2,983 research outputs found
A Fast Mellin and Scale Transform
A fast algorithm for the discrete-scale (and -Mellin) transform is proposed. It performs a discrete-time discrete-scale approximation of the continuous-time transform, with subquadratic asymptotic complexity. The algorithm is based on a well-known relation between the Mellin and Fourier transforms, and it is practical and accurate. The paper gives some theoretical background on the Mellin, -Mellin, and scale transforms. Then the algorithm is presented and analyzed in terms of computational complexity and precision. The effects of different interpolation procedures used in the algorithm are discussed
The Mellin Transform Technique for the Extraction of the Gluon Density
A new method is presented to determine the gluon density in the proton from
jet production in deeply inelastic scattering. By using the technique of Mellin
transforms not only for the solution of the scale evolution equation of the
parton densities but also for the evaluation of scattering cross sections, the
gluon density can be extracted in next-to-leading order QCD. The method
described in this paper is, however, more general, and can be used in
situations where a repeated fast numerical evaluation of scattering cross
sections for varying parton distribution functions is required.Comment: 13 pages (LaTeX); 2 figures are included via epsfig; the
corresponding postscript files are uuencode
Towards a global analysis of polarized parton distributions
We present a technique for implementing in a fast way, and without any
approximations, higher-order calculations of partonic cross sections into
global analyses of parton distribution functions. The approach, which is set up
in Mellin-moment space, is particularly suited for analyses of future data from
polarized proton-proton collisions, but not limited to this case. The
usefulness and practicability of this method is demonstrated for the
semi-inclusive production of hadrons in deep-inelastic scattering and the
transverse momentum distribution of ``prompt'' photons in pp collisions, and a
case study for a future global analysis of polarized parton densities is
presented.Comment: 20 pages, LaTeX, 6 eps figures, final version to appear in PRD (minor
changes
Solution of the Kwiecinski evolution equations for unintegrated parton distributions using the Mellin transform
The Kwiecinski equations for the QCD evolution of the unintegrated parton
distributions in the transverse-coordinate space (b) are analyzed with the help
of the Mellin-transform method. The equations are solved numerically in the
general case, as well as in a small-b expansion which converges fast for b
Lambda_QCD sufficiently small. We also discuss the asymptotic limit of large bQ
and show that the distributions generated by the evolution decrease with b
according to a power law. Numerical results are presented for the pion
distributions with a simple valence-like initial condition at the low scale,
following from chiral large-N_c quark models. We use two models: the Spectral
Quark Model and the Nambu--Jona-Lasinio model. Formal aspects of the equations,
such as the analytic form of the b-dependent anomalous dimensions, their
analytic structure, as well as the limits of unintegrated parton densities at x
-> 0, x -> 1, and at large b, are discussed in detail. The effect of spreading
of the transverse momentum with the increasing scale is confirmed, with
growing asymptotically as Q^2 alpha(Q^2). Approximate formulas for
for each parton species is given, which may be used in practical
applications.Comment: 18 pages, 6 figures, RevTe
Log-periodic route to fractal functions
Log-periodic oscillations have been found to decorate the usual power law
behavior found to describe the approach to a critical point, when the
continuous scale-invariance symmetry is partially broken into a discrete-scale
invariance (DSI) symmetry. We classify the `Weierstrass-type'' solutions of the
renormalization group equation F(x)= g(x)+(1/m)F(g x) into two classes
characterized by the amplitudes A(n) of the power law series expansion. These
two classes are separated by a novel ``critical'' point. Growth processes
(DLA), rupture, earthquake and financial crashes seem to be characterized by
oscillatory or bounded regular microscopic functions g(x) that lead to a slow
power law decay of A(n), giving strong log-periodic amplitudes. In contrast,
the regular function g(x) of statistical physics models with
``ferromagnetic''-type interactions at equibrium involves unbound logarithms of
polynomials of the control variable that lead to a fast exponential decay of
A(n) giving weak log-periodic amplitudes and smoothed observables. These two
classes of behavior can be traced back to the existence or abscence of
``antiferromagnetic'' or ``dipolar''-type interactions which, when present,
make the Green functions non-monotonous oscillatory and favor spatial modulated
patterns.Comment: Latex document of 29 pages + 20 ps figures, addition of a new
demonstration of the source of strong log-periodicity and of a justification
of the general offered classification, update of reference lis
Modelling non-perturbative corrections to bottom-quark fragmentation
We describe B-hadron production in e+e- annihilation at the Z pole by means
of a model including non-perturbative corrections to b-quark fragmentation as
originating, via multiple soft emissions, from an effective QCD coupling
constant, which does not exhibit the Landau pole any longer and includes
absorbitive effects due to parton branching. We work in the framework of
perturbative fragmentation functions at NLO, with NLL DGLAP evolution and NNLL
large-x resummation in both coefficient function and initial condition of the
perturbative fragmentation function. We include hadronization corrections via
the effective coupling constant in the NNLO approximation and do not add any
further non-perturbative fragmentation function. As part of our model, we
perform the Mellin transforms of our resummed expressions exactly. We present
results on the energy distribution of b-flavoured hadrons, which we compare
with LEP and SLD data, in both x- and N-spaces. We find that, within the
theoretical uncertainties on our calculation, our model is able to reasonably
reproduce the data at x<0.92 and the first five moments of the B cross section.Comment: 44 pages, 4 figures. Few changes after referee report. Sections 4 and
7 expanded, references added, numerical results unchange
Mellin Representation for the Heavy Flavor Contributions to Deep Inelastic Structure Functions
We derive semi--analytic expressions for the analytic continuation of the
Mellin transforms of the heavy flavor QCD coefficient functions for neutral
current deep inelastic scattering in leading and next-to-leading order to
complex values of the Mellin variable . These representations are used in
Mellin--space QCD evolution programs to provide fast evaluations of the heavy
flavor contributions to the structure functions and
.Comment: 13 pages Letex, 1 style file, 10 eps figure
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