. J. Marciano, in Quantum Electrodynamics, edited by T. Kinoshita (World Scientific, Singapore, 1990), p. 419 M. A. Samuel and G. Li, Phys. Rev. D 44, 3935 (1991)

[c5] T. Kinoshita, B. Nizic, and Y. Okamoto, Phys. Rev. D 41, 593 (1990)

[c6] T. Kinosita, in Quantum Electrodynamics [[4]], p. 218

[c7] M. A. Samuel and L. R. Surguladze, Phys. Rev. D 44, 1602 (1991) S. G. Gorishny, A. L. Kataev, and S. A. Larin, Phys. Lett. B 259, 144 (1991)

[c8] O. V. Tarasov, A. A. Vladimirov, and A. Yu. Zharkov, Phys. Lett. 93B, 429 (1980)

[c9] M. Luban and H. Chew, Phys. Rev. D 31, 2643 (1985)

[c10] J. Fleischer, M. Pindor, P. A. Raczka, and R. Raczka, "Approximate Four-Loop Analysis of the $R (e^{+} e^{-})$ Ratio in QCD," Bielefeld Report No. BI-TP 05/89, 1989 (unpublished)

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Estimating perturbative coefficients in quantum field theory using Padé approximants

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References (10)

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