Eur. Phys. J. C (2006) 48: 457-466
https://doi.org/10.1140/epjc/s10052-006-0050-4

Theoretical Physics

Truncated first moment of the parton distribution – A modified approach

¹ Division of Physics, Opole University of Technology, Ozimska 75, 45-370, Opole, Poland
² Division of Mathematics, Opole University of Technology, Luboszycka 3, 45-036, Opole, Poland

^* e-mail: dstrozik@po.opole.pl

Received: 7 May 2006
Revised: 30 August 2006
Published online: 24 October 2006

Abstract

We derive the LO DGLAP evolution equation for the full Mellin moments of the first moment of the nonsinglet parton distribution truncated at x₀. This “moment of moment” approach allows one to determine the small-x₀ behaviour of the truncated first moment. We compare our predictions to results obtained from x-space solutions for parton distributions with use of the Chebyshev-polynomial method and to solutions of the evolution equations for the truncated moments proposed by other authors. The comparison is performed for different input parametrisations for 10^-5≤x₀≤0.1 and 1≤Q²≤100 GeV². We give an example of an application to the determination of the contribution to the Bjorken sum rule.