rpp2010-rev-g-2-muon-anom-mag-moment

rpp2010-rev-g-2-muon-anom-mag-moment - 1 THE MUON ANOMALOUS...

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–1– THE MUON ANOMALOUS MAGNETIC MOMENT Updated July 2009 by A. H¨ ocker (CERN), and W.J. Marciano (BNL). The Dirac equation predicts a muon magnetic moment, ± M = g μ e 2 m μ ± S , with gyromagnetic ratio g μ = 2. Quantum loop efects lead to a small calculable deviation From g μ =2 , parameterized by the anomalous magnetic moment a μ g μ 2 2 . (1) That quantity can be accurately measured and, within the Standard Model (SM) Framework, precisely predicted. Hence, comparison oF experiment and theory tests the SM at its quan- tum loop level. A deviation in a exp μ From the SM expectation would signal efects oF new physics, with current sensitivity reaching up to mass scales oF O (TeV) [1,2]. ±or recent and very thorough muon g 2 reviews, see ReFs. [3,4]. The E821 experiment at Brookhaven National Lab (BNL) studied the precession oF μ + and μ in a constant external magnetic ²eld as they circulated in a con²ning storage ring. It Found [6] 1 a exp μ + = 11 659 204(6)(5) × 10 10 , a exp μ = 11 659 215(8)(3) × 10 10 , (2) where the ²rst errors are statistical and the second systematic. Assuming CPT invariance and taking into account correlations between systematic errors, one ²nds For their average [6] a exp μ = 11 659 208 . 9(5 . 4)(3 . 3) × 10 10 . (3) These results represent about a Factor oF 14 improvement over the classic CERN experiments oF the 1970’s [7]. The SM prediction For a SM μ is generally divided into three parts (see ±ig. 1 For representative ±eynman diagrams) a SM μ = a QED μ + a EW μ + a Had μ . (4) 1 The original results reported by the experiment have been updated in Eqs. (2) and (3) to the newest value For the abso- lute muon-to-proton magnetic ratio λ =3 . 183345137(85) [5]. The change induced in a exp μ with respect to the value oF λ = 3 . 18334539(10) used in ReF. [6] amounts to +0 . 92 × 10 10 . CITATION: K. Nakamura et al. (Particle Data Group), JPG 37 , 075021 (2010) (URL: http://pdg.lbl.gov) July 30, 2010 14:34
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–2– γ γ μμ γ Z γ WW ν γ γγ had Figure 1: Representative diagrams contribut- ing to a SM μ . From left to right: ±rst order QED (Schwinger term), lowest-order weak, lowest- order hadronic. The QED part includes all photonic and leptonic ( e, μ, τ )loops starting with the classic α/ 2 π Schwinger contribution. It has been computed through 4 loops and estimated at the 5-loop level [8] a QED μ = α 2 π +0 . 765857410(27) ³ α π ´ 2 +24 . 05050964(43) ³ α π ´ 3 + 130 . 8055(80) ³ α π ´ 4 + 663(20) ³ α π ´ 5 + ··· (5) Employing α 1 = 137 . 035999084(51), determined [8,9] from the electron a e measurement, leads to a QED μ = 116 584 718 . 09(0 . 15) × 10 11 , (6) where the error results from uncertainties in the coefficients of Eq. (5) and in α .
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rpp2010-rev-g-2-muon-anom-mag-moment - 1 THE MUON ANOMALOUS...

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