The logarithmic and constant contributions to the Wilson coefficient of the longitudinal heavy quark structure function to \(O(\alpha_s^3)\) are calculated using mass factorization techniques in ...Mellin space. The small \(x\) behaviour of the Wilson coefficient is determined. Numerical illustrations are presented.
The non-singlet and singlet anomalous dimensions of the twist--2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in \(O(\alpha_s)\). We apply these results ...for the derivation of evolution equations for partition functions, structure functions, and wave functions which are defined as Fourier transforms of the matrix elements of the light-ray operators. Special cases are the Altarelli-Parisi and Brodsky-Lepage kernels. Finally we extend Radyushkin's solution from the non-singlet to the singlet case.
We discuss the quantitative consequences of the resummation of the small-x
contributions to the anomalous dimensions beyond next-to-leading order in
alpha_s and up to next order in ln(1/x) (NLx) in a ...framework based on the
renormalization group equations. We find large and negative effects leading to
negative values for the {\sf total} splitting function P_{gg}(x,alpha_s)
already for x \lsim 0.01 at Q^2 \simeq 20 GeV^2. Terms less singular than those
under consideration turn out to be quantitatively as important and need to be
included. We derive the effects of the conformal part of the NLx contributions
to the anomalous dimensions and discuss the exponent omega describing the
s^omega behavior of inclusive cross sections.
Acta Phys.Polon. B29 (1998) 2581-2590 The role of various symmetries in the evaluation of splitting functions and
coefficient functions is discussed. The scale invariance in hard processes is
known ...to be a guiding tool to understand the dynamics. We discuss the
constraints on splitting functions coming from various symmetries such as
scale, conformal and supersymmetry. We also discuss the Drell-Levy-Yan relation
among splitting and coefficient functions in various schemes. The relations
coming from conformal symmetry are also presented.
Phys.Rev.D58:091502,1998 We recalculate the gluon Regge trajectory in next-to-leading order to clarify
a discrepancy between two results in the literature on the constant part. We
confirm the result ...obtained by Fadin et al.~\cite{FFK}. The effects on the
anomalous dimension and on the $s^{\omega}$ behavior of inclusive cross
sections are also discussed.
Harmonic sums and mellin transforms Blümlein, Johannes
Nuclear physics. Section B, Proceedings supplement,
10/1999, Letnik:
79, Številka:
1
Journal Article
Odprti dostop
The finite and infinite harmonic sums form the general basis for the Mellin transforms of all individual functions
fi(x) describing inclusive quantities such as coefficient and splitting functions ...which emerge in massless field theories. We discuss the mathematical structure of these quantities.
The general evolution kernels of the twist 2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in \({\cal O}(\alpha_s)\). From these evolution kernels a ...series of special evolution equations can be derived, among them the Altarelli-Parisi equations and the evolution equation for the meson wave function. In the case of twist 3 the results of Balitzki and Braun are confirmed.
The non-singlet and singlet evolution kernels of the twist--2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in \(O(\alpha_s)\) for the general case of ...virtualities \(q^2, q'^2 \neq 0\). Special cases as the kernels for the general single-variable evolution equation and the Altarelli-Parisi and Brodsky-Lepage limits are derived from these results.
We present a determination of parton distribution functions (ABM11) and the strong coupling constant alpha_s at next-to-leading order and next-to-next-to-leading order (NNLO) in QCD based on world ...data for deep-inelastic scattering and fixed-target data for the Drell-Yan process. The analysis is performed in the fixed-flavor number scheme for n_f=3,4,5 and uses the MSbar-scheme for alpha_s and the heavy-quark masses. At NNLO we obtain the value alpha_s(M_Z) = 0.1134 +- 0.0011. The fit results are used to compute benchmark cross sections at hadron colliders to NNLO accuracy and to compare to data from the LHC.
A summary is given on the main aspects which were discussed by the working
group. They include new results on the deep inelastic scattering structure
functions $F_2, xF_3, F_L$ and $F_2^{c\bar{c}}$ ...and their parametrizations, the
measurement of the gluon density, recent theoretical work on the small $x$
behavior of structure functions, theoretical and experimental results on
$\alpha_s$, the direct photon cross section, and a discussion of the event
rates in the high $p_T$ range at Tevatron and the high $Q^2$ range at HERA, as
well as possible interpretations.
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