1. Spin dependent fragmentation function analysis at Belle
October 5,京都,日本
M. Grosse Perdekamp
(University of Illinois and RBRC)
A. Ogawa (BNL/RBRC)
R. Seidl (University of Illinois and RBRC)

2. Measurement of the Collins fragmentation function at BELLE
KEKB: L>1.6x1034cm-2s-1 !!
Asymmetric collider
8GeV e GeV e+
Ös = 10.58GeV (U(4S))
e+e-U(4S)BB
Off-resonance: GeV
e+e-qq (u,d,s,c)
Integrated Luminosity: >600 fb-1
>60fb-1 => off-resonance
Belle detector
KEKB
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

3. Good tracking and particle identification!
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

4. Collins fragmentation in e+e- : Angles and Cross section cos(f1+f2) method
e+e- CMS frame:
j2-p
thrustaxis e- Q j1 j2 j1
[D.Boer: PhD thesis(1998)] e+
2-hadron inclusive transverse momentum dependent cross section:
First |kT| moments of
Collins Function H1⊥
Net (anti-)alignment of
transverse quark spins
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

5. Collins fragmentation in e+e- : Angles and Cross section cos(2f0) method
e+e- CMS frame:
Independent of thrust-axis
Convolution integral I over transverse momenta involved e- Q2 j0
[Boer,Jakob,Mulders: NPB504(1997)345] e+
2-hadron inclusive transverse momentum dependent cross section:
Convolution integral erklaeren!
Net (anti-)alignment of
transverse quark spins
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

6. Measurement of the Collins fragmentation function at BELLE
Applied cuts, binning
Originally off_resonance data, now also on_resonance data (29.1  547 fb-1)
Track selection:
pT > 0.1GeV
vertex cut: dr<2cm, |dz|<4cm
Acceptance cut
-0.6 < cosqi < 0.9
Event selection:
Ntrack  3
Thrust > 0.8
Z1, Z2>0.2
Hemisphere cut
QT < 3.5 GeV
Pion PID selection
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

7. Examples of fits to azimuthal asymmetries
N(f)/N0
Cosine modulations
clearly visible
2f0
(f1+f2)
Radiativen Term schon einfuehren, proportional zu 1
D1 : spin averaged fragmentation function,
H1: Collins fragmentation function
No change in cosine moments when
including sine and higher harmonics
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

8. Measurement of the Collins fragmentation function at BELLE
Methods to eliminate gluon contributions: Double ratios and subtractions
Double ratio method:
Pros: Acceptance cancels out
Cons: Works only if effects are small (both gluon radiation and signal)
Subtraction method:
Pros: Gluon radiation cancels out exactly
Cons: Acceptance effects remain
2 methods give very small difference in the result
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

9. Other Favored/Unfavored Combinations charged pions or p0
Challenge: current double ratios not very sensitive to favored to disfavored Collins function ratio  Examine other combinations:
Unlike-sign pion pairs (U):
(favored x favored + unfavored x unfavored)
Like-sign pion pairs (L):
(favored x unfavored + unfavored x favored)
p±p0 pairs
(favored + unfavored) x (favored + unfavored)
P.Schweitzer([hep-ph/ ]): charged pp pairs are similar
(and easier to handle) (C): UL UC
Build new double ratios:
Unlike-sign/ charged pp pairs (UC)
Favored = up+,dp-,cc.
Unfavored = dp+,up-,cc.
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

10. Measurement of the Collins fragmentation function at BELLE
Why is it possible to include on_resonance data? Different Thrust distributions
e+e-qq̅, q∈uds
e+e-cc̅
small B contribution (<1%) in high thrust sample
>75% of X-section continuum under
U (4S) resonance
29 fb-1  547 fb-1
many systematic errors reduce with more
statistics
Charm-tagged Data sample also increases
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

11. Improved Systematic errors (UC)
Tau contributions
PID systematics*
MC double ratios
Charged ratios (p+p+ /p-p- )
Higher order terms
Double ratio-subtraction method
A0 (cos(2f0)) moments
A12 (cos(f1 + f2)) moments
Reweighting asymmetries: underestimation of cos(f1+f2) asymmetries rescaled by 1.21
Correlation studies:
statistical errrors rescaled by 1.02 (UL) and 0.55 (UC)
Beam polarization studies
consistent with zero
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

12. Collins asymmetries I: 4x4 z1, z2 binning
A0 (cos(2f0)) moments
A12 (cos(f1 + f2)) moments
PRELIMINARY
PRELIMINARY
547 fb-1 charm corrected data sample,
UL and UC double ratios
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

13. Collins asymmetries II: sin2 q/(1+cos2 q) binning (UL)
Nonzero quark polarization ~ sin2 q
Unpolarized de-nominator ~ 1+cos2 q
Clear linear behavior seen when using either thrustz or 2nd hadron as polar angle
Better agreement for thrust axis (~approximate quark axis)
UC plots similar
PRELIMINARY
thrustz q2
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

14. Interference Fragmentation – thrust method
e+e- (p+p-)jet1(p-p+)jet2X
Stay in the mass region around r-mass
Find pion pairs in opposite hemispheres
Observe angles j1+j2
between the event-plane (beam, jet-axis) and the two two-pion planes.
Transverse momentum is integrated
(universal function, evolution easy
 directly applicable to
semi-inclusive DIS and pp)
Theoretical guidance by papers of Boer,Jakob,Radici and Artru,Collins
Early work by Collins, Heppelman, Ladinski
j2-p
p-j1
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

15. Measurement of the Collins fragmentation function at BELLE
Unpolarized FFs
Performed Systematic studies:
Smearing
Tracking efficiency
Acceptance
Energy scale
Particle ID study not yet finished
AKK: Try flavor tagged/enhanced analysis?
How about 2 hadron analysis
 favored,disfavored FF
MC simulation, ~1.4 fb-1
1.4 fb-1, 4.5·106 events
2.5 % of off_resonance data 2.
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

16. Measurement of the Collins fragmentation function at BELLE
Summary and outlook
Double ratios:
double ratios from data
most systematic errors cancel
Analysis procedure passes all null tests
Systematic uncertainties understood
Statistics increased from 29  547 fb-1
 Significant nonzero asymmetry with double ratios are observed
UL/C about half as large UL/L double ratios
Data can be used for more sophisticated analysis
Paper with 29 fb-1 U/L double ratios published (PRL96:232002,2006)
Analysis almost finalized,
smalller additions planned
(kt dependence of Collins effect, parameterizations)
Interference fragmentation function analysis started
Many more QCD/Spin related studies possible (unpol FFs, timelike DVCS, L Polarimetry)
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

17. Measurement of the Collins fragmentation function at BELLE
Backup Slides
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

18. Why correction factors of 1.2 and 0.55?
Charged pion pairs are the sum of U and L
Errors are correlated when building double ratios UC or LC
Division of histograms takes correlation not into account
Proper error calculation confirms correction factors found in correlation studies and c2 distributions
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

19. Collins asymmetries IIa: sin2 q/(1+cos2 q) binning (UC)
Nozeron quark polarization ~ sin2 q
Unpolarized de-nominator ~ 1+cos2 q
Clear linear behavior seen when using either thrustz or 2nd hadron as polar angle
Better agreement for thrust axis (~approximate quark axis)
Similar behavior, smaller magnitude as UL asymmetries
PRELIMINARY
thrustz q2
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

20. Collins asymmetries III: QT binning (UL)
PRELIMINARY
Reduced asymmetries in low thrust sample
At low thrust significant B contribution
(for t<0.8 ~20 % B
for t>0.8 < 1 % B)
A12 thrust axis dependent
High QT (>3.5 GeV) asymmetries from beam related BG
UC plots similar
Thrust>0.8
Thrust<0.8 (not corrected for heavy quark contributions)
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

21. Collins asymmetries IIIa: QT binning (UC)
PRELIMINARY
Reduced asymmetries in low thrust sample
At low thrust significant heavy quark contribution
High QT (>3.5 GeV) asymmetries from beam related BG
similar behavior, but smaller magnitude as UL asymmetries
Thrust>0.8
Thrust<0.8 (not corrected for heavy quark contributions)
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

22. Measurement of the Collins fragmentation function at BELLE
Final charm corrected results for e+ e- p p X (29fb-1 of continuum data)
Significant non-zero asymmetries
Rising behavior vs. z
UL/C asymmetries about 40-50% of UL/L asymmetries
First direct measurements of the Collins function
UL/L data published
Final results
Preliminary results
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

23. Final charm corrected results for e+ e- p p X (547 fb-1)
Significance largely increased
Behavior unchanged
Reduced systematics
Precise measurements of the Collins function
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

24. B, charm and uds contributions in the data
thrust>0.8
thrust<0.8
uds quarks
charm quarks
Charged B-mesons
Netral B-mesons
Open symbols: charm enhanced data sample used for charm correction
Full symbols: main data sample
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE

25. Collins effect in quark fragmentation
J.C. Collins, Nucl. Phys. B396, 161(1993) q
Collins Effect:
Fragmentation with of a quark q with spin sq into a spinless
hadron h carries an
azimuthal dependence:
Spin2006, October 6th
Measurement of the Collins fragmentation function at BELLE