Predictions for <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mi>−</mi><mn>2</mn></math></span> of the muon and <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 mathvariant="normal">QED</mi></mrow></msub></mrow><mrow><msubsup><mrow><mo>(</mo><mi>M</mi></mrow><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow><mo>)</mo></math></span>

K. Hagiwara; A. D. Martin; Daisuke Nomura; T. Teubner

doi:10.1103/PhysRevD.69.093003

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Predictions for $g - 2$ of the muon and $α_{QED} {(M}_{Z}^{2})$

K. Hagiwara¹, A. D. Martin², Daisuke Nomura², and T. Teubner^3,*

¹Theory Group, KEK, Tsukuba, Ibaraki 305-0801, Japan
²Department of Physics and Institute for Particle Physics Phenomenology, University of Durham, Durham DH1 3LE, United Kingdom
³Theory Division, CERN, CH-1211 Geneva 23, Switzerland

^*Present address: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom.

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Phys. Rev. D 69, 093003 – Published 17 May, 2004

DOI: https://doi.org/10.1103/PhysRevD.69.093003

Abstract

We calculate $g - 2$ of the muon and the QED coupling $α {(M}_{Z}^{2}),$ by improving the determination of the hadronic vacuum polarization contributions and their uncertainties. We include the recently reanalyzed CMD-2 data on $e^{+} e^{-} \to π^{+} π^{-} .$ We carefully combine a wide variety of data for the $e^{+} e^{-}$ production of hadrons and obtain the optimum form of $R (s) \equiv σ_{had}^{0} (s) / σ_{pt} (s),$ together with its uncertainty. Our results for the hadronic contributions to $g - 2$ of the muon are $a_{μ}^{h a d, L O} = (692.4 \pm {5.9}_{\exp} \pm {2.4}_{rad}) \times 10^{- 10}$ and $a_{μ}^{h a d, N L O} = (- 9.8 \pm {0.1}_{\exp} \pm {0.0}_{rad}) \times 10^{- 10},$ and for the QED coupling $Δ α_{had}^{(5)} {(M}_{Z}^{2}) = (275.5 \pm {1.9}_{\exp} \pm {1.3}_{rad}) \times 10^{- 4} .$ These yield $(g - 2) / 2 = 0.00116591763 (74),$ which is about $2.4 σ$ below the present world average measurement, and $α {(M}_{Z}^{2})^{- 1} = 128.954 \pm 0.031.$ We compare our $g - 2$ value with other predictions and, in particular, make a detailed comparison with the latest determination of $g - 2$ by Davier et al.

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[c10] CMD-2 Collaboration, R.R. Akhmetshin et al., Phys. Lett. B 578, 285 (2004).

[c11] CMD-2 Collaboration, R.R. Akhmetshin et al., Phys. Lett. B 527, 161 (2002).

[c12] K. Hagiwara, A.D. Martin, D. Nomura, and T. Teubner, Phys. Lett. B 557, 69 (2003).

[c13] CMD-2 Collaboration, R.R. Akhmetshin et al., Phys. Lett. B 476, 33 (2000).

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[c20] NA7 Collaboration, S.R. Amendolia et al., Phys. Lett. 138B, 454 (1984).

[c21] CMD and OLYA Collaborations, L.M. Barkov et al., Nucl. Phys. B256, 365 (1985).

[c22] CMD, ND, and ARGUS Collaborations, S.I. Dolinsky et al., Phys. Rep. 202, 99 (1991).

[c23] DM1 Collaboration, A. Quenzer et al., Phys. Lett. 76B, 512 (1978).

[c24] DM2 Collaboration, D. Bisello et al., Phys. Lett. B 220, 321 (1989).

[c25] BCF Collaboration, D. Bollini et al., Lett. Nuovo Cimento Soc. Ital. Fis. 14, 418 (1975).

[c26] BCF Collaboration, M. Bernardini et al., Phys. Lett. 46B, 261 (1973).

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[c29] ORSAY-ACO Collaboration, G. Cosme et al., Report No. LAL-1287, 1976.

[c30] CMD-2 Collaboration, S.I. Eidelman, Nucl. Phys. B (Proc. Suppl.) 98, 281 (2001).

[c31] SND Collaboration, M.N. Achasov et al., Phys. Lett. B 559, 171 (2003).

[c32] SND Collaboration, M.N. Achasov et al., Eur. Phys. J. C 12, 25 (2000).

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Predictions for $g - 2$ of the muon and $α_{QED} {(M}_{Z}^{2})$

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Predictions for g−2 of the muon and αQED(MZ2)

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Predictions for $g - 2$ of the muon and $α_{QED} {(M}_{Z}^{2})$