999 research outputs found
Some methods to evaluate complicated Feynman integrals
I discuss a progress in calculations of Feynman integrals based on the
Gegenbauer Polynomial Technique and the Differential Equation Method.Comment: 2 pages, 1 figure, latex. Talk presented at the 8th International
Workshop on Advanced Computing and Analysis Techniques in Physics Research
(ACAT 2002), Moscow, Russia, June 200
Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass
For a large class of two-loop selfenergy- and vertex-type diagrams with only
one non-zero mass () and the vertices also with only one non-zero external
momentum squared () the first few expansion coefficients are calculated by
the large mass expansion. This allows to `guess' the general structure of these
coefficients and to verify them in terms of certain classes of `basis
elements', which are essentially harmonic sums. Since for this case with only
one non-zero mass the large mass expansion and the Taylor series in terms of
are identical, this approach yields analytic expressions of the Taylor
coefficients, from which the diagram can be easily evaluated numerically in a
large domain of the complex plane by well known methods. It is also
possible to sum the Taylor series and present the results in terms of
polylogarithms.Comment: LaTeX, 27 pages + 3 ps figures, uses axodraw.sty, some references
reviste
Two-loop sunset diagrams with three massive lines
In this paper, we consider the two-loop sunset diagram with two different
masses, m and M, at spacelike virtuality q^2 = -m^2. We find explicit
representations for the master integrals and an analytic result through
O(epsilon) in d=4-2epsilon space-time dimensions for the case of equal masses,
m = M.Comment: 11 page
Small x behaviour of parton distributions with soft initial conditions
We present an analytical parametrization of the QCD description of the small
x behaviour of parton distribution functions in the leading twist approximation
of the Wilson operator product expansion, in the case of soft initial
conditions. The results are in very good agreement with deep inelastic
scattering experimental data from HERA.Comment: 21 pages, latex + 3 ps figure
Twist 3 of the sl(2) sector of N=4 SYM and reciprocity respecting evolution
We consider the bosonic sl(2) sector of the maximally supersymmetric N=4 SYM
model and show that anomalous dimension of the twist-3 single-trace composite
operators built of scalar fields, recently calculated up to the four-loop
order, can be generated by a compact reciprocity respecting evolution kernel.Comment: 18 pages, 1 eps figur
About calculation of massless and massive Feynman integrals
We report some results of calculations of massless and massive Feynman
integrals particularly focusing on difference equations for coefficients of for
their series expansionsComment: 51 pages; contribution to the proceedings of Helmholtz International
Summer School "Quantum Field Theory at the Limits: from Strong Fields to
Heavy Quarks" (July 22 - August 2, 2019; Dubna, Russia
Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
The pp-wave/BMN limit of the AdS/CFT correspondence has exposed the Maldacena
conjecture to a new regimen of direct tests. In one line of pursuit,
finite-radius curvature corrections to the Penrose limit (which appear in
inverse powers of the string angular momentum J) have been found to induce a
complicated system of interaction perturbations to string theory on the
pp-wave; these have been successfully matched to corresponding corrections to
the BMN dimensions of N=4 super Yang-Mills (SYM) operators to two loops in the
't Hooft coupling lambda. This result is tempered by a well-established
breakdown in the correspondence at three loops. Notwithstanding the third-order
mismatch, we proceed with this line of investigation by subjecting the string
and gauge theories to new and significantly more rigorous tests. Specifically,
we extend our earlier results at O(1/J) in the curvature expansion to include
string states and SYM operators with three worldsheet or R-charge impurities.
In accordance with the two-impurity problem, we find a perfect and intricate
agreement between both sides of the correspondence to two-loop order in lambda
and, once again, the string and gauge theory predictions fail to agree at third
order.Comment: 45 pages, LaTeX; notation and references correcte
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