References - Bogoliubov Laboratory of Theoretical Physics - JINR

IMPACT PARAMETER REPRESENTATION
AND x-DEPENDENCE OF THE TRANSVERSITY SPIN STRUCTURE
OF THE NUCLEONS
O.V. Selyugin
BLTPh,JINR,Dubna,Russia
E-mail: selugin@theor.jinr.ru
Abstract
In the frame work of the our model of t-dependence of generalized parton distributions
we obtain its impact parameter representation. On this basis we calculate
and compare with the results of other models the transversity spin structure of the
proton and neutron. We calculate as function of x the unpolarized density, the
density of unpolarized quarks in the transversely polarized nucleon.
1 Introduction
The electromagnetic hadrons form factors are related to the first moments of the Generalized
Parton distributions (GPDs) [1, 3, 2]
F q
� 1
1 (t) =
0
dx H q (x, t), F q
� 1
2 (t) =
0
dx E q (x, t). (1)
Taking the matrix elements of energy-momentum tensor Tμν instead of the electromagnetic
current J μ one can obtain the gravitational form factors of quarks which are related to
the second moments. For ξ = 0 one has
� 1
0
dx xHq(x, t) =Aq(t);
� 1
0
dx xEq(x, t) =Bq(t). (2)
Non-forward parton densities also provide information about the distribution of the parton
in impact parameter space [4] which is connected with t-dependence of GP Ds. Now we
cannot obtain this dependence from the first principles, but it must be obtained from the
phenomenological description with GP Ds of the nucleon electromagnetic form factors.
Note that in [5, 6] it was shown that at large x → 1 and momentum transfer the
behavior of GPDs requires a larger power of (1 − x) inthet-dependent exponent with
n ≥ 2. It was noted that n = 2 naturally leads to the Drell-Yan-West duality between
parton distributions at large x and the form factors.
In [7], a simple ansatz was proposed which will be good for describing the form factors
of the proton and neutron by taking into account a number of new data that have appeared
inthelastyears.Wechoosethet-dependence of GPDs in the form
H q (x, t) = q(x) exp[a+
(1 − x) 2
x m t]; E q (x) = kq
118
Nq
(1 − x) κ1 q(x)exp[a−
(1 − x) 2
x m
t], (3)