3,321 research outputs found
Analytical and Numerical Contributions of Some Tenth-Order Graphs Containing Vacuum Polarization Insertions to the Muon (G-2) in QED
The contributions to the g-2 of the muon from some tenth-order (five-loop)
graphs containing one-loop and two-loop vacuum polarization insertions have
been evaluated analytically in QED perturbation theory, expanding the results
in the ratio of the electron to muon mass (m_e /m_\mu). Some results contain
also terms known only in numerical form. Our results agree with the
renormalization group results already existing in the literature.Comment: 13 pages + 2 figures appended as 2 postscript files, plain TeX, DFUB
94-0
High-precision e-expansions of massive four-loop vacuum bubbles
In this paper we calculate at high-precision the expansions in e=(4-D)/2 of
the master integrals of 4-loop vacuum bubble diagrams with equal masses, using
a method based on the solution of systems of difference equations. We also show
that the analytical expression of a related on-shell 3-loop self-mass master
integral contains new transcendental constants made up of complete elliptic
integrals of first and second kind.Comment: 7 pages, 2 figures, LaTex, to be published in Physics Letters
High-precision calculation of multi-loop Feynman integrals by difference equations
We describe a new method of calculation of generic multi-loop master
integrals based on the numerical solution of systems of difference equations in
one variable. We show algorithms for the construction of the systems using
integration-by-parts identities and methods of solutions by means of expansions
in factorial series and Laplace's transformation. We also describe new
algorithms for the identification of master integrals and the reduction of
generic Feynman integrals to master integrals, and procedures for generating
and solving systems of differential equations in masses and momenta for master
integrals. We apply our method to the calculation of the master integrals of
massive vacuum and self-energy diagrams up to three loops and of massive vertex
and box diagrams up to two loops. Implementation in a computer program of our
approach is described. Important features of the implementation are: the
ability to deal with hundreds of master integrals and the ability to obtain
very high precision results expanded at will in the number of dimensions.Comment: 55 pages, 5 figures, LaTe
The Analytical Contribution of Some Eighth-Order Graphs Containing Vacuum Polarization Insertions to the Muon (G-2) in QED
The contributions to the of the muon from some eighth-order (four-loop)
graphs containing one-loop and two-loop vacuum polarization insertions have
been evaluated analytically in QED perturbation theory, expanding the results
in the ratio of the electron to muon mass . The results agree
with the numerical evaluations and the asymptotic analytical results already
existing in the literature.Comment: plain TEX, 10 pages + 3 figures (figures are available upon request),
DFUB 93-0
Calculation of master integrals by difference equations
In this paper we describe a new method of calculation of master integrals
based on the solution of systems of difference equations in one variable. An
explicit example is given, and the generalization to arbitrary diagrams is
described. As example of application of the method, we have calculated the
values of master integrals for single-scale massive three-loop vacuum diagrams,
three-loop self-energy diagrams, two-loop vertex diagrams and two-loop box
diagrams.Comment: 7 pages, 1 figure, LaTex, to be published in Physics Letters
High-precision calculation of the 4-loop contribution to the electron g-2 in QED
I have evaluated up to 1100 digits of precision the contribution of the 891
4-loop Feynman diagrams contributing to the electron - in QED. The total
mass-independent 4-loop contribution is . I have fit a semi-analytical expression to
the numerical value. The expression contains harmonic polylogarithms of
argument , , ,
one-dimensional integrals of products of complete elliptic integrals and six
finite parts of master integrals, evaluated up to 4800 digits.Comment: 14 pages, 3 figures, 3 tables v2: version published in PRL (specified
"mass-independent contribution", figure 2 reformatted
Calculation of Feynman integrals by difference equations
In this paper we describe a method of calculation of master integrals based
on the solution of systems of difference equations in one variable. Various
explicit examples are given, as well as the generalization to arbitrary
diagrams.Comment: LaTex, 10 pages, uses appolb.cls. Presented at the XXVII
International Conference of Theoretical Physics "Matter to the Deepest",
Ustron, Poland, 15-21 September 2003. To appear in Acta Physica Polonica.
v2:added reference
Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
We show that dimensional recurrence relation and analytical properties of the
loop integrals as functions of complex variable (space-time
dimensionality) provide a regular way to derive analytical representations of
loop integrals. The representations derived have a form of exponentially
converging sums. Several examples of the developed technique are given.Comment: Several misprints correcte
Analytic evaluation of Feynman graph integrals
We review the main steps of the differential equation approach to the
analytic evaluation of Feynman graphs, showing at the same time its application
to the 3-loop sunrise graph in a particular kinematical configuration.Comment: 5 pages, 1 figure, uses npb.sty. Presented at RADCOR 2002 and Loops
and Legs in Quantum Field Theory, 8-13 September 2002, Kloster Banz, Germany.
Revised version: minor typos corrected, one reference adde
The muon anomalous magnetic moment in QED: three-loop electron and tau contributions
We present an analytic calculation of electron and tau O(alpha^3) loop
effects on the muon anomalous magnetic moment. Computation of such three-loop
diagrams with three mass scales is possible using asymptotic and eikonal
expansions. An evaluation of a new type of eikonal integrals is presented in
some detail.Comment: 9 pages, late
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