7,540 research outputs found
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
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
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 . We also evaluated the
contribution to the muon from the same set of diagrams and found .Comment: 27 page
Tenth-order lepton g-2: Contribution from diagrams containing a sixth-order light-by-light-scattering subdiagram internally
This paper reports the result of our evaluation of the tenth-order QED
correction to the lepton g-2 from Feynman diagrams which have sixth-order
light-by-light-scattering subdiagrams, none of whose vertices couple to the
external magnetic field. The gauge-invariant set of these diagrams, called Set
II(e), consists of 180 vertex diagrams. In the case of the electron g-2 (a_e),
where the light-by-light subdiagram consists of the electron loop, the
contribution to a_e is found to be - 1.344 9 (10) (\alpha /\pi)^5. The
contribution of the muon loop to a_e is - 0.000 465 (4) (\alpha /\pi)^5. The
contribution of the tau-lepton loop is about two orders of magnitudes smaller
than that of the muon loop and hence negligible. The sum of all of these
contributions to a_e is - 1.345 (1) (\alpha /\pi)^5. We have also evaluated the
contribution of Set II(e) to the muon g-2 (a_\mu). The contribution to a_\mu
from the electron loop is 3.265 (12) (\alpha /\pi)^5, while the contribution of
the tau-lepton loop is -0.038 06 (13) (\alpha /\pi)^5. The total contribution
to a_\mu, which is the sum of these two contributions and the mass-independent
part of a_e, is 1.882 (13) (\alpha /\pi)^5.Comment: 18 pages, 3 figures, REVTeX4, axodraw.sty used, changed title,
corrected uncertainty of a_mu, added a referenc
Improved Term of the Muon Anomalous Magnetic Moment
We have completed the evaluation of all mass-dependent QED
contributions to the muon , or , in two or more different
formulations. Their numerical values have been greatly improved by an extensive
computer calculation. The new value of the dominant term is 132.6823 (72), which supersedes the old value 127.50 (41).
The new value of the three-mass term
is 0.0376 (1). The term is crudely estimated to
be about 0.005 and may be ignored for now. The total QED contribution to
is , where 0.02 and
1.15 are uncertainties in the and terms and 0.85 is from
the uncertainty in measured by atom interferometry. This raises the
Standard Model prediction by , or about 1/5 of the
measurement uncertainty of . It is within the noise of current
uncertainty () in the estimated hadronic
contributions to .Comment: Appendix A has been rewritten extensively. It includes the 4th-order
calculation for illustration. Version accepted by PR
Isolated effective coherence (iCoh): causal information flow excluding indirect paths
A problem of great interest in real world systems, where multiple time series
measurements are available, is the estimation of the intra-system causal
relations. For instance, electric cortical signals are used for studying
functional connectivity between brain areas, their directionality, the direct
or indirect nature of the connections, and the spectral characteristics (e.g.
which oscillations are preferentially transmitted). The earliest spectral
measure of causality was Akaike's (1968) seminal work on the noise contribution
ratio, reflecting direct and indirect connections. Later, a major breakthrough
was the partial directed coherence of Baccala and Sameshima (2001) for direct
connections. The simple aim of this study consists of two parts: (1) To expose
a major problem with the partial directed coherence, where it is shown that it
is affected by irrelevant connections to such an extent that it can
misrepresent the frequency response, thus defeating the main purpose for which
the measure was developed, and (2) To provide a solution to this problem,
namely the "isolated effective coherence", which consists of estimating the
partial coherence under a multivariate auto-regressive model, followed by
setting all irrelevant associations to zero, other than the particular
directional association of interest. Simple, realistic, toy examples illustrate
the severity of the problem with the partial directed coherence, and the
solution achieved by the isolated effective coherence. For the sake of
reproducible research, the software code implementing the methods discussed
here (using lazarus free-pascal "www.lazarus.freepascal.org"), including the
test data as text files, are freely available at:
https://sites.google.com/site/pascualmarqui/home/icoh-isolated-effective-coherenceComment: 2014-02-21 pre-print, technical report, KEY Institute for Brain-Mind
Research, University of Zurich, et a
Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen
The sixth-order electron-loop vacuum-polarization contribution to the
Lamb shift of the muonic hydrogen ( bound
state) has been evaluated numerically. Our result is 0.007608(1) meV. This
eliminates the largest uncertainty in the theoretical calculation. Combined
with the proposed precision measurement of the Lamb shift it will lead to a
very precise determination of the proton charge radius.Comment: 4 pages, 5 figures the totoal LS number is change
Numerical and analytical investigation towards performance enhancement of a newly developed rockfall protective cable-net structure
In a previous companion paper, we presented a three-tier modelling of a particular type of rockfall protective cable-net structure (barrier), developed newly in Japan. Therein, we developed a three-dimensional, Finite Element based, nonlinear numerical model having been calibrated/back-calculated and verified with the element- and structure-level physical tests. Moreover, using a very simple, lumped-mass, single-degree-of-freedom, equivalently linear analytical model, a global-displacement-predictive correlation was devised by modifying the basic equation – obtained by combining the principles of conservation of linear momentum and energy – based on the back-analysis of the tests on the numerical model. In this paper, we use the developed models to explore the performance enhancement potential of the structure in terms of (a) the control of global displacement – possibly the major performance criterion for the proposed structure owing to a narrow space available in the targeted site, and (b) the increase in energy dissipation by the existing U-bolt-type Friction-brake Devices – which are identified to have performed weakly when integrated into the structure. A set of parametric investigations have revealed correlations to achieve the first objective in terms of the structure's mass, particularly by manipulating the wire-net's characteristics, and has additionally disclosed the effects of the impacting-block's parameters. Towards achieving the second objective, another set of parametric investigations have led to a proposal of a few innovative improvements in the constitutive behaviour (model) of the studied brake device (dissipator), in addition to an important recommendation of careful handling of the device based on the identified potential flaw
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