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New Determination of the Fine Structure Constant and Test of the Quantum Electrodynamics

Pierre Cladé, Rym Bouchendira, Saïda Guellati, François Nez, François Biraben

2011
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Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011
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unpublished

We report a new measurement of the ratio h/m Rb between the Planck constant and the mass of 87 Rb atom. A new value of the fine structure constant is deduced, α −1 = 137.035 999 037 (91) with a relative uncertainty of 6.6 × 10 −10 . Using this determination, we obtain a theoretical value of the electron anomaly ae = 0.001 159 652 181 13(84) which is in agreement with the experimental measurement of Gabrielse (ae = 0.001 159 652 180 73 (28) ). The comparison of these values provides the most
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... ngent test of the QED. Moreover, the precision is large enough to verify for the first time the muonic and hadronic contributions to this anomaly. PACS numbers: 06.20.Jr,12.20.Fv,37.25.+k,03.75.Dg The fine structure constant α characterizes the strength of the electromagnetic interaction. This dimensionless quantity is defined as: where ǫ 0 is the permittivity of vacuum, c the speed of light, e the electron charge and the reduced Planck constant ( = h/2π). It appears in the expressions of the ionization energy of hydrogen atom, of the fine and hyperfine structures of atomic energy levels, and it is the parameter of the quantum electrodynamics (QED) calculations. Its measurement in different domains of physics is a test of the consistency of the theory. The most accurate value is deduced from the combination of the measurement of the electron anomaly a e with a very difficult QED calculation. The last result, by Gabrielse at Harvard University, gives a value of α with a relative uncertainty of 3.7 × 10 −10 [1, 2]. Nevertheless this impressive result is fully dependent on QED calculations and can be liable to a possible error: in 2007, Aoyama et al detected an error which shifted the α value by 4.7 × 10 −9 [2-4]. Consequently, to check these calculations, another determination of α is required. Up to now the other QED independent determinations of α were less accurate by at least an order of magnitude. The measurement of the quantum Hall effect provides an α value with an uncertainty of 1.8 × 10 −8 [5] and the accuracies of the determinations deduced from the recoil velocity measurement were respectively 7.7×10 −9 and 4.6×10 −9 for the Cesium and Rubidium experiments [6, 7] . In this Letter we present a new measurement of the ratio h/m Rb between the Planck constant and the mass of 87 Rb atom and we obtain a new value of α: α −1 = 137.035 999 037 (91). ( With a relative uncertainty of 6.6 × 10 −10 , this value improves our precedent result by a factor of about seven [7]. (a -1 -137.03) × 10 5 599,8 599,85 599,9 599,95 600 600,05 600,1 600,15 h/m(Cs) a e (UW) a e (Harvard, 2006) CODATA 2006 h/m(Rb) 2006 h/m(Rb) 2008 a e after QED reevaluation a e (Harvard, 2008) This work Harvard UW (a -1 -137.03) × 10 5 599,8 599,85 599,9 599,95 600 600,05 600,1 600,15 (a -1 -137.03) × 10 5 599,8 599,85 599,9 599,95 600 600,05 600,1 600,15 h/m(Cs) a e (UW) a e (Harvard, 2006) CODATA 2006 h/m(Rb) 2006 h/m(Rb) 2008 a e after QED reevaluation a e (Harvard, 2008) This work Harvard UW h/m(Cs) a e (UW) a e (Harvard, 2006) CODATA 2006 h/m(Rb) 2006 h/m(Rb) 2008 a e after QED reevaluation a e (Harvard, 2008) This work Harvard UW FIG. 1: Determinations of α with a relative uncertainty smaller than 10 −8 ; ae(UW): measurement by Dehmelt at the University of Washington [8]; h/mCs: measurement of the Cesium recoil velocity at Stanford [6]; h/m Rb : measurement of the Rubidium recoil velocity at Paris in 2006 [9] and 2008 [7]; ae(Harvard): measurement of g − 2 at Harvard University in 2006 [3] and 2008 [1]; CODATA 2006: best adjustment by the Committee on Data for Science and Technology [5]; the arrow corresponds to the shift of the values of α due to the reevaluation of the QED calculation of ae in 2007 [2, 4]. The comparison with the value deduced from the electron anomaly provides the most stringent test of QED [1] . Indeed there is a very good agreement with this last value (α −1 = 137.035 999 084 (51)) as illustrated on Fig. 1 . This agreement confirms together the recent g − 2 measurement of Gabrielse by comparison with the value obtained by Dehmelt at the University of Washington [8] and the recent correction found in the calculation of the electron anomaly [2] . The discussion on this agreement will be presented at the end of this Letter. The fine structure constant is deduced from the measurement of h/m Rb thanks to the relation:

doi:10.1364/iqec.2011.i91
fatcat:e7v7qnikkjc2racjlaxfpghjgm