References - Bogoliubov Laboratory of Theoretical Physics - JINR

1.1 Nucleon Helicity Structure at large x
The photon-nucleon asymmetry A1(x, Q 2 ) reflects the valence spin structure of the nucleon.
Valence quarks are the irreducible kernel of each hadron, responsible for its charge,
baryon number and other macroscopic properties. The region x → 1 is a relatively clean
region to study the valence structure of the nucleon since this region is dominated by
valence quarks while the small x region is dominated by gluon and sea densities. Due to
its relative Q 2 -independence in the DIS region, the virtual photon asymmetry A1, whichis
approximately given by the ratio of spin-dependent to spin averaged structure functions,
A1(x) ≈ g1(x)
, (1)
F1(x)
is one of the best physics observables to study the valence spin structure of the nucleon.
At leading order,
A1(x, Q 2 � 2 ei Δqi(x, Q
)=
2 )
�
2 ei qi(x, Q2 , (2)
)
where q = q ↑ +q ↓ nd Δq = q ↑ −q ↓ are the sum and difference between quark
distributions with spin aligned and anti-aligned with the spin of the nucleon. The x
dependence of the parton distributions provide a wealth of information about the quarkgluon
dynamics of the nucleon. in particular spin degrees of freedom allow access to
information about the structure of hadrons not available through unpolarized processes.
Furthermore, the spin dependent distributions are more sensitive than the spin-averaged
ones to the quark-gluon dynamics responsible for spin-flavor symmetry breaking. Several
models make specific predictions for the large x behavior of quark distributions.
1.2 Moments and Sum Rules
The spin structure function g1 is important in understanding the quark and gluon spin
components of the nucleon spin, and their relative contributions in different kinematic
regions. At high Q 2 , g1 provides information on how the nucleon spin is composed of
the spin of its constituent quarks and gluons. At low Q 2 , hadronic degrees of freedom
become more important and dominate the measurements. There is particular interest
in the first moment of g1, Γ1(Q 2 ) = � 1−
0 g1(x, Q 2 )dx, which is constrained at low Q 2
by the Gerasimov-Drell-Hearn sum rule [1] and at high Q 2 by the Bjorken sum rule [2]
and previous DIS experiments. In our definition the upper limit of the integral does not
include the elastic peak. Ji and Osborne [3] have shown that the GDH sum rule can be
generalized to all Q 2 via
S1(ν =0,Q 2 )= 8
Q 2
� Γ1(Q 2 )+Γ el
1 (Q 2 ) � , (3)
where S1(ν, Q 2 ) is the spin-dependent virtual photon Compton amplitude. S1 can be
calculated in Chiral Perturbation Theory (χPT) at low Q 2 and with perturbative QCD
(pQCD) at high Q 2 . Therefore, Γ1 represents a calculable observable that spans the entire
energy range from hadronic to partonic descriptions of the nucleon. Higher moments are
also of interest: generalized spin polarizabilities, γ0 and δLT , are linked to higher moments
of spin structure functions by sum rules based on similar grounds as the GDH sum rule.
Higher moments are less sensitive to the unmeasured low-x part since they are more
weighted at high-x.
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