References - Bogoliubov Laboratory of Theoretical Physics - JINR

4 Perspectives
Evolution equations for the truncated Mellin moments of the parton densities can be a
promising tool in the QCD analysis of the nucleon structure functions. Here we list a few
of the valuable future applications of TMMA:
Δq NS (x,Q 2 0 )
• Studying the fundamental properties of nucleon structure, concerning moments of
F1, F2 and g1. These are: momentum fraction carried by quarks, quark helicities
10
8
6
4
2
Reconstruction
from 1 st trunc. moment
x min
0
1e-05 1e-04 0.001 0.01 0.1 1
x
x min
data for x>0.001
data for x>0.02
original function
Δq NS (x,Q 2 0 )
10
8
6
4
2
Reconstruction
from 1 st and 2 nd
truncated moments
x min
0
1e-05 1e-04 0.001 0.01 0.1 1
(a) (b)
x
x min
data for x>0.001
data for x>0.02
original function
Figure 1: (a) Reconstruction of the initial parton density at Q 2 0 =1GeV 2 from the first
truncated moment given at Q 2 =10GeV 2 in the broad range 0.001 ≤ x ≤ 0.7 (dashed)
and in the limited one 0.02 ≤ x ≤ 0.7 (dotted). Comparison with the original function
(6) (solid), where α = −0.4 reflects the theoretical knowledge on the small-x behaviour
- see e.g. [7]. (b) Similarly as in (a) but after additional precise reconstruction of the
parameter γ (6) from the second truncated moment.
xΔq(x,Q 2 0 )
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
x(Δu v - Δd v )
-0.15
0.001 0.01 0.1 1
x
xΔu v
xΔd v
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
1 NS ∫x0 g1 dx
0
0.01 0.1 1
x0 (a) (b)
Figure 2: (a) Reconstruction of the initial parton densities from HERMES data for the
first truncated moment of g NS
1
at Q 2 =5GeV 2 [9] (dotted) in comparison with original
BB fit [8]. Plots for x(Δuv − Δdv) overlap each other. (b) The first truncated moment
vs the truncation point x0, calculated
of the nonsinglet polarised structure function gNS 1
from the reconstructed fit (solid). Q2 =5GeV 2 . Comparison with HERMES data [9]
basedonBBfit[8](pointswitherrorbars).
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