9 research outputs found
Revised and Improved Value of the QED Tenth-Order Electron Anomalous Magnetic Moment
In order to improve the theoretical prediction of the electron anomalous
magnetic moment we have carried out a new numerical evaluation of the 389
integrals of Set V, which represent 6,354 Feynman vertex diagrams without
lepton loops. During this work, we found that one of the integrals, called
, was given a wrong value in the previous calculation due to an incorrect
assignment of integration variables. The correction of this error causes a
shift of to the Set~V contribution, and hence to the tenth-order
universal (i.e., mass-independent) term . The previous evaluation
of all other 388 integrals is free from errors and consistent with the new
evaluation. Combining the new and the old (excluding ) calculations
statistically, we obtain as the best estimate of
the Set V contribution. Including the contribution of the diagrams with fermion
loops, the improved tenth-order universal term becomes
. Adding hadronic and electroweak contributions leads
to the theoretical prediction . From this and the best measurement of
, we obtain the inverse fine-structure constant . The theoretical prediction of the muon anomalous
magnetic moment is also affected by the update of QED contribution and the new
value of , but the shift is much smaller than the theoretical
uncertainty.Comment: 32 pages, 1 figure, references adde
Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant
This paper presents the complete QED contribution to the electron g-2 up to
the tenth order. With the help of the automatic code generator, we have
evaluated all 12672 diagrams of the tenth-order diagrams and obtained 9.16
(58)(\alpha/\pi)^5. We have also improved the eighth-order contribution
obtaining -1.9097(20)(\alpha/\pi)^4, which includes the mass-dependent
contributions. These results lead to a_e(theory)=1 159 652 181.78 (77) \times
10^{-12}. The improved value of the fine-structure constant \alpha^{-1} =
137.035 999 174 (35) [0.25 ppb] is also derived from the theory and measurement
of a_e.Comment: 4 pages, 2 figures. Some numbers are slightly change
Tenth-Order Lepton Anomalous Magnetic Moment -- Sixth-Order Vertices Containing Vacuum-Polarization Subdiagrams
This paper reports the values of contributions to the electron g-2 from 300
Feynman diagrams of the gauge-invariant Set III(a) and 450 Feynman diagrams of
the gauge-invariant Set III(b). The evaluation is carried out in two versions.
Version A is to start from the sixth-order magnetic anomaly M_6 obtained in the
previous work. The mass-independent contributions of Set III(a) and Set III(b)
are 2.1275 (2) and 3.3271 (6) in units of (alpha/pi)^5, respectively. Version B
is based on the recently-developed automatic code generation scheme. This
method yields 2.1271 (3) and 3.3271 (8) in units of (alpha/pi)^5, respectively.
They are in excellent agreement with the results of the first method within the
uncertainties of numerical integration. Combining these results as
statistically independent we obtain the best values, 2.1273 (2), and 3.3271 (5)
times (alpha/pi)^5, for the mass-independent contributions of the Set III(a)
and Set III(b), respectively. We have also evaluated mass-dependent
contributions of diagrams containing muon and/or tau-particle loop. Including
them the total contribution of Set III(a) is 2.1349 (2) and that of Set III(b)
is 3.3299 (5) in units of (alpha/pi)^5. The total contributions to the muon g-2
of various leptonic vacuum-polarization loops of Set III(a) and Set III(b) are
112.418 (32) and 15.407 (5) in units of (alpha/pi)^5, respectively.Comment: 31 pages, 4 figure
Improved Term of the Electron Anomalous Magnetic Moment
We report a new value of electron , or , from 891 Feynman diagrams
of order . The FORTRAN codes of 373 diagrams containing closed
electron loops have been verified by at least two independent formulations. For
the remaining 518 diagrams, which have no closed lepton loop, verification by a
second formulation is not yet attempted because of the enormous amount of
additional work required. However, these integrals have structures that allow
extensive cross-checking as well as detailed comparison with lower-order
diagrams through the renormalization procedure. No algebraic error has been
uncovered for them. The numerical evaluation of the entire term by
the integration routine VEGAS gives , where the
uncertainty is obtained by careful examination of error estimates by VEGAS.
This leads to ,
where the uncertainties come from the term, the estimated
uncertainty of term, and the inverse fine structure constant,
, measured by atom interferometry combined
with a frequency comb technique, respectively. The inverse fine structure
constant derived from the theory and the Seattle
measurement of is .Comment: 64 pages and 10 figures. Eq.(16) is corrected. Comments are added
after Eq.(40
Theory of the Anomalous Magnetic Moment of the Electron
The anomalous magnetic moment of the electron a e measured in a Penning trap occupies a unique position among high precision measurements of physical constants in the sense that it can be compared directly with the theoretical calculation based on the renormalized quantum electrodynamics (QED) to high orders of perturbation expansion in the fine structure constant α , with an effective parameter α / π . Both numerical and analytic evaluations of a e up to ( α / π ) 4 are firmly established. The coefficient of ( α / π ) 5 has been obtained recently by an extensive numerical integration. The contributions of hadronic and weak interactions have also been estimated. The sum of all these terms leads to a e ( theory ) = 1 159 652 181.606 ( 11 ) ( 12 ) ( 229 ) × 10 − 12 , where the first two uncertainties are from the tenth-order QED term and the hadronic term, respectively. The third and largest uncertainty comes from the current best value of the fine-structure constant derived from the cesium recoil measurement: α − 1 ( Cs ) = 137.035 999 046 ( 27 ) . The discrepancy between a e ( theory ) and a e ( ( experiment ) ) is 2.4 σ . Assuming that the standard model is valid so that a e (theory) = a e (experiment) holds, we obtain α − 1 ( a e ) = 137.035 999 1496 ( 13 ) ( 14 ) ( 330 ) , which is nearly as accurate as α − 1 ( Cs ) . The uncertainties are from the tenth-order QED term, hadronic term, and the best measurement of a e , in this order