Single-Spin Asymmetries at CLAS
H.Avakian
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
Abstract. Significant single-spin azimuthal asymmetries have been observed in semi-inclusive
pion production in the deep-inelastic scattering (DIS) of longitudinally polarized electrons off
unpolarized hydrogen and polarized NH 3 targets at CLAS detector at Thomas Jefferson National
Accelerator Facility (JLab). Issues related to the separation of current fragmentation, and the
factorization of dependencies on x-Bjorken and the fractional energy z, at lowest beam energies
where the DIS region is accessible, are also discussed.
Single-spin asymmetries (SSA) in hadronic reactions have been among the most difficult phenomena to understand from first principles in QCD. Large SSAs have been
observed in hadronic reactions for decades [1, 2]. Recently, significant SSAs were reported in pion production in semi-inclusive DIS (SIDIS) by the HERMES collaboration
at HERA [3, 4] for a longitudinally polarized target, by the SMC collaboration at CERN
for a transversely polarized target [5], and by the CLAS collaboration at the Thomas
Jefferson National Accelerator Facility (JLab)[6] with a polarized beam.
In general, such single-spin asymmetries require a correlation of a particle spin direction and the orientation of the production or scattering plane and they are related to
the orbital angular momentum of partons in the nucleon. The interference of wavefunctions with different orbital angular momentum responsible for single-spin asymmetries
[7, 8, 9, 10, 11, 12], also yields the helicity-flip Generalized Parton Distribution (GPD)
E [13] entering Deeply Virtual Compton Scattering[14, 15] and the Pauli form factor
F2 . The connection of SSAs and GPDs also has been discussed in terms of transverse
distribution of quarks in the nucleon [16].
It is also argued that in both semi-inclusive [17] and hard exclusive [18, 19] pion
production, scaling sets in for cross section ratios and spin asymmetries at lower squared
four-momentum transfer, Q2 , than it does for the absolute cross section. This makes it
possible for the measurement of spin-asymmetries to be a major tool for the study of
parton distributions in the Q 2 domain of a few GeV2 .
The complete tree-level description of single pion electroproduction up to order
1Q containing contributions from twist-2 and twist-3 distribution and fragmentation
functions has been given in Ref. [20]. Terms contributing to the sin φ moment are given
by:
sin φ
σUT
∝ ST 1 ysinφ φS ∑ e2a xha1 xH1a z
(1)
sin φ
xDa z
σUT
∝ ST 1 ysinφ φS ∑ e2a x f1T
1
(2)
aā
aā
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
Sources and Polarimeters, edited by Y. I. Makdisi, A. U. Luccio, and W. W. MacKay
© 2003 American Institute of Physics 0-7354-0136-5/03/$20.00
434
sin φ
σUL
∝ SL sinφ 2 y 1 y
sin φ
σLU
∝ λe sinφ y 1 y
M
e2a x2 haL xH1a z H̃ 2z
Q∑
aā
M
e2a x2 ea xH1a z
Q∑
aā
(3)
(4)
Here the first and second subscripts specify the beam and target polarizations with
U L T denoting unpolarized, longitudinally polarized and transversely polarized cases,
respectively. The azimuthal angle φ is defined by a triple product:
sin φ
k2 P
k1 k2 P
k1
where k1 and k2 are the initial and final electron momenta, and P is the transverse
momentum of the observed hadron with respect to the virtual photon q. The λ e is the
helicity of the electron and SL and ST are proton longitudinal and transverse polarizations, ∑aā sum over quarks and anti-quarks. The x is the Bjorken variable, y and z
are fractions of the incoming electron energy carried by the virtual photon and virtual
photon energy carried by the final pion, respectively.
Eq. 1,2 correspond to leading twist contributions from Collins [21, 20, 23, 17] and
Sivers [7, 8, 9, 11, 12] effects, and give access to chiral-odd transversity, h 1 x[22], and
, respectively. Collins (H ) and Sivers
time-reversal odd (T-odd) Sivers function, f 1T
1
T-odd functions in Eq. 1-4 are first moments of corresponding transverse momentum
dependent functions [20, 23]. Eq. 3,4[20, 24, 25] correspond to twist-3 contributions,
and may be related to observed SSA at HERMES [3] with polarized target and at CLAS
[6] with polarized beam.
Distribution and fragmentation functions responsible for non zero beam SSA in SIDIS
(Eq.4) identified by Levelt and Mulders [25], include the twist-3 unpolarized distribution
function ex introduced by Jaffe and Ji [22] and the Collins function [21]. Contributions
to beam SSA were also predicted to arise from the absorbtive part of the one-loop
corrections to the γ q qg and γ g qq̄ [26].
Important issues at low beam energies are the separation of current and target fragmentation regions and the presence of factorization when the fragmentation functions
depend only on the fractional energy, z. At low beam energies in DIS the current fragmentation region (CFR) is contaminated with events coming from the target fragmentation region (TFR). At low beam energies and low z a significant overlap is expected of
current and target fragmentation regions [27]. A quantitative estimate is available from
LUND Monte-Carlo (MC)[28]. The LUND model was successfully used by different
experimental groups for different processes and in a wide energy range. A very good
agreement of kinematic distributions measured at CLAS and LUND simulation was
shown to take place at energies as low as 4.3 GeV. All this is making the LUND-MC a
major tool in SIDIS studies. The relative yield of current fragmentation events extracted
from LUND-MC for different beam energies (see. Fig. 1) shows no significant dependence of the CFR fraction on the beam energy in range 05 z 08. In addition, we
find that in that z-range kinematic distributions of final state electrons and pions at CLAS
435
CFR/(CFR+TFR)
1
0.9
0.8
e p → e' π X
+
27.5GeV
12.0GeV
5.7GeV
4.3GeV
0.7
0.6
0.5
0.4
0.3
0.4
0.5
0.6
0.7
0.8
0.9
z
Counts
FIGURE 1. The separation of CFR with 05 z 08 is not changing significantly with beam energy.
10
4
10
3
0.2 > x > 0.1
0.3 > x > 0.2
0.4 > x > 0.3
0.5
0.6
0.7
0.8
N(z) ratio
z
1.2
1.1
1
0.9
0.8
ep→e'π+X (Ee=5.759GeV, MX > 1.1)
N(0.3 > x > 0.2)/ N(0.4 > x > 0.3)
N(0.2 > x > 0.1)/ N(0.4 > x > 0.3)
0.5
0.6
0.7
0.8
z
FIGURE 2. z-distributions of pions in ep
(bottom plot) for CLAS E1 data at 6 GeV.
e π X for different bins in x (top plot) and their ratios
¼
are in good agreement with the LUND-MC even though the LUND MC was developed
and tuned at much higher beam energies.
Factorization in the z-distributions of pions was studied using the 6 GeV data from
the CLAS E1 experiment. Distributions of pions in z, for different x bins, are shown in
Fig. 2. No significant dependence (10%) within statistical uncertainties was observed
in the z-distributions for different values of x (bottom plot in Fig.2).
SSA were measured in single pion production scattering of longitudinally polarized
electrons off unpolarized liquid-hydrogen and polarized NH3 targets. The total number
of π events in the DIS range (Q2 1 GeV2 ,W 2 4 GeV2 ) selected by quality, vertex,
acceptance, fiducial, and kinematic cuts was 4 105 and 27 106 respectively. The
φ -dependent spin asymmetries are formed by extracting moments of the cross section
436
for the two helicity states weighted by the corresponding φ -dependent functions. The
sin φ moment is thus given by:
φ
Asin
LU UL
2 N
sin φi P N i∑
1
(5)
where N and P are the number of events and the luminosity weighted polarization
for positive/negative helicities of the electron and proton, respectively. The azimuthal
moment Asin φ can be computed for each polarization state, and the comparison of
LU UL
two results provides a strong test of systematics. The sin φ azimuthal moment of the
cross section , unlike the cos φ azimuthal moment, typically is not affected significantly
by the detector acceptance and is practically an “acceptance free” observable. The
sum of all contributions to the systematic uncertainties including the acceptance, beam
polarization, particle mis-identification and radiative corrections is limited to 20% of the
value of the measured asymmetry in all kinematic ranges (Fig. 3).
0.1
0.08
0.5
e p → e' π X( MX > 1.1)
+
e p → e' π X
+
0.4
CLAS PRELIMINARY
0.3
0.04
UL
sinφ
0.2
A
LU
A
sinφ
0.06
0.1
0
0.02
HERMES π+
HERMES π0
+
CLAS π (eg1a-4.3GeV)
-0.1
0
-0.02
0.4
-0.2
-0.3
0.5
0.6
z
0.7
0.8
CLAS π (eg1b-5.7GeV)
+
0.2
0.4
0.6
0.8
1
z
FIGURE 3. The left panel shows the beam-spin azimuthal asymmetry (sin φ moment of the cross
section) extracted from hydrogen data at 4.3GeV as a function of z in a range 015 x 04. The band
represents the systematic uncertainties. The right panel shows the comparison of target SSA from CLAS
4.3 GeV and HERMES data. The squares show the projected error bars expected from the CLAS 5.7GeV
running with NH 3 target. The dashed line shows the z-shape of the fit to Collins function H 1uπ z from
HERMES ALU .
sin φ ) analyzed in terms of the fragmentation effect (Eq. 3),
While the target SSA (AUL
in addition to a contribution from the Collins function, contains other contributions
[29, 30], the beam SSA, depends only on the convolution of ex and the Collins
fragmentation function [20, 25], making it a very attractive observable for extraction of
the z-shape of the Collins fragmentation function at large z, where the analyzing power
is large.
The z-dependence of the beam SSA for positive pions measured at CLAS (Fig. 3)
differs significantly from the shape of the z-dependence of the target SSA measured
by HERMES [3, 4]. Preliminary results on beam SSA presented by the HERMES
collaboration [31] and target SSA from CLAS (see Fig.3) confirm, that there is a
437
difference between z-shapes of beam and target SSA, rather than a difference between
measurements performed at different beam energies.
The x-dependence of beam SSA in SIDIS, analyzed in terms of the fragmentation
effect, is defined by the ratio of the twist-3 unpolarized distribution function ex and the
leading twist distribution function f 1 x. The first extraction of the twist-3 distribution
function from CLAS beam SSA data, assuming factorization, was reported recently by
Efremov et al.[32].
In conclusion, we have presented measurements of beam and target single-spin asymmetries at CLAS in single-pion electro-production off the unpolarized and longitudinally
polarized protons. Beam and target SSA measured at CLAS and HERMES are in good
agreement, suggesting there is no significant scale dependence for SSA observables.
Higher statistics in the DIS range of ongoing experiments with CLAS at 6 GeV using
unpolarized hydrogen and deuteron targets, as well as polarized NH 3 and ND3 targets
(3 billion triggers accumulated so far) will enable the extraction of the important Q 2
dependence at fixed x for different final state particles.
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