References - Bogoliubov Laboratory of Theoretical Physics - JINR

Unpolarized target asymmetries. The azimuthal asymmetry for hadron production
in lepton DIS off unpolarized target was predicted to be non-zero many years ago due to
the fact that the kinematics is noncollinear when the quark intrinsic transverse momentum
is taken into account. Other possible sources of the asymmetry are perturbative gluon
radiation and Boer-Mulders mechanism, which is due to the correlation of the quark
intrinsic transverse momentum and intrinsic transverse spin. This correlation is described
by the Boer-Mulders distribution function h ⊥ 1 (x, kT ), which represents the transversepolarization
distribution of quarks inside an unpolarized nucleon.
The cross-section for hadron production in lepton-nucleon DIS lN −→ l ′ hX for the case
of unpolarized target and unpolarized beam can be written in the following form [11]:
d 5 σ
dxdydzdP 2 h⊥ dφh
∝ A(y)FUU,T + B(y)FUU,L +
cos φh
C(y)cosφhFUU cos 2φh
+ B(y)cos2φhFUU Here, φh is the angle between the lepton scattering plane and the hadron production plane,
cos φh
cos 2φh
A(y), B(y), and C(y) are kinematic factors, FUU,T(L), FUU ,andFUU are structure
functions responsible for 1, cos φh, cos2φhazimuthal modulations, respectively.
At HERMES, the extraction of the unpolarized modulations was performed using a multidimensional
unfolding procedure to correct for radiative and acceptance effects on hydrogen
and deuterium data, separately for positive and negative hadrons. The cos φh
amplitudes as function of x, y, z, andPh⊥for positive and negative hadrons produced off
hydrogen target are presented in top panel of Fig. 6. The cos 2φh amplitudes are presented
in bottom panel of Fig. 6. An important feature shown by HERMES data is the different
behaviour of the amplitudes for positive and negative hadrons. Such difference can be
considered as an evidence of a non-zero Boer-Mulders function.
Analogous results were obtained for the hadron asymmetries with deuterium target.
2〈
cos( φ ) 〉
h UU
UU
〉
)
2〈
cos(2φ
h
0.2
0.1
0
-0.1
-0.2
-0.3
0.2
0.1
0
-0.1
-0.2
Hydrogen
-
h
+
h
Hydrogen
-
h
+
h
-1
2
.1
0
.1
2
3
10 1
x
2
.1
0
.1
2
-1
10 1
x
2
.1
0
.1
2
3
0.4 0.6 0.8 0.2 0.4 0.6 0.8 1
y
z
2
.1
0
.1
2
2
0.4 0.6 0.8 0.2 0.4 0.6 0.8 1
y
z
2
.1
0
.1
2
3
2
.1
0
.1
HERMES Preliminary
0.2 0.4 0.6
[GeV]
Ph
HERMES Preliminary
0.2 0.4 0.6
[GeV]
Figure 6: 2 〈cos (φh)〉 UU amplitude (top panel) and 2 〈cos (2φh)〉 UU amplitude (bottom panel) for negative
(circles) and positive (squares) hadrons. Data are from hydrogen target. The error bars represent
the statistical errors while the band represents the systematic errors. The open points at high z are not
included in the projections over the other variables.
226
Ph
(2)