Abstract
We revisit the determination of α S (m 2 τ ) using a fit to inclusive τ hadronic spectral moments in light of (1) the recent calculation of the fourth-order perturbative coefficient K 4 in the expansion of the Adler function, (2) new precision measurements from BABAR of e+e− annihilation cross sections, which decrease the uncertainty in the separation of vector and axial-vector spectral functions, and (3) improved results from BABAR and Belle on τ branching fractions involving kaons. We estimate that the fourth-order perturbative prediction reduces the theoretical uncertainty, introduced by the truncation of the series, by 20% with respect to earlier determinations. We discuss to some detail the perturbative prediction of two different methods: fixed-order perturbation theory (FOPT) and contour-improved perturbative theory (CIPT). The corresponding theoretical uncertainties are studied at the τ and Z mass scales. The CIPT method is found to be more stable with respect to the missing higher order contributions and to renormalization scale variations. It is also shown that FOPT suffers from convergence problems along the complex integration contour. Nonperturbative contributions extracted from the most inclusive fit are small, in agreement with earlier determinations. Systematic effects from quark-hadron duality violation are estimated with simple models and found to be within the quoted systematic errors. The fit based on CIPT gives α S (m 2 τ )=0.344±0.005±0.007, where the first error is experimental and the second theoretical. After evolution to M Z we obtain α S (M 2 Z )=0.1212±0.0005±0.0008±0.0005, where the errors are respectively experimental, theoretical and due to the evolution. The result is in agreement with the corresponding N3LO value derived from essentially the Z width in the global electroweak fit. The α S (M 2 Z ) determination from τ decays is the most precise one to date.
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References
M. Davier, A. Höcker, Z. Zhang, Rev. Mod. Phys. 78, 1043 (2006). hep-ph/0507078
S. Narison, A. Pich, Phys. Lett. B 211, 183 (1988)
E. Braaten, Phys. Rev. D 39, 1458 (1989)
E. Braaten, S. Narison, A. Pich, Nucl. Phys. B 373, 581 (1992)
F. Le Diberder, A. Pich, Phys. Lett. B 289, 165 (1992)
P. Baikov, K.G. Chetyrkin, J.H. Kühn, SFB-CPP-08-04, TTP08-01 (2008). arXiv:0801.1821
BABAR Collaboration, B. Aubert et al., SLAC-PUB-12968, BABAR-PUB-07-052 (2007). arXiv:0710.4451
W. Marciano, A. Sirlin, Phys. Rev. L 61, 1815 (1988)
M. Davier, S. Eidelman, A. Höcker, Z. Zhang, Eur. Phys. J. C 27, 497 (2003). hep-ph/0208177
Particle Data Group, W.M. Yao et al., J. Phys. G 33, 1 (2006) and 2007 partial update for the 2008 edition
CKMfitter Group, J. Charles et al., Eur. Phys. J. C 41, 1 (2005). hep-ph/0406184. Updates at http://ckmfitter.in2p3.fr
ALEPH Collaboration, R. Barate et al., Eur. Phys. J. C 11, 599 (1999). hep-ex/9903015
F. Mané et al., DM1 Collaboration, Phys. Lett. B 112, 178 (1982)
D. Bisello et al., DM2 Collaboration, Z. Phys. C 52, 227 (1991)
CLEO Collaboration, D. Asner et al., Phys. Rev. D 61, 012002 (2000). hep-ex/9902022
CLEO Collaboration, T.E. Coan et al., Phys. Rev. L 92, 232001 (2004). hep-ex/0401005
J.J. Gomez-Cadenas, M.C. Gonzalez-Garcia, A. Pich, Phys. Rev. D 42, 3093 (1990)
P. Roig, AIP Conf. Proc. 964, 40–46 (2007). arXiv:0709.3734
M. Finkemeier, E. Mirkes, Z. Phys. C 69, 243 (1996). hep-ph/9503474
BABAR Collaboration, B. Aubert et al., Phys. Rev. L 100, 011801 (2008). arXiv:0707.2981
BABAR Collaboration, B. Aubert et al., Phys. Rev. D-RC 76, 051104 (2007)
BABAR Collaboration, D. Epifanov et al., Phys. Lett. B 654, 65 (2007). arXiv:0706.2231
ALEPH Collaboration, D. Buskulic et al., Phys. Lett. B 307, 209 (1993)
CLEO Collaboration, T. Coan et al., Phys. Lett. B 356, 580 (1995)
OPAL Collaboration, K. Ackerstaff et al., Eur. Phys. J. C 7, 571 (1999). hep-ex/9808019
F. Le Diberder, A. Pich, Phys. Lett. B 286, 147 (1992)
A.A. Pivovarov, Sov. J. Nucl. Phys. 54, 676 (1991)
A.A. Pivovarov, Z. Phys. C 53, 461 (1992)
G. Grunberg, Phys. Lett. B 95, 70 (1980); Erratum: Phys. Lett. B 110, 501 (1982)
G. Grunberg, Phys. Rev. D 29, 2315 (1984)
A. Dhar, Phys. Lett. B 128, 407 (1983)
A. Dhar, V. Gupta, Phys. Rev. D 29, 2822 (1983)
P.M. Stevenson, Phys. Rev. D 23, 2916 (1981)
P. Ball, M. Beneke, V.M. Braun, Nucl. Phys. B 452, 563 (1995). hep-ph/9502300
G. Altarelli, P. Nason, G. Ridolfi, Z. Phys. C 68, 257 (1995). hep-ph/9501240
M. Neubert, Nucl. Phys. B 463, 511 (1996). hep-ph/9509432
ALEPH Collaboration, R. Barate et al., Z. Phys. C 76, 15 (1997)
ALEPH Collaboration, R. Barate et al., Eur. Phys. J. C 4, 409 (1998)
M.A. Shifman, A.L. Vainshtein, V.I. Zakharov, Nucl. Phys. B 147, 385 (1979)
M.A. Shifman, A.L. Vainshtein, V.I. Zakharov, Nucl. Phys. B 147, 448 (1979)
M.A. Shifman, A.L. Vainshtein, V.I. Zakharov, Nucl. Phys. B 147, 519 (1979)
E. Poggio, H. Quinn, S. Weinberg, Phys. Rev. D 13, 1958 (1976)
E. Braaten, Phys. Rev. L 60, 1606 (1988)
M.A. Shifman, Quark-hadron duality, in Boris Ioffe Festschrift at the Frontier of Particle Physics, Handbook of QCD, ed. by M.A. Shifman (World Scientific, Singapore, 2001). hep-ph/0009131
O. Cata, M. Golterman, S. Peris, J. High Energy Phys. 0508, 076 (2005). hep-ph/0506004
E. Braaten, C.S. Li, Phys. Rev. D 42, 3888 (1990)
O. Cata, M. Golterman, S. Peris (2008). arXiv:0803.0246
S. Adler, Phys. Rev. D 10, 3714 (1974)
L.R. Surguladze, M.A. Samuel, Phys. Rev. L 66, 560 (1991); Erratum: Phys. Lett. 66, 2416 (1991)
S.G. Gorishnii, K.L. Kataev, S.A. Larin, Phys. Lett. B 259, 144 (1991)
K.G. Chetyrkin, A.L. Kataev, F.V. Tkachov, Phys. Lett. 85, 277 (1979)
M. Dine, J.R. Sapirstein, Phys. Rev. L 43, 668 (1979)
W. Celmaster, R.J. Gonsalves, Phys. Rev. L 44, 560 (1980)
S.A. Larin, T. van Ritbergen, J.A.M. Vermaseren, Phys. Lett. B 400, 379 (1997). hep-ph/9701390
S.A. Larin, T. van Ritbergen, J.A.M. Vermaseren, Phys. Lett. B 404, 153 (1997). hep-ph/9702435
A.L. Kataev, V.V. Starshenko, Mod. Phys. Lett. A 10, 235 (1995). hep-ph/9502348
C.J. Maxwell, D.G. Tonge, Nucl. Phys. B 481, 681 (1996). hep-ph/9606392
C.J. Maxwell, D.G. Tonge, Nucl. Phys. B 535, 19 (1998). hep-ph/9705314
P.A. Raczka, Phys. Rev. D 57, 6862 (1998). hep-ph/9707366
J.G. Körner, F. Krajewski, A.A. Pivovarov, Phys. Rev. D 63, 036001 (2001). hep-ph/0002166
D.J. Broadhurst, Z. Phys. C 58, 339 (1993)
M. Beneke, V.M. Braun, Phys. Lett. B 348, 513 (1999). hep-ph/9411229
D.J. Broadhurst, S.C. Generalis, Phys. Lett. 165, 175 (1985)
ALEPH Collaboration, S. Schael et al., Phys. Rep. 421, 191 (2005). hep-ex/0506072
S. Bethke, Prog. Part. Nucl. Phys. 58, 351 (2007). hep-ex/0606035
G. Dissertori et al., J. High Energy Phys. 0802, 040 (2008). arXiv:0712.0327
K.G. Chetyrkin, B.A. Kniehl, M. Steinhauser, Phys. Rev. L 79, 2184 (1997). hep-ph/9706430
K.G. Chetyrkin, B.A. Kniehl, M. Steinhauser, Nucl. Phys. B 510, 61 (1998). hep-ph/9708255
J. Schieck et al., Eur. Phys. J. C 48, 3 (2006); Erratum: Eur. Phys. J. C 50, 769 (2007) arXiv:0707.0392
W. Bernreuther, W. Wetzel, Nucl. Phys. B 197, 228 (1982); Erratum: Nucl. Phys. B 513, 758 (1998)
W. Wetzel, Nucl. Phys. B 196, 259 (1982)
G. Rodrigo, A. Pich, A. Santamaria, Phys. Lett. B 424, 367 (1998). hep-ph/9707474
Gfitter Group, M. Göbel et al., Programme library for electroweak fits and beyond (publication in preparation); more information at: https://twiki.cern.ch/twiki/bin/view/Gfitter/WebHome
J. Santiago, F.J. Ynduráin, Nucl. Phys. B 611, 447 (2001)
Q. Mason et al., Phys. Rev. L 95, 052002 (2005)
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Davier, M., Descotes-Genon, S., Höcker, A. et al. The determination of α S from τ decays revisited. Eur. Phys. J. C 56, 305–322 (2008). https://doi.org/10.1140/epjc/s10052-008-0666-7
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DOI: https://doi.org/10.1140/epjc/s10052-008-0666-7