References - Bogoliubov Laboratory of Theoretical Physics - JINR

Gj(y) are the unpolarized valon distributions, where j refers to U and D type valons
[2]. The functions δFj(y) are given in [3]. δqvalon i (z = x/y, Q2 ) is the polarized parton
distribution in the valon . Polarized parton distributions inside the valon are evaluated
according to the DGLAP evolution equation subject to physically sensible initial conditions
[3]. In the valon model the hadron structure is obtained by the convolution of valon
structure and its distribution inside the hadron. Having specified the various components
that contribute to the spin of a valon, we now turn to the polarized hadron structure,
which is obtained by a convolution integral as follows:
g h 1 (x, Q2 )= �
� 1
dy
y δGhvalon (y)gvalon 1 ( x
y ,Q2 ). (3)
valon
x
The valon structure is generated by perturbative dressing in QCD. In such processes
with massless quarks, helicity is conserved and therefore, the hard gluons can not induce
sea quark polarization perturbatively. According to this description, it turns out that
sea polarization is consistent with zero [3, 4]. This finding is supported by HERMES
experiment and by the newly released data from COMPASS experiment [5–7].
There is an excellent agreement between the model predictions with the experimental
data for spin structure functions. A sample is given in Figure 1.
2 Axial coupling constants: a3 and a8
The axial coupling constant can be write as a combination of PPDFs as follows:
g 3 A ≡ s μ =Δu(Q 2 ) − Δd(Q 2 ),
g 8 A ≡ s μ =Δu(Q 2 )+Δd(Q 2 ) − 2Δs(Q 2 ).
In the model described in the section 1, we showed that [3, 4], the calculations in the
framework of NLO perturbation theory, shows that the sea quark contribution to the spin
of proton is essentially consistent with zero, then we have:
xg1p
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
10 -4
SLAC-E143
SMC-low x
HERMES
AAC
BB
GRSV
MODEL
10 -3
10 -2
x
10 -1
10 0
0.03
0.02
0.01
0
-0.01
10 -3
COMPASS Q2>1 (Gev2)
COMPASS Q2>0.7 (Gev2)
SMC
HERMES
AAC
BB
GRSV
MODEL
Figure 1: Left: Polarized proton structure function, xg p
1 at Q2 =5GeV 2 . Right: Polarized deuteron
structure function, xg d 1 at Q 2 =3GeV 2 . The results from model compared with the global fits [9–11]
and the experimental data [5, 7, 12–14]
144
xg1d
10 -2
x
10 -1
10 0
(4)