Further precise determinations of <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math></span> from lattice QCD

C. T. H. Davies; K. Hornbostel; G. P. Lepage; P. McCallum; J. Shigemitsu; J. Sloan

doi:10.1103/PhysRevD.56.2755

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Further precise determinations of $α_{s}$ from lattice QCD

C. T. H. Davies¹, K. Hornbostel², G. P. Lepage³, P. McCallum¹, J. Shigemitsu⁴, and J. Sloan⁵

¹University of Glasgow and the UKQCD Collaboration, Glasgow G12 8QQ, United Kingdom
²Southern Methodist University, Dallas, Texas 75275
³Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853
⁴The Ohio State University, Columbus, Ohio 43210
⁵Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055

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Phys. Rev. D 56, 2755 – Published 1 September, 1997

DOI: https://doi.org/10.1103/PhysRevD.56.2755

Abstract

We present a new determination of the strong coupling constant from lattice QCD simulations. We use four different short-distance quantities to obtain the coupling, three different (infrared) meson splittings to tune the simulation parameters, and a wide range of lattice spacings, quark masses, and lattice volumes to test for systematic errors. Our final result consists of ten different determinations of $α_{P}^{(3)} (8.2 GeV),$ which agree well with each other and with our previous results. The most accurate of these, when evolved perturbatively to the $Z^{0}$ mass, gives $α_{\bar{MS}}^{(5)} {(M}_{Z}) = 0.1174 (24) .$ We compare our results with those obtained from other recent lattice simulations.

References (31)

See, for example, P. N. Burrows, Acta Phys. Pol. B 28, 701 (1997).
C. T. H. Davies, K. Hornbostel, G. P. Lepage, A. Lidsey, J. Shigemitsu, and J. Sloan, Phys. Lett. B 345, 42 (1995). Our formula for $\ln W_{1, 1}$ is slightly different from that in our earlier paper because we have shifted the $α_{P}$ scale from $3.41 / a$ to $3.40 / a .$ The latter is the correct scale at infinite volume.
An independent analysis of this effect that uses preliminary versions of our data is given in B. Grinstein and I. Z. Rothstein, Phys. Lett. B 385, 265 (1996).
See for example, R. Gupta and T. Bhattacharya, Phys. Rev. D 55, 7203 (1997); B. J. Gough, G. M. Hockney, A. X. El-Khadra, A. S. Kronfeld, P. B. Mackenzie, B. P. Mertens, T. Onogi, J. N. Simone, Fermilab Report No. FERMILAB-PUB-96-283-T, hep-ph/9610223, 1996 (unpublished).
G. P. Lepage and B. A. Thacker, in Field Theory on the Lattice, Proceedings of the International Symposium, Seilloc, France, 1987, edited by A. Billoire et al. [Nucl. Phys. B (Proc. Suppl.) 4, 199 (1988)]; B. A. Thacker and G. P. Lepage, Phys. Rev. D 43, 196 (1991); G. P. Lepage, L. Magnea, C. Nakhleh, U. Magnea, and K. Hornbostel, 46, 4052 (1992).
C. T. H. Davies, K. Hornbostel, A. Langnau, G. P. Lepage, A. Lidsey, J. Shigemitsu, and J. Sloan, Phys. Rev. D 50, 6963 (1994).
C. T. H. Davies, K. Hornbostel, G. P. Lepage, A. J. Lidsey, J. Shigemitsu, and J. Sloan, Phys. Rev. D 52, 6519 (1995).
C. T. H. Davies, K. Hornbostel, A. Langnau, G. P. Lepage, A. J. Lidsey, C. Morningstar, J. Shigemitsu, and J. Sloan, Phys. Rev. Lett. 73, 2654 (1994).
These gauge-field configurations were provided by G. Kilcup and collaborators. There were 105 configurations on $16^{3} \times 24$ lattices.
These gauge-field configurations were provided by J. Kogut and collaborators. There were 149 configurations on $16^{3} \times 32$ lattices.
These gauge-field configurations were provided by the UKQCD collaboration. There were 200 configurations on $12^{3} \times 24$ lattices for $β = 5.7,$ and 216 configurations on $24^{3} \times 48$ lattices for $β = 6.2.$
The gauge-field configurations were provided by the HEMCGC Collaboration, K. Bitar et al., in Lattice ’91, Proceedings of the International Symposium, Tsukuba, Japan, edited by M. Fukugita et al. [Nucl. Phys. B (Proc. Suppl.) 26, 259 (1992)]; Phys. Rev. D 46, 2169 (1992); 48, 370 (1993). There were 399 configurations at $a m = 0.01$ and 199 at $a m = 0.025,$ all on $16^{3} \times 32$ lattices. The staggered quark action was used for the light quarks, and the hybrid molecular dynamics algorithm for the dynamical configurations.
The gauge-field configurations were provided by the MILC Collaboration, C. Bernard et al., in Lattice ’92, Proceedings of the International Symposium, Amsterdam the Netherlands, edited by J. Smit and P. van Baal [Nucl. Phys. B (Proc. Suppl.) 30, 369 (1996)]; Phys. Rev. D 48, 4419 (1993); in Lattice ’93, Proceedings of the International Symposium, Dallas, Texas, edited by T. Draper et al. [Nucl. Phys. B (Proc. Suppl.) 34, 366 (1994)]; Phys. Rev. D 45, 3854 (1992). There were 299 configurations at $a m = 0.0125$ on $16^{3} \times 32$ lattices. The staggered quark action was used for the light quarks, and the hybrid molecular dynamics algorithm for the dynamical configurations.
S. M. Catterall, F. R. Devlin, I. T. Drummond, and R. R. Horgan, Phys. Lett. B 321, 246 (1994).
H. Trottier, Phys. Rev. D 55, 6844 (1997).
F. J. Yndurain, The Theory of Quark and Gluon Interactions (Springer, Berlin, 1993).
G. P. Lepage and P. B. Mackenzie, Phys. Rev. D 48, 2250 (1993).
S. J. Brodsky, G. P. Lepage, and P. B. Mackenzie, Phys. Rev. D 28, 228 (1983).
The second-order coefficients were obtained by extrapolating to infinite volume those found in U. Heller and F. Karsch, Nucl. Phys. B251, 254 (1985); B258, 29 (1985); H. Hamber and C. Wu, Phys. Lett. 127B, 119 (1983). Third-order coefficients are from Monte Carlo simulations, W. Dimm, G. Hockney, G. P. Lepage, and P. B. Mackenzie (unpublished). These have a similar uncertainty. See also P. Weisz, Phys. Lett. 100B, 331 (1981); H. S. Sharatchandra, H. J. Thun, and P. Weisz, Nucl. Phys. B192, 205 (1981); K. M. Bitar et al., Phys. Rev. D 48, 370 (1993).
This coefficient is obtained by combining the definition of $α_{P}^{{(n}_{f})}$ (see [2]) with results in B. Alles, M. Campostrini, A. Feo, and H. Panagopoulos, Phys. Lett. B 324, 433 (1994); M. Luscher and P. Weisz, 349, 165 (1995); Nucl. Phys. B452, 234 (1995).
M. Peter, Phys. Rev. Lett. 78, 602 (1997).
T. Appelquist, M. Dine, and I. J. Muzinich, Phys. Rev. D 17, 2074 (1978); Phys. Lett. 69B, 231 (1977).
The $n_{f} = 0$ Monte Carlo results are from the Fermilab study discussed in Ref. [17]; those for $n_{f} = 2$ are from [12][13].
See [17] and also S. P. Booth, D. S. Henty, A. Hulsebos, A. C. Irving, C. Michael, and P. W. Stephenson, Phys. Lett. B 294, 385 (1992); M. Lüscher, R. Sommer, P. Weisz, and U. Wolff, Nucl. Phys. B413, 481 (1994); K. Schilling and G. S. Bali, in Lattice ’93 [13], p. 147, and references therein.
A. X. El-Khadra, G. Hockney, A. S. Kronfeld, and P. B. Mackenzie, Phys. Rev. Lett. 69, 729 (1992); A. X. El-Khadra, in Lattice ’93 [13], p. 141; G. P. Lepage, in Lattice ’91 [12], p. 45; T. Onogi, S. Aoki, M. Fukugita, S. Hashimoto, N. Ishizuka, H. Mino, M. Okawa, and A. Ukawa, in Lattice ’93 [13], p. 492.
Another determination based upon an $n_{f} = 2$ simulation and a perturbative correction for $n_{f}$ is given in S. Aoki, M. Fukugita, S. Hashimoto, N. Ishizuka, H. Mino, M. Okawa, T. Onogi, and A. Ukawa, Phys. Rev. Lett. 74, 22 (1995). Their results agree with ours, within larger errors.
For a useful discussion of this procedure, see G. Rodrigo and A. Santamaria, Phys. Lett. B 313, 441 (1993).
The $b$ -quark mass is from [8].
P. Weisz, in Lattice ’95, Proceedings of the International Symposium, Melbourne, Australia, edited by T. D. Kieu et al. [Nucl. Phys. B (Proc. Suppl.) 47, 71 (1996)].
J. Shigemitsu, in Lattice ’96, Proceedings of the International Symposium, St. Louis, Missouri, edited by C. Bernard et al. [Nucl. Phys. B (Proc. Suppl.) 53, 16 (1997)].
M. Alford, W. Dimm, G. P. Lepage, G. Hockney, and P. B. Mackenzie, Phys. Lett. B 361, 87 (1995).

[c1] See, for example, P. N. Burrows, Acta Phys. Pol. B 28, 701 (1997).

[c2] C. T. H. Davies, K. Hornbostel, G. P. Lepage, A. Lidsey, J. Shigemitsu, and J. Sloan, Phys. Lett. B 345, 42 (1995). Our formula for $\ln W_{1, 1}$ is slightly different from that in our earlier paper because we have shifted the $α_{P}$ scale from $3.41 / a$ to $3.40 / a .$ The latter is the correct scale at infinite volume.

[c3] An independent analysis of this effect that uses preliminary versions of our data is given in B. Grinstein and I. Z. Rothstein, Phys. Lett. B 385, 265 (1996).

[c4] See for example, R. Gupta and T. Bhattacharya, Phys. Rev. D 55, 7203 (1997); B. J. Gough, G. M. Hockney, A. X. El-Khadra, A. S. Kronfeld, P. B. Mackenzie, B. P. Mertens, T. Onogi, J. N. Simone, Fermilab Report No. FERMILAB-PUB-96-283-T, hep-ph/9610223, 1996 (unpublished).

[c5] G. P. Lepage and B. A. Thacker, in Field Theory on the Lattice, Proceedings of the International Symposium, Seilloc, France, 1987, edited by A. Billoire et al. [Nucl. Phys. B (Proc. Suppl.) 4, 199 (1988)]; B. A. Thacker and G. P. Lepage, Phys. Rev. D 43, 196 (1991); G. P. Lepage, L. Magnea, C. Nakhleh, U. Magnea, and K. Hornbostel, 46, 4052 (1992).

[c6] C. T. H. Davies, K. Hornbostel, A. Langnau, G. P. Lepage, A. Lidsey, J. Shigemitsu, and J. Sloan, Phys. Rev. D 50, 6963 (1994).

[c7] C. T. H. Davies, K. Hornbostel, G. P. Lepage, A. J. Lidsey, J. Shigemitsu, and J. Sloan, Phys. Rev. D 52, 6519 (1995).

[c8] C. T. H. Davies, K. Hornbostel, A. Langnau, G. P. Lepage, A. J. Lidsey, C. Morningstar, J. Shigemitsu, and J. Sloan, Phys. Rev. Lett. 73, 2654 (1994).

[c9] These gauge-field configurations were provided by G. Kilcup and collaborators. There were 105 configurations on $16^{3} \times 24$ lattices.

[c10] These gauge-field configurations were provided by J. Kogut and collaborators. There were 149 configurations on $16^{3} \times 32$ lattices.

[c11] These gauge-field configurations were provided by the UKQCD collaboration. There were 200 configurations on $12^{3} \times 24$ lattices for $β = 5.7,$ and 216 configurations on $24^{3} \times 48$ lattices for $β = 6.2.$

[c12] The gauge-field configurations were provided by the HEMCGC Collaboration, K. Bitar et al., in Lattice ’91, Proceedings of the International Symposium, Tsukuba, Japan, edited by M. Fukugita et al. [Nucl. Phys. B (Proc. Suppl.) 26, 259 (1992)]; Phys. Rev. D 46, 2169 (1992); 48, 370 (1993). There were 399 configurations at $a m = 0.01$ and 199 at $a m = 0.025,$ all on $16^{3} \times 32$ lattices. The staggered quark action was used for the light quarks, and the hybrid molecular dynamics algorithm for the dynamical configurations.

[c13] The gauge-field configurations were provided by the MILC Collaboration, C. Bernard et al., in Lattice ’92, Proceedings of the International Symposium, Amsterdam the Netherlands, edited by J. Smit and P. van Baal [Nucl. Phys. B (Proc. Suppl.) 30, 369 (1996)]; Phys. Rev. D 48, 4419 (1993); in Lattice ’93, Proceedings of the International Symposium, Dallas, Texas, edited by T. Draper et al. [Nucl. Phys. B (Proc. Suppl.) 34, 366 (1994)]; Phys. Rev. D 45, 3854 (1992). There were 299 configurations at $a m = 0.0125$ on $16^{3} \times 32$ lattices. The staggered quark action was used for the light quarks, and the hybrid molecular dynamics algorithm for the dynamical configurations.

[c14] S. M. Catterall, F. R. Devlin, I. T. Drummond, and R. R. Horgan, Phys. Lett. B 321, 246 (1994).

[c15] H. Trottier, Phys. Rev. D 55, 6844 (1997).

[c16] F. J. Yndurain, The Theory of Quark and Gluon Interactions (Springer, Berlin, 1993).

[c17] G. P. Lepage and P. B. Mackenzie, Phys. Rev. D 48, 2250 (1993).

[c18] S. J. Brodsky, G. P. Lepage, and P. B. Mackenzie, Phys. Rev. D 28, 228 (1983).

[c19] The second-order coefficients were obtained by extrapolating to infinite volume those found in U. Heller and F. Karsch, Nucl. Phys. B251, 254 (1985); B258, 29 (1985); H. Hamber and C. Wu, Phys. Lett. 127B, 119 (1983). Third-order coefficients are from Monte Carlo simulations, W. Dimm, G. Hockney, G. P. Lepage, and P. B. Mackenzie (unpublished). These have a similar uncertainty. See also P. Weisz, Phys. Lett. 100B, 331 (1981); H. S. Sharatchandra, H. J. Thun, and P. Weisz, Nucl. Phys. B192, 205 (1981); K. M. Bitar et al., Phys. Rev. D 48, 370 (1993).

[c20] This coefficient is obtained by combining the definition of $α_{P}^{{(n}_{f})}$ (see [2]) with results in B. Alles, M. Campostrini, A. Feo, and H. Panagopoulos, Phys. Lett. B 324, 433 (1994); M. Luscher and P. Weisz, 349, 165 (1995); Nucl. Phys. B452, 234 (1995).

[c21] M. Peter, Phys. Rev. Lett. 78, 602 (1997).

[c22] T. Appelquist, M. Dine, and I. J. Muzinich, Phys. Rev. D 17, 2074 (1978); Phys. Lett. 69B, 231 (1977).

[c23] The $n_{f} = 0$ Monte Carlo results are from the Fermilab study discussed in Ref. [17]; those for $n_{f} = 2$ are from [12][13].

[c24] See [17] and also S. P. Booth, D. S. Henty, A. Hulsebos, A. C. Irving, C. Michael, and P. W. Stephenson, Phys. Lett. B 294, 385 (1992); M. Lüscher, R. Sommer, P. Weisz, and U. Wolff, Nucl. Phys. B413, 481 (1994); K. Schilling and G. S. Bali, in Lattice ’93 [13], p. 147, and references therein.

[c25] A. X. El-Khadra, G. Hockney, A. S. Kronfeld, and P. B. Mackenzie, Phys. Rev. Lett. 69, 729 (1992); A. X. El-Khadra, in Lattice ’93 [13], p. 141; G. P. Lepage, in Lattice ’91 [12], p. 45; T. Onogi, S. Aoki, M. Fukugita, S. Hashimoto, N. Ishizuka, H. Mino, M. Okawa, and A. Ukawa, in Lattice ’93 [13], p. 492.

[c26] Another determination based upon an $n_{f} = 2$ simulation and a perturbative correction for $n_{f}$ is given in S. Aoki, M. Fukugita, S. Hashimoto, N. Ishizuka, H. Mino, M. Okawa, T. Onogi, and A. Ukawa, Phys. Rev. Lett. 74, 22 (1995). Their results agree with ours, within larger errors.

[c27] For a useful discussion of this procedure, see G. Rodrigo and A. Santamaria, Phys. Lett. B 313, 441 (1993).

[c28] The $b$ -quark mass is from [8].

[c29] P. Weisz, in Lattice ’95, Proceedings of the International Symposium, Melbourne, Australia, edited by T. D. Kieu et al. [Nucl. Phys. B (Proc. Suppl.) 47, 71 (1996)].

[c30] J. Shigemitsu, in Lattice ’96, Proceedings of the International Symposium, St. Louis, Missouri, edited by C. Bernard et al. [Nucl. Phys. B (Proc. Suppl.) 53, 16 (1997)].

[c31] M. Alford, W. Dimm, G. P. Lepage, G. Hockney, and P. B. Mackenzie, Phys. Lett. B 361, 87 (1995).

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Further precise determinations of $α_{s}$ from lattice QCD

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Further precise determinations of αs from lattice QCD

Abstract

References (31)

Further precise determinations of $α_{s}$ from lattice QCD