41,578 research outputs found
Problems of the Strategy of Regions
Problems that arise in the application of general prescriptions of the
so-called strategy of regions for asymptotic expansions of Feynman integrals in
various limits of momenta and masses are discussed with the help of
characteristic examples of two-loop diagrams. The strategy is also reformulated
in the language of alpha parameters.Comment: 12 pages, LaTeX with axodraw.st
Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in
Applications of a method recently suggested by one of the authors (R.L.) are
presented. This method is based on the use of dimensional recurrence relations
and analytic properties of Feynman integrals as functions of the parameter of
dimensional regularization, . The method was used to obtain analytical
expressions for two missing constants in the -expansion of the most
complicated master integrals contributing to the three-loop massless quark and
gluon form factors and thereby present the form factors in a completely
analytic form. To illustrate its power we present, at transcendentality weight
seven, the next order of the -expansion of one of the corresponding
most complicated master integrals. As a further application, we present three
previously unknown terms of the expansion in of the three-loop
non-planar massless propagator diagram. Only multiple values at integer
points are present in our result.Comment: Talk given at the International Workshop `Loops and Legs in Quantum
Field Theory' (April 25--30, 2010, W\"orlitz, Germany)
The static quark potential to three loops in perturbation theory
The static potential constitutes a fundamental quantity of Quantum
Chromodynamics. It has recently been evaluated to three-loop accuracy. In this
contribution we provide details on the calculation and present results for the
14 master integrals which contain a massless one-loop insertion.Comment: 6 pages, talk presented at Loops and Legs in Quantum Field Theory
2010, W\"orlitz, Germany, April 25-30, 201
Some recent results on evaluating Feynman integrals
Some recent results on evaluating Feynman integrals are reviewed. The status
of the method based on Mellin-Barnes representation as a powerful tool to
evaluate individual Feynman integrals is characterized. A new method based on
Groebner bases to solve integration by parts relations in an automatic way is
described.Comment: 5 pages, LaTeX, Conference Proceedings Radcor 200
Bounds on scalar leptoquark and scalar gluon masses from S, T, U in the minimal four color symmetry model
The contributions into radiative correction parameters S, T, U from scalar
leptoquark and scalar gluon doublets are investigated in the minimal four color
symmetry model. It is shown that the current experimental data on S, T, U allow
the scalar leptoquarks and the scalar gluons to be relatively light (with
masses of order of 1 TeV or less), the lightest particles are preferred to lie
below 400 GeV. In particular, the lightest scalar leptoquarks with masses below
300 GeV are shown to be compatible with the current data on S, T, U at for in comparison with
in the Standard Model. The lightest scalar gluon in this case is expected to
lie below 850 (720) GeV. The possible significance of such particles in the
t-quark physics at LHC is emphasized.Comment: 14 pages, 2 figures, to appear in Physics Letters
Counting the local fields in SG theory.
In terms of the form factor bootstrap we describe all the local fields in SG
theory and check the agreement with the free fermion case. We discuss the
interesting structure responsible for counting the local fields.Comment: 16 pages AMSTEX References to the papers by A. Koubek and G. Mussargo
are added. In view of them the stasus of the problem with scalar S-matrices
is reconsidered
On the deformation of abelian integrals
We consider the deformation of abelian integrals which arose from the study
of SG form factors. Besides the known properties they are shown to satisfy
Riemann bilinear identity. The deformation of intersection number of cycles on
hyperelliptic curve is introduced.Comment: 8 pages, AMSTE
Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box
The dimensionally regularized massless on-shell planar triple box Feynman
diagram with powers of propagators equal to one is analytically evaluated for
general values of the Mandelstam variables s and t in a Laurent expansion in
the parameter \ep=(4-d)/2 of dimensional regularization up to a finite part. An
explicit result is expressed in terms of harmonic polylogarithms, with
parameters 0 and 1, up to the sixth order. The evaluation is based on the
method of Feynman parameters and multiple Mellin-Barnes representation. The
same technique can be quite similarly applied to planar triple boxes with any
numerators and integer powers of the propagators.Comment: 8 pages, LaTeX with axodraw.st
Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators
We present an algorithm for the analytical evaluation of dimensionally
regularized massless on-shell double box Feynman diagrams with arbitrary
polynomials in numerators and general integer powers of propagators. Recurrence
relations following from integration by parts are solved explicitly and any
given double box diagram is expressed as a linear combination of two master
double boxes and a family of simpler diagrams. The first master double box
corresponds to all powers of the propagators equal to one and no numerators,
and the second master double box differs from the first one by the second power
of the middle propagator. By use of differential relations, the second master
double box is expressed through the first one up to a similar linear
combination of simpler double boxes so that the analytical evaluation of the
first master double box provides explicit analytical results, in terms of
polylogarithms \Li{a}{-t/s}, up to , and generalized polylogarithms
, with and , dependent on the Mandelstam variables
and , for an arbitrary diagram under consideration.Comment: LaTeX, 16 pages; misprints in ff. (8), (24), (30) corrected; some
explanations adde
The Leading Power Regge Asymptotic Behaviour of Dimensionally Regularized Massless On-Shell Planar Triple Box
The leading power asymptotic behaviour of the dimensionally regularized
massless on-shell planar triple box diagram in the Regge limit t/s -> 0 is
analytically evaluated.Comment: 9 pages, LaTeX with axodraw.st
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