Comparison of numerical solutions for Q^2 evolution equations

Q^2 evolution equations are important not only for describing hadron reactions in accelerator experiments but also for investigating ultrahigh-energy cosmic rays. The standard ones are called DGLAP evolution equations, which are integrodifferential equations. There are methods for solving the Q^2 evolution equations for parton-distribution and fragmentation functions. Because the equations cannot be solved analytically, various methods have been developed for the numerical solution. We compare brute-force, Laguerre-polynomial, and Mellin-transformation methods particularly by focusing on the numerical accuracy and computational efficiency. An efficient solution could be used, for example, in the studies of a top-down scenario for the ultrahigh-energy cosmic rays.Comment: 12 pages, LaTeX, 13 eps files, Journal of Computational Physics in press, http://hs.phys.saga-u.ac.j

Two-integral distribution functions for axisymmetric stellar systems with separable densities

We show different expressions of distribution functions (DFs) which depend only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known axisymmetric densities. The density of the system is required to be a product of functions separable in the potential and the radial coordinate, where the functions of the radial coordinate are powers of a sum of a square of the radial coordinate and its unit scale. The even part of the two-integral DF corresponding to this type of density is in turn a sum or an infinite series of products of functions of the energy and of the magnitude of the angular momentum about the axis of symmetry. A similar expression of its odd part can be also obtained under the assumption of the rotation laws. It can be further shown that these expressions are in fact equivalent to those obtained by using Hunter and Qian's contour integral formulae for the system. This method is generally computationally preferable to the contour integral method. Two examples are given to obtain the even and odd parts of their two-integral DFs. One is for the prolate Jaffe model and the other for the prolate Plummer model. It can be also found that the Hunter-Qian contour integral formulae of the two-integral even DF for axisymmetric systems can be recovered by use of the Laplace-Mellin integral transformation originally developed by Dejonghe.Comment: 1 figur

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

Improved Fourier Mellin Invariant for Robust Rotation Estimation with Omni-cameras

Spectral methods such as the improved Fourier Mellin Invariant (iFMI) transform have proved faster, more robust and accurate than feature based methods on image registration. However, iFMI is restricted to work only when the camera moves in 2D space and has not been applied on omni-cameras images so far. In this work, we extend the iFMI method and apply a motion model to estimate an omni-camera's pose when it moves in 3D space. This is particularly useful in field robotics applications to get a rapid and comprehensive view of unstructured environments, and to estimate robustly the robot pose. In the experiment section, we compared the extended iFMI method against ORB and AKAZE feature based approaches on three datasets showing different type of environments: office, lawn and urban scenery (MPI-omni dataset). The results show that our method boosts the accuracy of the robot pose estimation two to four times with respect to the feature registration techniques, while offering lower processing times. Furthermore, the iFMI approach presents the best performance against motion blur typically present in mobile robotics.Comment: 5 pages, 4 figures, 1 tabl

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

A Mellin Space Program for W^{+/-} and Z^0 Production at NNLO

We present a program for the evaluation of full unpolarized cross sections for the W^{+/-} and Z^0 production in the narrow width approximation at NNLO in perturbative QCD using Mellin space techniques.Comment: 4 pages, 1 figure. Proceedings of the 10th Hellenic School on Elementary Particle Physics and Gravity, Corfu 2010, to be published in Fortschritte der Physi

New prospects for the numerical calculation of Mellin-Barnes integrals in Minkowskian kinematics

During the last several years remarkable progress has been made in numerical calculations of dimensionally regulated multi-loop Feynman diagrams using Mellin-Barnes (MB) representations. The bottlenecks were non-planar diagrams and Minkowskian kinematics. The method has been proved to work in highly non-trivial physical application (two-loop electroweak bosonic corrections to the $Z \to b \bar{{b}}$ decay), and cross-checked with the sector decomposition (SD) approach. In fact, both approaches have their pros and cons. In calculation of multidimensional integrals, depending on masses and scales involved, they are complementary. A powerful top-bottom approach to the numerical integration of multidimensional MB integrals is automatized in the MB-suite AMBRE/MB/ MBtools/MBnumerics/CUBA. Key elements are a dedicated use of the Cheng-Wu theorem for non-planar topologies and of shifts and deformations of the integration contours. An alternative bottom-up approach starting with complex 1-dimensional MB-integrals, based on the exploration of steepest descent integration contours in Minkowskian kinematics, is also discussed. Short and long term prospects of the MB-method for multi-loop applications to LHC- and LC-physics are discussed.Comment: Presented at the Epiphany Cracow conference 2017, refs adde