Evolution equations for truncated moments of the parton distributions

Abstract

We derive evolution equations for the truncated Mellin moments of the parton distributions. We find that the equations have the same form as those for the partons themselves. The modified splitting function for n-th moment $P^{\prime }(n,x)$ is $x^{n}P(x)$, where $P(x)$ is the well-known splitting function from the DGLAP equation. The obtained equations are exact for each n-th moment and for every truncation point $x_0\in (0;1)$. They can be solved with use of standard methods of solving the DGLAP equations. This approach allows us to avoid the problem of dealing with the unphysical region $x\to 0$. Furthermore, it refers directly to the physical values - moments (rather than to the parton distributions), what enables one to use a wide range of deep-inelastic scattering data in terms of smaller number of parameters. We give an example of an application.

6 pages, 3 figures

References in corpus (9)

• Polarised Quark Distributions in the Nucleon from Semi-Inclusive Spin Asymmetries
• Truncated moments of parton distributions
• QCD expectations for the spin structure function $g_1$ in the low $x$ region
• Evolution of truncated moments of singlet parton distributions
• Unified description of the non-singlet spin dependent structure function $g_1$ incorporating Altarelli-Parisi evolution and the double logarithmic $l{n}^2(1/x)$ effects at low $x$
• Solving the Altarelli-Parisi equations with truncated moments
• Comparison of numerical solutions for Q^2 evolution equations
• Integral equation for spin dependent unintegrated parton distributions incorporating double ln^2(1/x) effects at low x
• Truncated first moment of the parton distribution - a modified approach

Cited by in corpus (13)

• Novel approaches in Hadron Spectroscopy
• Phenomenology with a recoil-free jet axis: TMD fragmentation and the jet shape
• Quark-hadron duality and truncated moments of nucleon structure functions
• Resonant contributions to inclusive nucleon structure functions from exclusive meson electroproduction data
• Optimized determination of the polarized Bjorken sum rule in pQCD
• Direct observation of quark-hadron duality in the free neutron F_2 structure function
• Unpolarized structure functions at Jefferson Lab
• Resonant contributions to polarized proton structure functions
• Cut moments and a generalization of DGLAP equations
• Cut Moments approach in the analysis of DIS data
• Analysis of DIS structure functions of the nucleon within truncated Mellin moments approach
• Evolution of the Truncated Mellin Moments of the parton distributions in QCD analysis
• Generalized DGLAP evolution