References - Bogoliubov Laboratory of Theoretical Physics - JINR

Γ p 1
0.15
0.125
0.1
0.075
0.05
0.025
0
-0.025
Burkert-Ioffe
Soffer-Teryaev
CLAS EG1b
CLAS EG1a
HERMES
SLAC E143
RSS
GDH slope
Ji, χPt
Bernard, χPt
Poly Fit
-0.01
-0.02
-0.03
-0.04
-0.05
0 1 2 3 0 0.1 0.2 0.3 -0.06
Q 2 (GeV/c) 2
0.01
0
(per nucleon)
Γ d 1
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
Burkert-Ioffe
Soffer-Teryaev
CLAS EG1b
CLAS EG1a
HERMES
SLAC E143
RSS
GDH slope
Ji, χPt
Bernard, χPt
Poly Fit
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07
0 1 2 3 0 0.1 0.2 0.3
Q 2 (GeV/c) 2
(a) (b)
Figure 2: (a) Γ p
1 as a function of Q2 . (b) Γ d 1 as a function of Q2 . The EG1a [7], SLAC [8] and
Hermes data [9] are shown for comparison. The filled circles represent the present data, including an
extrapolation over the unmeasured part of the x spectrum using a model of world data.
Treating the deuteron as the incoherent sum of a
proton and a neutron and correcting for the D-state,
Γ d 1(Q 2 )= 1
2 (1 − 1.5ωD) � Γ p
1(Q 2 )+Γ n 1(Q 2 ) � , (6)
one finds that Γ d 1 (Q2 )=−0.451Q 2 +3.26Q 4 .ThelowQ 2
results for Γ p
1 and Γ d 1 have been fit to a function of the
form aQ 2 + bQ 4 + cQ 6 + dQ 8 where a is fixed at −0.455
(proton) and −0.451 (deuteron) by the GDH sum rule.
For the proton, b =3.81 ± 0.31 (stat) +0.44 − 0.57
(syst) is extracted and for the deuteron, b =2.91 ± 0.52
(stat) ±0.69 (syst) was obtained, both consistent with
the Q 4 term predicted by Ji et.al.
Our fit is shown in the right-hand panel of plots in
γ p 0 (10 -4 fm 4 )
3
2
1
0
-1
-2
-3
-4
-5
0.01
0 0.2 0.4 0.6
0
Kao et al, O(p 3 )+Δ(ε 3 )
Kao et al, O(p 3 )+O(p 4 )
MAID 2003 (π)
Bernard et al.
Models
syst_err_expt
syst_err_extr
Mainz
EG1b Data
EG1b Data+extr.
10 -1
0.02
0.015
0.01
0.005
-0.005
-0.01
-0.015
-0.02
1
Q 2 (GeV/c) 2
Figure 3: Generalized forward spin
polarizability γ p
0 as a function of Q2
for the full integral (closed circles)
and the measured portion of the integral
(open circles)
Figs. 2 along with Ji’s prediction. We find that the Q 6 term becomes important even
below Q 2 =0.1GeV 2 and that this term needs to be included in the χPT calculations in
order to extend the range of their validity.
Higher moments of g1 are interesting as well. In our kinematic domain these moments
emphasize the resonance region over DIS kinematics because of extra factors of x in the
integrand. The generalized forward spin polarizability of the nucleon is given by [13]
γ0(Q 2 2 16αM
)=
Q6 � x0
x 2
�
g1(x, Q 2 ) − Q2x2 4M 2 g2(x, Q 2 �
) dx, (7)
0
where α is the fine structure constant. First results for the generalized forward spin
polarizability of the proton for a range of Q2 from 0.05 to 4 GeV2 are shown in Fig. 3
Our data lie closest to the MAID 2003 [14] model, which is a phenomenological fit to
single pion production data and includes only the resonance region. However, since γ0 is
weighted by an additional factor of x2 compared to Γ1, the contribution to the integral
from the DIS part of the spectrum is rather small. The MAID model follows the trend of
the data but significantly underpredicts them numerically.
296
0
γ p 0* Q6 /(16αM 2 )