Precise mass-dependent QED contributions to leptonic g-2 at order alpha^2 and alpha^3

Improved values for the two- and three-loop mass-dependent QED contributions to the anomalous magnetic moments of the electron, muon, and tau lepton are presented. The Standard Model prediction for the electron (g-2) is compared with its most precise recent measurement, providing a value of the fine-structure constant in agreement with a recently published determination. For the tau lepton, differences with previously published results are found and discussed. An updated value of the fine-structure constant is presented in "Note added after publication."Comment: 6 pages, 1 figure. v2: New determination of alpha presented (based on the recent electron g-2 measurement). v3: New formulae added in Sec.IIB. v4: Updated value of alpha presente

Revised value of the eighth-order electron g-2

The contribution to the eighth-order anomalous magnetic moment (g-2) of the electron from a set of diagrams without closed lepton loops is recalculated using a new FORTRAN code generated by an automatic code generator. Comparing the contributions of individual diagrams of old and new calculations, we found an inconsistency in the old treatment of infrared subtraction terms in two diagrams. Correcting this error leads to the revised value -1.9144 (35) (alpha/pi)^4 for the eighth-order term. This theoretical change induces the shift of the inverse of the fine structure constant by -6.41180(73)x10^{-7}.Comment: 4 pages, 1 figure, typo is correcte

Improved α4\alpha^4 Term of the Electron Anomalous Magnetic Moment

We report a new value of electron $g-2$, or $a_e$, from 891 Feynman diagrams of order $\alpha^4$. 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 $\alpha^4$ term by the integration routine VEGAS gives $-1.7283 (35) (\alpha/\pi)^4$, where the uncertainty is obtained by careful examination of error estimates by VEGAS. This leads to $a_e = 1 159 652 175.86 (0.10) (0.26) (8.48) \times 10^{-12}$, where the uncertainties come from the $\alpha^4$ term, the estimated uncertainty of $\alpha^5$ term, and the inverse fine structure constant, $\alpha^{-1} = 137.036 000 3 (10)$, measured by atom interferometry combined with a frequency comb technique, respectively. The inverse fine structure constant $\alpha^{-1} (a_e)$ derived from the theory and the Seattle measurement of $a_e$ is $137.035 998 83 (51)$.Comment: 64 pages and 10 figures. Eq.(16) is corrected. Comments are added after Eq.(40

Everyone Makes Mistakes - Including Feynman

This talk is dedicated to Alberto Sirlin in celebration of his seventieth birthday. I wish to convey my deep appreciation of his many important contributions to particle physics over 40 years and look forward to many more years of productive research.Comment: 16 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Improved α4\alpha^4 Term of the Muon Anomalous Magnetic Moment

We have completed the evaluation of all mass-dependent $\alpha^4$ QED contributions to the muon $g-2$, or $a_\mu$, in two or more different formulations. Their numerical values have been greatly improved by an extensive computer calculation. The new value of the dominant $\alpha^4$ term $A_2^{(8)} (m_\mu / m_e)$ is 132.6823 (72), which supersedes the old value 127.50 (41). The new value of the three-mass term $A_3^{(8)} (m_\mu / m_e, m_\mu / m_\tau)$ is 0.0376 (1). The term $A_2^{(8)} (m_\mu / m_\tau)$ is crudely estimated to be about 0.005 and may be ignored for now. The total QED contribution to $a_\mu$ is $116 584 719.58 (0.02)(1.15)(0.85) \times 10^{-11}$, where 0.02 and 1.15 are uncertainties in the $\alpha^4$ and $\alpha^5$ terms and 0.85 is from the uncertainty in $\alpha$ measured by atom interferometry. This raises the Standard Model prediction by $13.9 \times 10^{-11}$, or about 1/5 of the measurement uncertainty of $a_\mu$. It is within the noise of current uncertainty ($\sim 100 \times 10^{-11}$) in the estimated hadronic contributions to $a_\mu$.Comment: Appendix A has been rewritten extensively. It includes the 4th-order calculation for illustration. Version accepted by PR

Proper Eighth-Order Vacuum-Polarization Function and its Contribution to the Tenth-Order Lepton g-2

This paper reports the Feynman-parametric representation of the vacuum-polarization function consisting of 105 Feynman diagrams of the eighth order, and its contribution to the gauge-invariant set called Set I(i) of the tenth-order lepton anomalous magnetic moment. Numerical evaluation of this set is carried out using FORTRAN codes generated by an automatic code generation system gencodevpN developed specifically for this purpose. The contribution of diagrams containing electron loop to the electron g-2 is 0.017 47 (11) (alpha/pi)^5. The contribution of diagrams containing muon loop is 0.000 001 67 (3) (alpha/pi)^5. The contribution of tau-lepton loop is negligible at present. The sum of all these terms is 0.017 47 (11) (alpha/pi)^5. The contribution of diagrams containing electron loop to the muon g-2 is 0.087 1 (59) (alpha/pi)^5. That of tau-lepton loop is 0.000 237 (1) (alpha/pi)^5. The total contribution to a_mu, the sum of these terms and the mass-independent term, is 0.104 8 (59) (alpha/pi)^5.Comment: 48 pages, 6 figures. References are correcte

Eighth-Order Vacuum-Polarization Function Formed by Two Light-by-Light-Scattering Diagrams and its Contribution to the Tenth-Order Electron g-2

We have evaluated the contribution to the anomalous magnetic moment of the electron from six tenth-order Feynman diagrams which contain eighth-order vacuum-polarization function formed by two light-by-light scattering diagrams connected by three photons. The integrals are constructed by two different methods. In the first method the subtractive counter terms are used to deal with ultraviolet (UV) singularities together with the requirement of gauge-invariance. In the second method, the Ward-Takahashi identity is applied to the light-by-light scattering amplitudes to eliminate UV singularities. Numerical evaluation confirms that the two methods are consistent with each other within their numerical uncertainties. Combining the two results statistically and adding small contribution from the muons and/or tau leptons, we obtain $0.000 399 9 (18) (\alpha/\pi)^5$. We also evaluated the contribution to the muon $g-2$ from the same set of diagrams and found $-1.263 44 (14) (\alpha/\pi)^5$.Comment: 27 page

Electroweak Fermion-loop Contributions to the Muon Anomalous Magnetic Moment

The two-loop electroweak corrections to the anomalous magnetic moment of the muon, generated by fermionic loops, are calculated. An interesting role of the top quark in the anomaly cancellation is observed. New corrections, including terms of order $G_\mu \alpha m_t^2$, are computed and a class of diagrams previously thought to vanish are found to be important. The total fermionic correction is $-(23\pm 3) \times 10^{-11}$ which decreases the electroweak effects on $g-2$, predicted from one-loop calculations, by 12\%. We give an updated theoretical prediction for $g-2$ of the muon.Comment: Corrected versio

Genetic and Structural Analyses of Cytoplasmic Filaments of Wild-Type Treponema phagedenis and a Flagellar Filament-Deficient Mutant

Unique cytoplasmic filaments are found in the treponeme genus of spirochete bacteria. Their function is unknown, but their location underneath the periplasmic flagellar filaments (PFF) suggests a role in motility and/or cell structure. To better understand these unique structures, the gene coding for the cytoplasmic filaments, cfpA, was identified in various treponemal species. Treponema phagedenis cfpA was 2,037 nucleotides long, and the encoded polypeptide showed 78 to 100% amino acid sequence identity with the partial sequence of CfpA from T. denticola, T. vincentii, and T. pallidum subsp. pertenue. Wild-type T. phagedenis and a PFF-deficient isolate were analyzed by electron microscopy to assess the structural relationship of the cytoplasmic filaments and the PFF. The number of cytoplasmic filaments per cell of T. phagedenis (mean, 5.7) was compared with the number of PFF at each end of the cell (mean, 4.7); the results suggest that there is no direct one-to-one correlation at the cell end. Moreover, a structural link between these structures could not be demonstrated. The cytoplasmic filaments were also analyzed by electron microscopy at different stages of cell growth; this analysis revealed that they are cleaved before or during septum formation and before the nascent formation of PFF. A PFF-deficient mutant of T. phagedenis possessed cytoplasmic filaments similar to those of the wild type, suggesting that intact PFF are not required for their assembly and regulation. The extensive conservation of CfpA among pathogenic spirochetes suggests an important function, and structural analysis suggests that it is unlikely that the cytoplasmic filaments and the flagellar apparatus are physically linked