20,034 research outputs found
New exact results on density matrix for XXX spin chain
Using the fermionic basis we obtain the expectation values of all
\slt-invariant and -invariant local operators on 10 sites for the
anisotropic six-vertex model on a cylinder with generic Matsubara data. This is
equivalent to the generalised Gibbs ensemble for the XXX spin chain. In the
case when the \slt and symmetries are not broken this computation is
equivalent to finding the entire density matrix up to 10 sites. As application,
we compute the entanglement entropy without and with temperature, and compare
the results with CFT predictions.Comment: 20 pages, 4 figure
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
Analytic Results for Massless Three-Loop Form Factors
We evaluate, exactly in d, the master integrals contributing to massless
three-loop QCD form factors. The calculation is based on a combination of a
method recently suggested by one of the authors (R.L.) with other techniques:
sector decomposition implemented in FIESTA, the method of Mellin--Barnes
representation, and the PSLQ algorithm. Using our results for the master
integrals we obtain analytical expressions for two missing constants in the
ep-expansion of the two most complicated master integrals and present the form
factors in a completely analytic form.Comment: minor revisions, to appear in JHE
Analytical Result for Dimensionally Regularized Massless Master Double Box with One Leg off Shell
The dimensionally regularized massless double box Feynman diagram with powers
of propagators equal to one, one leg off the mass shell, i.e. with non-zero
q^2=p_1^2, and three legs on shell, p_i^2=0, i=2,3,4, is analytically
calculated for general values of q^2 and the Mandelstam variables s and t. An
explicit result is expressed through (generalized) polylogarithms, up to the
fourth order, dependent on rational combinations of q^2,s and t, and a
one-dimensional integral with a simple integrand consisting of logarithms and
dilogarithms.Comment: 10 pages, LaTeX with axodraw.sty, one reference is correcte
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
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
On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
One of the two existing strategies of resolving singularities of multifold
Mellin-Barnes integrals in the dimensional regularization parameter, or a
parameter of the analytic regularization, is formulated in a modified form. The
corresponding algorithm is implemented as a Mathematica code MBresolve.mComment: LaTeX, 10 page
The Four-Loop Dressing Phase of N=4 SYM
We compute the dilatation generator in the su(2) sector of planar N=4 super
Yang-Mills theory at four-loops. We use the known world-sheet scattering matrix
to constrain the structure of the generator. The remaining few coefficients can
be computed directly from Feynman diagrams. This allows us to confirm previous
conjectures for the leading contribution to the dressing phase which is
proportional to zeta(3).Comment: 19 pages, v2: referenced adde
Evaluating multiloop Feynman integrals by Mellin-Barnes representation
The status of analytical evaluation of double and triple box diagrams is
characterized. The method of Mellin-Barnes representation as a tool to evaluate
master integrals in these problems is advocated. New MB representations for
massive on-shell double boxes with general powers of propagators are presented.Comment: 5 pages, Talk given at the 7th DESY workshop on Elementary Particle
Theory, "Loops and Legs in Quantum Field Theory", April 25-30, 2004,
Zinnowitz, Germany, to appear in the proceeding
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