Spin%20dependent%20fragmentation%20function%20analysis%20at%20Belle

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Spin dependent fragmentation function analysis at
Belle
Spin 2006 October 5,??,??

• M. Grosse Perdekamp
• (University of Illinois and RBRC)
• A. Ogawa (BNL/RBRC)
• R. Seidl (University of Illinois and RBRC)

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KEKB Lgt1.6x1034cm-2s-1 !!

• Asymmetric collider
• 8GeV e- 3.5GeV e
• Ös 10.58GeV (U(4S))
• ee-?U(4S)?B?B
• Off-resonance 10.52 GeV
• ee-?q?q (u,d,s,c)
• Integrated Luminosity gt600 fb-1
• gt60fb-1 gt off-resonance

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Good tracking and particle identification!
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Collins fragmentation in ee- Angles and Cross
section cos(f1f2) method
ee- 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
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Collins fragmentation in ee- Angles and Cross
section cos(2f0) method
ee- 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
Net (anti-)alignment of transverse quark spins
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Applied cuts, binning

• Hemisphere cut
• QT lt 3.5 GeV
• Pion PID selection

• Originally off_resonance data, now also
  on_resonance data (29.1 ? 547 fb-1)
• Track selection
• pT gt 0.1GeV
• vertex cutdrlt2cm, dzlt4cm
• Acceptance cut
• -0.6 lt cosqi lt 0.9
• Event selection
• Ntrack ? 3
• Thrust gt 0.8
• Z1, Z2gt0.2

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Examples of fits to azimuthal asymmetries
N(f)/N0

• Cosine modulations
• clearly visible

2f0
(f1f2)
D1 spin averaged fragmentation function, H1
Collins fragmentation function
No change in cosine moments when including sine
and higher harmonics
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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)
Pros Gluon radiation cancels out exactly Cons
Acceptance effects remain
Subtraction method
2 methods give very small difference in the result
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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)
• pp0 pairs
• (favored unfavored) x (favored unfavored)
• P.Schweitzer(hep-ph/0603054) charged pp pairs
  are similar
• (and easier to handle) (C)
• (favored unfavored) x (favored unfavored)

UL
UC

• Build new double ratios
• Unlike-sign/ charged pp pairs (UC)

Favored u?p,d?p-,cc. Unfavored d?p,u?p-,cc.
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Why is it possible to include on_resonance
data?Different Thrust distributions
ee-?qq, q?uds
ee-?cc

• small B contribution (lt1) in high thrust sample
  
• gt75 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

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Improved Systematic errors (UC)

• Tau contributions
• PID systematics
• MC double ratios
• Charged ratios (pp /p-p- )
• Higher order terms
• Double ratio-subtraction method

A0 (cos(2f0)) moments
A12 (cos(f1 f2)) moments
Reweighting asymmetries ?underestimation of
cos(f1f2) asymmetries ?rescaled by
1.21 Correlation studies ?statistical errrors
rescaled by 1.02 (UL) and 0.55 (UC) Beam
polarization studies ?consistent with zero
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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

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Collins asymmetries II sin2 q/(1cos2 q)
binning (UL)

• Nonzero quark polarization sin2 q
• Unpolarized de-nominator 1cos2 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
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Interference Fragmentation thrust method

• ee-? (pp-)jet1(p-p)jet2X
• Stay in the mass region around r-mass
• Find pion pairs in opposite hemispheres
• Observe angles j1j2
• 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
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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, 4.5106 events 2.5 of off_resonance
data
2.
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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
  (PRL96232002,2006)

• 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)

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Backup Slides
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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

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Collins asymmetries IIa sin2 q/(1cos2 q)
binning (UC)

• Nozeron quark polarization sin2 q
• Unpolarized de-nominator 1cos2 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
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Collins asymmetries III QT binning (UL)

• Reduced asymmetries in low thrust sample
• At low thrust significant B contribution
• (for tlt0.8 20 B
• for tgt0.8 lt 1 B)
• A12 thrust axis dependent
• High QT (gt3.5 GeV) asymmetries from beam related
  BG
• UC plots similar

PRELIMINARY
Thrustgt0.8 Thrustlt0.8 (not corrected for heavy
quark contributions)
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Collins asymmetries IIIa QT binning (UC)

• Reduced asymmetries in low thrust sample
• At low thrust significant heavy quark
  contribution
• High QT (gt3.5 GeV) asymmetries from beam related
  BG
• similar behavior, but smaller magnitude as UL
  asymmetries

PRELIMINARY
Thrustgt0.8 Thrustlt0.8 (not corrected for heavy
quark contributions)
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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
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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

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B, charm and uds contributions in the data
thrustgt0.8
thrustlt0.8
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
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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