Azimuthal Asymmetries in Fragmentation
Processes at KEKB
Kazumi Hasuko † , Matthias Grosse Perdekamp , Akio Ogawa , Jens
Soeren Lange ‡ and Viktor Siegle
RIKEN BNL Research Center, Upton, NY 11973-5000, USA
†
RIKEN, Wako, Saitama 351-0198, Japan
Brookhaven National Laboratory, Upton, NY 11973-5000, USA
‡
University of Frankfurt, Frankfurt 60486, Germany
Abstract. In unpolarized electron-positron annihilation, there may exist interesting and possibly
non-zero azimuthal asymmetries, which measure novel chiral-odd fragmentation functions, such
as the Collins-Heppelmann function, H 1 , and the two-pion interference fragmentation function,
δ q̂h . We will present the experimental method to extract these functions using e e collision data
from the Belle experiment at KEK B-factory (KEKB). In addition to the considerable interest in the
properties of these new fragmentation functions, they are expected to be a powerful tool in accessing
proton quark transversity distributions.
INTRODUCTION
The study of spin effects in high-energy interactions provides sensitive tests for models
of strong interaction dynamics. Recently much attention has been paid to transverse spin
phenomena. In this paper we discuss future measurements of two of the relevant objects,
the chiral-odd fragmentation functions describing the fragmentation of transversely
polarized quarks into one or two charged pions. Chiral-odd fragmentation functions may
arise from the non-perturbative dynamic in the fragmentation process and have been the
subject of extensive theoretical discussion. However, experimentally these functions are
presently unknown.
Collins et al. pointed out that there exists a non-trivial azimuthal angle asymmetry in
the fragmentation of transversely polarized quarks into single pions [1]. In unpolarized
electron-positron annihilations these fragmentation functions can be accessed through
the observation of azimuthal asymmetries that are proportional to the product of chiralodd fragmentation functions. In the following we discuss the experimental method
employed to extract the Collins-Heppelmann and interference fragmentation functions
from e e collisions at Belle.
While there is substantial interest in the symmetry properties of these new fragmentation functions, they are also a useful tool to access proton quark transversity distributions, δ q, in semi inclusive deep inelastic lepton scattering (SIDIS) experiments
(HERMES at DESY and COMPASS at CERN) and polarized proton-proton scattering experiments (STAR and PHENIX at BNL, RAMPEX at Protvino). At leading twist
transversity distributions remain the last unknown quark distribution functions and their
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
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knowledge is essential for a complete understanding of nucleon structure. Presently it
is thought that transverse single spin asymmetries A T in SIDIS and pp scattering offer the most practical way to measure transversity distributions. This possibility relies
on the presence of the spin-dependent quark fragmentation functions (FF) which we
intend to extract from Belle data. The experimental asymmetries A T are proportional
to ∑q δ q aif FF, where aif are the transversity dependent partonic initial-final-state
asymmetries which can be calculated from pQCD.
The analyzing power in this process arises from the spin dependence of the partonic
cross section as well as from the spin dependence of the fragmentation process: Collins
suggested that the quark spin direction might be reflected in the azimuthal distribution
of a final state pion [1]. Collins further demonstrated that the symmetry properties of the
process do not require the proposed FF to be identical to zero.
Recent result from HERMES [2] and SMC [3] in fact seem to suggest that these FF
and δ q are different from 0.
SPIN-DEPENDENT FRAGMENTATION FUNCTIONS
We intend to study the following spin-dependent quark fragmentations in e e annihilation:
The Collins-Heppelmann function H1 describes the fragmentation of a transversely
polarized quark into a charged pion and the azimuthal distribution of the final state
pion with respect to the initial quark momentum (jet-axis).
• Interference fragmentation functions δ q̂h1 h2 parameterize the fragmentation of
transversely polarized quarks into pairs of hadrons including interference between
different partial wave amplitudes; e.g. π π pairs in the ρ -σ invariant mass region.
•
BELLE EXPERIMENT
The spin-dependent fragmentation functions discussed above can be extracted from the
data taken by the Belle detector at KEKB. KEKB is an asymmetric storage ring that
collides 8 GeV electrons against 3.5 GeV positrons [4]. The experimental data are
recorded at the ϒ(4S) resonance and in the continuum 60 MeV below the resonance,
corresponding to integrated luminosities of more than 100 f b 1 on resonance and 10%
of this off-resonance.
The Belle detector is a general purpose, spectrometer based on a 1.5 T superconducting solenoid magnet. Charged particles are reconstructed with a three-layer double-sided
silicon vertex detector (SVD) and a central drift chamber (CDC) that consists of 50-layer
segmented into 6 axial and 5 stereo super-layers. The CDC covers the polar angle range
between 17Æ and 150Æ in the laboratory frame, which corresponds to 92% of the full
solid angle in the center of mass frame. Together with the SVD, a transverse momentum
resolution of σ pt pt 2 00019pt 2 000302 is achieved, where pt is in GeV/c.
Particle identification (PID) for charged hadrons is provided by a combination of
three sub-system devices: a sub-system of 1188 aerogel Čerenkov counters (ACC)
455
e+
π-
jet1
φ2 π+
e+
φ1
πjet2 jet1
φ2
e-
π-
π+
e- π+
KH004V02
(a)
φ1
jet2
KH005V01
(b)
FIGURE 1. Kinematics of e e π jet1 π jet2 X (a) and e e π π jet1 π π jet2 X (b)
covering the momentum range 1-3.5 GeV/c, a time-of-flight scintillation counter subsystem (TOF) for track momenta below 1.5 GeV/c, and dE dx information from the
CDC for particles with very low or high momenta. Information from these three devices
is combined to give the likelihood of a particle being a kaon, L K , or pion, Lπ . Kaonpion separation is then accomplished based on the likelihood ratio L π Lπ LK . The
pion identification efficiencies are measured using a high momentum D data samples,
where D D0 π and D0 K π . With this pion selection criterion, the typical
efficiency for identifying pions in the momentum region 0.5 GeV/c < p < 4 GeV/c
is (88.50.1)%. By comparing the D data sample with a Monte Carlo sample, the
systematic error in the PID is estimated to be 1.4% for the mode with three charged
tracks and 0.9% for the modes with two [5].
Surrounding the charged PID devices, a Cs(Tl) electromagnetic calorimeter and
muon/KL detector using iron plates interleaved with resistive plate counters are
equipped. A detailed description of the Belle detector can be found elsewhere [6].
ANALYSIS METHOD AND SENSITIVITY
The Collins-Heppelmann function H1 can be obtained from e e collisions using the
recipe introduced in reference [7]: First identify a sample of two-jet events from light
quark production. In each event, two unlike-sign pion tracks are selected, one in each
event hemisphere. The fundamental observable is the angle between the two “pionplanes” formed by the pion momentum vectors and the jet axis. The pion planes include
the angles φ1 and φ2 with the event plane defined by the beam axis and jet axis. The
definition of the angles is shown in Figure 1-(a). The measured angular dependence
in the angle φ1 φ2 is then proportional to the product of the Collins-Heppelmann
fragmentation function on each side taken at their respective fractional pion energy z 1
and z2 : Aφ1 φ2 H1 z1 H1 z2 .
We use a model by Jaffe et al. [8] in order to discuss some of the properties of the
interference fragmentation function δ q̂ This fragmentation function describes quark
fragmentation into two pions in a state which is a linear superposition of s-wave and
p-wave states. These two partial waves are active in the ρ -region. The effect is an s-p
interference and the fragmentation function peaks just above and below the ρ resonance
and is changing it’s sign across the ρ . This sign change should help to identify the
fragmentation function and discriminate against possible systematic effects.
In extracting the interference fragmentation function we follow the recipe provided
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15000
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5000
2500
0
-1
-0.8
-0.6
-0.4
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0.2
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FIGURE 2. The distribution of the angle between two unlike-sign charged hadron tracks for data
(triangle) and MC (histogram)
0.25
0.2
0.15
0.1
0.05
0
0
0.25
0.5
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[radian]
FIGURE 3. The distribution of the angle between thrust axis and q (q̄) direction
by Atru and Collins [9]: In a sample of two-jet events, for each event π π pairs are
identified in each hemisphere of the event and the angle between the planes formed
by the two pion pairs is measured. The distribution in this angle is the product of
twice the interference fragmentation function evaluated at the invariant masses of the
two pion pairs m12 , m34 and z1234 , the longitudinal momentum fractions of the pairs.
The kinematics is shown in Figure 1-(b). Schematically, the angular distribution is
proportional to f z12 m12 Q2 f z34 m34 Q2 .
Figure 2 shows the distribution of the angle between two unlike-sign hadron tracks
for Belle continuum data and Monte Carlo generated data [10]. The distribution clearly
displays jet-like correlations with peaks for the near side and away side jets. The jet
axis can be measured by using the thrust axis. The difference between the reconstructed
thrust axis and the initial q (q̄) direction in MC is shown in Figure 3. Three- or more-jet
events are rejected by applying a thrust cut of T 08.
The essential experimental requirements for fragmentation function measurements
with Belle lie in the ability to identify and to precisely measure the momenta and charge
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sign of pions. The momentum resolution must be high enough to reconstruct the ππ
mass to about 100MeV. This will permit a verification of the invariant mass dependence
of the fragmentation function in the ρ mass region. These requirements are easily within
the reach of the Belle detector [6, 11] which has been designed to meet the challenging
demands of B-physics.
The high luminosities at KEKB and Belle’s superior particle identification will allow
fragmentation function measurements over a large range in z E h Eq and for different combinations of final state hadrons. The relevant fragmentation functions scale as
log Q2 . Subsequently analyzing powers at Belle are expected to be four times larger than
for measurements using LEP data. Taking into account the larger luminosity at KEKB,
the sensitivity ∆H1 H1 will be higher by a factor 20 at Belle compared to LEP (this
assumes that off-resonance and resonance data can be used).
CONCLUSION
The existence of spin-dependence in fragmentation processes would be interesting and
a powerful tool for the study of transverse nucleon quark spin structure. A recent
discussion of the prospects of future programs to access nucleon transversity using
fragmentation function information from Belle can be found in reference [12].
The high luminosities at the KEK B-factory and the excellent momentum resolution
and particle identification capabilities of the detector make Belle an ideal place for
measurements of spin-dependent fragmentation functions.
REFERENCES
1.
Collins, J.C., Nucl. Phys. B396, 161 (1993); Collins, J.C., Heppelmann, S.F., and Ladinsky, G., Nucl.
Phys. B420, 563 (1994).
2. Airapetian, A. et al., Phys. Rev. Lett. 84, 4047 (2000).
3. Bravar, A., Nucl. Phys. (Proc. Suppl.) B79, 520 (1999).
4. KEK B Factory Design Report No. 95-7, 1995 (unpublished).
5. Iijima, T. et al., Nucl. Instrum. Meth. A379, 457-459 (1996).
6. Belle Collaboration, Mori, S. et al., Nucl. Instrum. Meth. A479, 117-232 (2002).
7. Boer, D., Jakob, R., and Mulders, P.J., Phys. Lett. B424, 143-151 (1998).
8. Jaffe, R.L., Jin, X., Tang, J. et al., Phys. Rev. Lett. 80, 1166 (1998);
9. Artru, X., and Collins, J., Z. Phys. C69, 277(1996).
10. These MC events are generated with the CLEO group’s QQ program;
see http://www.lns.cornell.edu/public/CLEO/soft/QQ;
The detector response is simulated using GEANT, R. Brun et al., GEANT 3.21, CERN Report
DD/EE/84-1 (1984).
11. Belle Collaboration, Gordon, A. et al., Phys. Lett. B542, 183-192 (2002).
12. Boer, D., “Transversity Single Spin Asymmetries” in 9th International Workshop on Deep Inelastic
Scattering (DIS 2001), edited by G. Bruni et al., World Scientific, 2001.
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