Truncated Mellin moments: Useful relations and implications for the spin structure function $g_2$

Abstract

We review our previous studies of truncated Mellin moments of parton distributions. We show in detail the derivation of the evolution equation for double truncated moments. The obtained splitting function has the same rescaled form as in a case of the single truncated moments. We apply the truncated moments formalism to QCD analyses of the spin structure functions of the nucleon, $g_1$ and $g_2$. We generalize the Wandzura-Wilczek relation in terms of the truncated moments and find new sum rules. We derive the DGLAP-like evolution equation for the twist-2 part of $g_2$ and solve it numerically. We find also useful relations between the truncated and untruncated moments.

17 pages, 4 figures

References in corpus (2)

• Quark-hadron duality and truncated moments of nucleon structure functions
• Study of the nucleon spin-dependent structure function $g_1$. A comparison with recent HERMES and COMPASS data

Cited by in corpus (5)

• 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