References - Bogoliubov Laboratory of Theoretical Physics - JINR

tries in the two Q 2 regions are fully consistent, while there is a hint of systematically
smaller K + asymmetries in the large Q 2 region.
2 〈sin(φ-φ S )〉 UT
〈Q 2 〉 [GeV 2 〈Q ]
2 〉 [GeV 2 ]
0.1
0
10
1
π +
10 -1
Q 2 < 〈Q 2 (x i )〉
Q 2 > 〈Q 2 (x i )〉
Figure 4: Sivers amplitudes for π + (left panel) and K + (right panel) as functions of x. TheQ 2 range
for each bin was divided into the two regions above and below 〈Q 2 (xi)〉 of that bin. In the bottom panel
the average Q 2 values are given for the two Q 2 ranges.
A two-dimensional extraction of the Collins and Sivers amplitudes may be of great interest
as it provides detailed information for the phenomenological study of specific distribution
and fragmentation functions. A measurement of such two-dimensional amplitudes was
done for charged pions (the statistics of charged kaons and neutral pions is too low for
such a study) in variables x, z, andPh⊥. As an example, in Fig. 5 the two-dimensional
Collins amplitude 2 〈sin (φ + φS)〉 π
UT is presented as a function of z in bins of x (top panels)
and as a function of x in bins of z (bottom panels).
2 〈sin(φ+φS )〉 π
UT
2 〈sin(φ+φS )〉 π
UT
2 〈sin(φ+φS )〉 π
UT
2 〈sin(φ+φS )〉 π
UT
0.2
0
0.1
0
-0.1
0.1
0
-0.1
0
-0.1
0.023 < x < 0.05
〈 Q 2 〉 = 1.3 GeV 2
π +
π -
0.2 0.4 0.6
0.05 < x < 0.09
〈 Q 2 〉 = 1.9 GeV 2
HERMES
x
K +
0.09 < x < 0.15
〈 Q 2 〉 = 2.8 GeV 2
10 -1
0.15 < x < 0.22
〈 Q 2 〉 = 4.2 GeV 2
PRELIMINARY
x
0.22 < x < 0.40
〈 Q 2 〉 = 6.2 GeV 2
2002-2005
Lepton Beam Asymmetries ⎯ 8.1 % scale uncertainty
0.2 0.4 0.6 0.2 0.4 0.6 0.2 0.4 0.6 0.2 0.4 0.6
π +
π -
0.20 < z < 0.30 0.30 < z < 0.40 0.40 < z < 0.50 0.50 < z < 0.60 0.60 < z < 0.70
-0.2
0 0.2
0 0.2 0 0.2 0 0.2 0 0.2
Figure 5: Collins amplitudes for π + (full squares) and π − (open triangles). Upper panels: z dependence
in five bins of Bjorken x. Lower panels: x dependence in five bins of z.
225
z
x