References - Bogoliubov Laboratory of Theoretical Physics - JINR

3 Semi-Inclusive DIS
Collins and Sivers asymmetries. HERMES has published its first results on azimuthal
single spin asymmetries for charged pions produced in semi-inclusive DIS [7] off transversely
polarized target using about 10% of the collected statistics. Preliminary results
for pions and charged kaons obtained with full statistics have been presented at many
conferences. The main contributions to the asymmetries were identified as due to the
Collins [8] and Sivers [9] mechanisms. The Collins mechanism produces a correlation
in the fragmentation process between the transverse spin of the struck quark and the
transverse momentum Ph⊥ of the produced hadron. This correlation is described by the
Collins fragmentation function H ⊥ 1 (z). The Sivers mechanism produces a correlation between
the transverse polarization of the target nucleon and the transverse momentum
pT of the struck quark. This correlation is described by the Sivers distribution function
f ⊥ 1T
2 〈sin(φ-φ S )〉 UT
2 〈sin(φ-φ S )〉 UT
2 〈sin(φ-φ S )〉 UT
2 〈sin(φ-φ S )〉 UT
2 〈sin(φ-φ S )〉 UT
2 〈sin(φ-φ S )〉 UT
(x). The contribution of the Collins mechanism to the asymmetry is proportional
0.1
0.05
0
0.1
0
-0.1
0.05
0
-0.05
0.2
0.1
0
0.1
0
-0.1
0.25
0
π +
π 0
π -
K +
K -
π + − π -
10 -1
x
0.4 0.6
z
0.5 1
P h⊥ [GeV]
Figure 3: Sivers amplitudes for pions, charged
kaons, and the pion-difference asymmetry (as denoted
in the panels) as functions of x, z, orPh⊥.
The systematic uncertainty is shown as a band at
the bottom of each panel. In addition there is a
7.3% scale uncertainty from the target-polarization
measurement.
224
to the convolution of the transversity with
the Collins function, while the contribution
of the Sivers mechanism is proportional
to the convolution of the Sivers function
with the usual spin-independent fragmentation
function. Fortunately, the contributions
can be easily disentangled as they
produce different azimuthal modulation of
the asymmetry, sin(φ+φS) andsin(φ−φS)
for the Collins and Sivers cases, respectively.
Here, azimuthal angles φ and φS
are the angles of the hadron momentum
�Ph and of the transverse component � ST of
the target-proton spin, respectively, about
the virtual-photon direction.
Final results for the Sivers amplitudes
were obtained recently [10]. The resulting
Sivers amplitudes for pions, charged kaons,
and for the pion-difference asymmetry are
presented in Fig. 3 as functions of x, z,
or Ph⊥. The amplitudes are positive and
increase with increasing z, except for π − ,
for which they are consistent with zero. In
order to test for higher-twist effects, the x
dependence of the Sivers amplitudes for π +
and K + is presented in Fig. 4, where each
x-bin is divided into two Q 2 regions below
and above the corresponding average Q 2
(〈Q 2 (xi)〉) for that x bin. While the averages
of the kinematics integrated over in
those x bins do not differ significantly, the
〈Q 2 〉 values for the two Q 2 ranges change
by a factor of about 1.7. The π + asymme-