201 research outputs found
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
Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms
The two-dimensional harmonic polylogarithms \G(\vec{a}(z);y), a
generalization of the harmonic polylogarithms, themselves a generalization of
Nielsen's polylogarithms, appear in analytic calculations of multi-loop
radiative corrections in quantum field theory. We present an algorithm for the
numerical evaluation of two-dimensional harmonic polylogarithms, with the two
arguments varying in the triangle , , $\
0\le (y+z) \le 1$. This algorithm is implemented into a {\tt FORTRAN}
subroutine {\tt tdhpl} to compute two-dimensional harmonic polylogarithms up to
weight 4.Comment: 22 pages, LaTe
Harmonic Sums and Mellin Transforms
The finite and infinite harmonic sums form the general basis for the Mellin
transforms of all individual functions describing inclusive quantities
such as coefficient and splitting functions which emerge in massless field
theories. We discuss the mathematical structure of these quantities.Comment: Contribution to the Proceedings of the 7th International Workshop on
Deep Inelastic Scattering and QCD, DIS99, DESY-Zeuthen, April 1999; Nucl.
Phys. B (Proc. Suppl.
Numerical Evaluation of Harmonic Polylogarithms
Harmonic polylogarithms , a generalization of Nielsen's
polylogarithms , appear frequently in analytic calculations of
radiative corrections in quantum field theory. We present an algorithm for the
numerical evaluation of harmonic polylogarithms of arbitrary real argument.
This algorithm is implemented into a {\tt FORTRAN} subroutine {\tt hplog} to
compute harmonic polylogarithms up to weight 4.Comment: 16 pages, LaTeX, minor changes, to appear in Comp. Phys. Com
The two-loop scalar and tensor pentabox graph with light-like legs
We study the scalar and tensor integrals associated with the pentabox
topology: the class of two-loop box integrals with seven propagators - five in
one loop and three in the other. We focus on the case where the external legs
are light-like and use integration-by-parts identities to express the scalar
integral in terms of two master-topology integrals and present an explicit
analytic expression for the pentabox scalar integral as a series expansion in
ep = (4-D)/2. We also give an algorithm based on integration by parts for
relating the generic tensor integrals to the same two master integrals and
provide general formulae describing the master integrals in arbitrary dimension
and with general powers of propagators.Comment: Detailed expansions of intermediate results adde
Precise Coulomb wave functions for a wide range of complex l, eta and z
A new algorithm to calculate Coulomb wave functions with all of its arguments
complex is proposed. For that purpose, standard methods such as continued
fractions and power/asymptotic series are combined with direct integrations of
the Schrodinger equation in order to provide very stable calculations, even for
large values of |eta| or |Im(l)|. Moreover, a simple analytic continuation for
Re(z) < 0 is introduced, so that this zone of the complex z-plane does not pose
any problem. This code is particularly well suited for low-energy calculations
and the calculation of resonances with extremely small widths. Numerical
instabilities appear, however, when both |eta| and |Im(l)| are large and
|Re(l)| comparable or smaller than |Im(l)|
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 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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