143 research outputs found
Algebraic-Numerical Evaluation of Feynman Diagrams: Two-Loop Self-Energies
A recently proposed scheme for numerical evaluation of Feynman diagrams is
extended to cover all two-loop two-point functions with arbitrary internal and
external masses. The adopted algorithm is a modification of the one proposed by
F. V. Tkachov and it is based on the so-called generalized Bernstein functional
relation. On-shell derivatives of self-energies are also considered and their
infrared properties analyzed to prove that the method which is aimed to a
numerical evaluation of massive diagrams can handle the infrared problem within
the scheme of dimensional regularization. Particular care is devoted to study
the general massive diagrams around their leading and non-leading Landau
singularities.Comment: 92 pages(Latex), 4 figure
Higgs-mass dependence of two-loop corrections to Delta r
The Higgs-mass dependence of the Standard Model contributions to the
correlation between the gauge-boson masses is studied at the two-loop level.
Exact results are given for the Higgs-dependent two-loop corrections associated
with the fermions, i.e. no expansion in the top-quark and the Higgs-boson mass
is made. The results for the top quark are compared with results of an
expansion up to next-to-leading order in the top-quark mass. Agreement is found
within 30% of the two-loop result. The remaining theoretical uncertainties in
the Higgs-mass dependence of Delta r are discussed.Comment: 10 pages, LaTeX, minor changes, version to appear in Phys. Lett.
Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral
It is shown that the study of the imaginary part and of the corresponding
dispersion relations of Feynman graph amplitudes within the differential
equations method can provide a powerful tool for the solution of the equations,
especially in the massive case. The main features of the approach are
illustrated by discussing the simple cases of the 1-loop self-mass and of a
particular vertex amplitude, and then used for the evaluation of the two-loop
massive sunrise and the QED kite graph (the problem studied by Sabry in 1962),
up to first order in the (d-4) expansion.Comment: 36 pages, v3 fixed a typo in Eq.(5.5
Two Loop Electroweak Bosonic Corrections to the Muon Decay Lifetime
A review of the calculation of the two loop bosonic corrections to
is presented. Factorization and matching onto the Fermi model are discussed. An
approximate formula, describing the quantity over the interesting range of
Higgs boson mass values from 100 GeV to 1 TeV is given.Comment: 5 pages, 3 figures, minor corrections, to appear in the proceedings
of the RADCOR 2002/Loops and Legs in Quantum Field Theory workshop, Kloster
Banz, Germany, 8-13 Sep 200
TSIL: a program for the calculation of two-loop self-energy integrals
TSIL is a library of utilities for the numerical calculation of dimensionally
regularized two-loop self-energy integrals. A convenient basis for these
functions is given by the integrals obtained at the end of O.V. Tarasov's
recurrence relation algorithm. The program computes the values of all of these
basis functions, for arbitrary input masses and external momentum. When
analytical expressions in terms of polylogarithms are available, they are used.
Otherwise, the evaluation proceeds by a Runge-Kutta integration of the coupled
first-order differential equations for the basis integrals, using the external
momentum invariant as the independent variable. The starting point of the
integration is provided by known analytic expressions at (or near) zero
external momentum. The code is written in C, and may be linked from C, C++, or
Fortran. A Fortran interface is provided. We describe the structure and usage
of the program, and provide a simple example application. We also compute two
new cases analytically, and compare all of our notations and conventions for
the two-loop self-energy integrals to those used by several other groups.Comment: 31 pages. Updated to reflect new functionality through v1.4 May 2016
and new information about use with C++. Source code and documentation are
available at http://www.niu.edu/spmartin/TSIL or
http://faculty.otterbein.edu/DRobertson/tsil
Hypergeometric representation of the two-loop equal mass sunrise diagram
A recurrence relation between equal mass two-loop sunrise diagrams differing
in dimensionality by 2 is derived and it's solution in terms of Gauss' 2F1 and
Appell's F_2 hypergeometric functions is presented. For arbitrary space-time
dimension d the imaginary part of the diagram on the cut is found to be the 2F1
hypergeometric function with argument proportional to the maximum of the Kibble
cubic form. The analytic expression for the threshold value of the diagram in
terms of the hypergeometric function 3F2 of argument -1/3 is given.Comment: 10 page
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