Approximate Next-to-Leading Order and Next-to-Next-to-Leading Order Corrections

For processes involving structure functions and/or fragmentation functions, arguments that, over a range of a proper kinematic variable, there is a part that dominates the next-to-leading order (NLO) corrections are briefly reviewed. The arguments are tested against more recent NLO and in particular complete next-to-next-to-leading order (NNLO) calculations. A critical examination of when these arguments may not be useful is also presented.Comment: 8 pages and 4 figure

Next-to-Leading Order Corrections to Heavy Flavour Production in Longitudinally Polarized Photon-Nucleon Collisions

A complete next-to-leading order calculation of longitudinally polarized heavy quark photoproduction is presented. All results of the purturbative calculation are given in detail. For reactions and energies of interest cross sections differential in the transverse momentum and rapidity of the heavy quark, total cross sections and the corresponding asymmetries are given. Errors in the asymmetries are estimated and the possibility to distinguish between various scerarios of the polarized gluon distribution is discussed. Our results are compared with other related publications.Comment: 38 pages including 12 postscript figures, late

Laurent series expansion of a class of massive scalar one-loop integrals up to {\cal O}(\ep^2) in terms of multiple polylogarithms

In a recent paper we have presented results for a set of massive scalar one-loop master integrals needed in the NNLO parton model description of the hadroproduction of heavy flavors. The one--loop integrals were evaluated in n=4-2\ep dimension and the results were presented in terms of a Laurent series expansion up to {\cal O}(\ep^2). We found that some of the \ep^2 coefficients contain a new class of functions which we termed the $L$ functions. The $L$ functions are defined in terms of one--dimensional integrals involving products of logarithm and dilogarithm functions. In this paper we derive a complete set of algebraic relations that allow one to convert the $L$ functions of our previous approach to a sum of classical and multiple polylogarithms. Using these results we are now able to present the \ep^2 coefficients of the one-loop master integrals in terms of classical and multiple polylogarithms.Comment: 32 pages, Latex, references added, matches published versio

Polarized Photoproduction of Heavy Quarks in Next-to-Leading Order

The results of a next-to-leading order calculation of heavy quark production in longitudinally polarized photon-nucleon collisions are presented. At c.m. energy $\sqrt{S}=10$ GeV, for $\vec \gamma +\vec p \to c+X$, cross sections differential in the transverse momentum and rapidity of the charmed quark $c$ and the corresponding asymmetries are presented; also, as functions of $\sqrt{S}$, integrated cross sections, $K$-factors and the corresponding asymmetries are given. Errors in the asymmetries are estimated and the possibility to distinguish between three scerarios differing essentially in the polarized gluon distribution is discussed.Comment: 8 pages, 3 figure

Next-to-next-to-leading order O(αs4){\cal O}(\alpha_s^4) results for heavy quark pair production in quark--antiquark collisions: The one-loop squared contributions

We calculate the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ one-loop squared corrections to the production of heavy quark pairs in quark-antiquark annihilations. These are part of the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ radiative QCD corrections to this process. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in the dimensional regularization scheme. We have found very intriguing factorization properties for the finite part of the amplitudes.Comment: 12 pages, 2 figures, electronic results file, abbreviation NNLO in Title and Abstract expanded, Summary expanded, reference updated, version to appear in Phys.Rev.

One-loop amplitudes for four-point functions with two external massive quarks and two external massless partons up to O(epsilon^2)

We present complete analytical ${\mathcal O}(\epsilon^2)$ results on the one-loop amplitudes relevant for the NNLO quark-parton model description of the hadroproduction of heavy quarks as given by the so-called loop-by-loop contributions. All results of the perturbative calculation are given in the dimensional regularization scheme. These one-loop amplitudes can also be used as input in the determination of the corresponding NNLO cross sections for heavy flavor photoproduction, and in photon-photon reactions.Comment: 25 pages, 6 figures in the text, Revtex, one reference added, minor improvements in the text, to appear in Phys.Rev.

The Importance of Surveyors and GPS Technology in Systematic Land Registration in Georgia: A Study of the Challenges and Opportunities

The purpose of this work is to explore the historical and contemporary importance of land registration, focusing on the crucial role played by Georgia’s surveyors. The paper concentrates on the combination of GIS-based state systems with GPS PlateTalk map registrations to resolve conflicting cadastral information as well as for accurate ownership record keeping. The Georgian absence of a unified legal and administrative framework significantly complicates land boundary delineation leading to disputes among surveyors. To standardize surveying practices and improve accuracy, an all-encompassing legal framework must be put in place. The study adopts historical, comparative legal, and hermeneutic research methods using examples from Germany and Holland that demonstrate how such advanced technologies as drones, LiDAR, and blockchain can enhance the precision, speed, and security of survey practice. Furthermore, professional education investment must be increased in both teachers and attorneys who are also informed about Geoinformation Systems (GIS), thus enabling them to perform their functions properly when it comes to law matters concerning land registers. Conclusions urge policy-makers to invest in modern technological gadgets as well as engage in legislative reforms that would make their cadastral systems stronger. That would result in the creation of robust cadastral systems by investing in modern technology as well as carrying out legal reforms that would modernize their existing cadastral systems