References - Bogoliubov Laboratory of Theoretical Physics - JINR

EVOLUTION EQUATIONS FOR TRUNCATED MELLIN MOMENTS OF
THE PARTON DENSITIES
D. Strózik-Kotlorz
Opole University of Technology
E-mail: d.strozik-kotlorz@po.opole.pl
Abstract
Evolution equations for truncated Mellin moments of the parton distributions
in the nucleon are presented. In this novel approach the equations are diagonal and
exact for each nth moment and for every truncation point x0 ∈ (0; 1). They have
the same form as those for the partons themselves. The modified splitting function
for nth truncated moment P ′ (n, x) is equal to x n P (x), where P (x) is DGLAP
splitting function for the partons. The evolution equations for truncated moments
can be used in different approximations: LO, NLO etc. and for polarised as well as
unpolarised densities. Presented approach can be an additional useful tool in the
PQCD analysis of the nucleon structure functions.
1 Introduction
Unpolarised and polarised parton distribution functions as well as their Mellin moments
are nowadays the subject of intensive theoretical and experimental studies. Usually, the
central role in the perturbative QCD analysis is played by the parton distribution functions
(PDFs), which obey the well-known DGLAP evolution equations [1]. However recently,
moments have become a great of importance and now they are also a powerful tool in
studying the structure functions of the nucleon. An approach based on the moments has
many advantages. Moments directly refer to sum rules - fundamental relations in QCD.
They provide knowledge about contributions to momentum or spin of the nucleon coming
from quarks and gluons. This is essential in resolving the ‘spin puzzle’. We propose a
novel - truncated Mellin moments approach (TMMA) with evolution equations, which
is a generalization of the full (untruncated) moments case and additionally offers new
possibilities. From the one hand, TMMA enables one directly to study the evolution
of physical values, and from the other hand, allows to avoid uncertainties from nonavailable
experimentally x−regions. The idea of truncated moments of parton densities
was introduced in [2]. The authors obtained non-diagonal evolution equations, where
each nth truncated moment couples to all higher moments. Then, truncated moments
were applied in ln 2 x approximation, where we obtained the diagonal solutions [3], and
also in NLO analysis of SIDIS data with use of polynomial expansion methods [4]. In
[5], [6] we derived within DGLAP approach diagonal and exact evolution equations for
truncated moments in the case of single and double truncation as well. Here we present
this promising treatment, its advantages, possible applications and perspectives.
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