1,213 research outputs found
Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically
We present a method to evaluate numerically Feynman diagrams directly from
their Feynman parameters representation. We first disentangle overlapping
singularities using sector decomposition. Threshold singularities are treated
with an appropriate contour deformation. We have validated our technique
comparing with recent analytic results for the gg->h two-loop amplitudes with
heavy quarks and scalar quarks.Comment: 8 pages, 3 figures; references added, version to appear in JHE
Analytic Continuation of Massless Two-Loop Four-Point Functions
We describe the analytic continuation of two-loop four-point functions with
one off-shell external leg and internal massless propagators from the Euclidean
region of space-like decay to Minkowskian regions relevant to all
and reactions with one space-like or time-like off-shell
external leg. Our results can be used to derive two-loop master integrals and
unrenormalized matrix elements for hadronic vector-boson-plus-jet production
and deep inelastic two-plus-one-jet production, from results previously
obtained for three-jet production in electron--positron annihilation.Comment: 26 pages, LaTe
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 Master Non-planar Double Box with One Leg off Shell
The dimensionally regularized massless non-planar double box Feynman diagram
with powers of propagators equal to one, one leg off the mass shell, i.e. with
p_1^2=q^2\neq 0, 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,t and u
(not necessarily restricted by the physical condition s+t+u=q^2). An explicit
result is expressed through (generalized) polylogarithms, up to the fourth
order, dependent on rational combinations of q^2,s,t and u, and simple finite
two- and three fold Mellin--Barnes integrals of products of gamma functions
which are easily numerically evaluated for arbitrary non-zero values of the
arguments.Comment: 9 pages, LaTeX with axodraw.sty, minor changes in references, to
appear in Physics Letters
Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box
The dimensionally regularized master planar double box Feynman diagram with
four massive and three massless lines, powers of propagators equal to one, all
four legs on the mass shell, i.e. with p_i^2=m^2, i=1,2,3,4, is analytically
evaluated for general values of m^2 and the Mandelstam variables s and t. An
explicit result is expressed in terms of polylogarithms, up to the third order,
depending on special combinations of m^2,s and t.Comment: 10 pages, LaTeX with axodraw.st
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
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
Scattering amplitudes for e^+e^- --> 3 jets at next-to-next-to-leading order QCD
We present the calculation of the fermionic contribution to the QCD two-loop
amplitude for e^+e^- --> q qbar g.Comment: 5 pages, 4 figures, espcrc2.sty (included), Talk given at QCD '02,
Montpellier, France, 2-9th July 200
NNLO phase space master integrals for two-to-one inclusive cross sections in dimensional regularization
We evaluate all phase space master integrals which are required for the total
cross section of generic 2 -> 1 processes at NNLO as a series expansion in the
dimensional regulator epsilon. Away from the limit of threshold production, our
expansion includes one order higher than what has been available in the
literature. At threshold, we provide expressions which are valid to all orders
in terms of Gamma functions and hypergeometric functions. These results are a
necessary ingredient for the renormalization and mass factorization of
singularities in 2 -> 1 inclusive cross sections at NNNLO in QCD.Comment: 37 pages, plus 3 ancillary files containing analytic expressions in
Maple forma
The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
The class of the two-loop massless crossed boxes, with light-like external
legs, is the final unresolved issue in the program of computing the scattering
amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order.
In this paper, we describe an algorithm for the tensor reduction of such
diagrams. After connecting tensor integrals to scalar ones with arbitrary
powers of propagators in higher dimensions, we derive recurrence relations from
integration-by-parts and Lorentz-invariance identities, that allow us to write
the scalar integrals as a combination of two master crossed boxes plus
simpler-topology diagrams.
We derive the system of differential equations that the two master integrals
satisfy using two different methods, and we use one of these equations to
express the second master integral as a function of the first one, already
known in the literature. We then give the analytic expansion of the second
master integral as a function of epsilon=(4-D)/2, where D is the space-time
dimension, up to order O(epsilon^0).Comment: 30 pages, 5 figure
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