References - Bogoliubov Laboratory of Theoretical Physics - JINR

The 4th order Heavy Baryon Chiral Perturbation calculation by Kao, Spitzenberg and
Vanderhaeghen [15], shown by the dashed line in Fig. 3, also underpredicts the data. The
authors note that the O(p 4 ) correction term is of opposite sign to the O(p 3 )termand
shows no sign of convergence. A leading order correction to account for Δ(1232) degrees
of freedom, not shown, is also negative. By contrast the χPT calculation of Bernard,
Hemmert and Meissner [16], indicated by the grey band, including the resonance contribution,
overpredicts the data. The Δ(1232) and vector meson contribution is negative
(around −2 × 10 −4 fm 4 ) but the discrepancy with the data suggests that this has been
underestimated.
3.3 Factorization tests
The semi-inclusive measurements of double spin asymmetries
allow us to study factorization of x, z = Eh/ν and pT
dependency for charged and neutral pions. We study the
quantity g1/F1 as a function of kinematic variables for all
three pion flavors [18]. The z-dependence of semi-inclusive
g1/F1 is examined in Fig. 4. We compare the data with
LO pQCD predictions obtained from the GRSV2000 [17]
parametrization. The ratio should be approximately independent
of z, broken by the different weights given to the
polarized u and d quarks by the favored and unfavored fragmentation
functions. This is indeed observed in the data,
g 1 /f 1
0.75
0.5
0.25
0
-0.25
π +
π -
π 0
0.12 < x < 0.48 Q 2 > 1.5 GeV 2
0.2 0.4 0.6 0.8
Figure 4: z-dependence of
semi-inclusive g1/F1 for the proton
target
which are in good agreement with the model in both magnitude and z-dependence up to
z = 0.7. The observed drop-off at high z for π − is also expected due to increased importance
of d(x) with increasing z. Thex-dependence of g1/F1 for π + ,π − ,π 0 are consistent
with each other and follow the same trend as the inclusive result, which is expected if
factorization works. The trend is for the ratio to increase with x, due to increasing dominance
of polarized u(x) athighx. The ratio g1/F1 has also been studied as a function of
transverse component of the hadron momentum pT . The data suggest that at small pT ,
g1/F1 tends to decrease for π + and to decrease for π − . This result indicates that quarks
aligned and anti-aligned with the nucleon spin might have different transverse momentum
distributions, but more data is needed to study this behavior.
4 Summary and Outlook
In conclusion, the spin asymmetries for the proton and the deuteron have been measured
over a vast kinematic region, allowing systematic studies of various aspects of the nucleon
spin structure at low and intermediate energies. Our data are consistent with an approach
to A1 =1asx→ 1 as required by pQCD. The first extraction of generalized forward spin
was shown to be poorly described by the chiral perturbation theory even
polarizability γ p
0
at our lowest Q2 =0.05GeV2 /c2 . The semi-inclusive studies have shown interesting pT
dependence suggesting that the transverse momentum distributions may have non-trivial
dependency on the flavor and helicity of quarks. These studies have led to several new
proposals with 6 and 11 GeV beams. A recently completed run with 6 GeV beam will
provide us with an order of magnitude more π + ,π− ,π0 for g1/F1 on the proton.
297
z