Light quark and spin dependent fragmentation function measurements at Belle

1
Light quark and spin dependent fragmentation
function measurements at Belle

• D G workshop,
• UIUC, June 17, 2008
• M. Grosse Perdekamp
• (University of Illinois)
• M. Leitgab (University of Illinois)
• A. Ogawa (BNL/RBRC)
• R. Seidl (RBRC)
• representing the Belle collaboration

• Outline
• The Belle detector
• unpolarized fragmentation function measurements
• Understanding the systematics for precision
  measurements at high z
• Expected precision
• The Collins function measurements
• Access to transversity over Collins fragmentation
  function
• Collins function measurements at Belle
• Interference fragmentation function measurements

2
KEKB Lgt1.7x1034cm-2s-1 !!

• Asymmetric collider
• 8GeV e- 3.5GeV e
• vs 10.58GeV (U(4S))
• ee-?U(4S)?B?B
• Continuum production
• 10.52 GeV
• ee-?q?q (u,d,s,c)
• Integrated Luminosity gt700 fb-1
• gt60fb-1 gt continuum

3
Belle Detector
Aerogel Cherenkov cnt.
n1.0151.030
SC solenoid 1.5T
3.5 GeV e
CsI(Tl) 16X0
TOF conter
8 GeV e-
Central Drift Chamber small cell He/C2H6
Good tracking and particle identification! e(K)85
, e(p?K)lt10
m / KL detection 14/15 lyr. RPCFe
Si vtx. det. 3/4 lyr. DSSD
4
Single hadron cross section
e-

• Process
• e e-?hX
• At leading order sum of unpolarized
  fragmentation functions from quark and anti-quark
  side

h
e
5
World data and motivation for precise FFs

• Most data obtained at LEP energies,
• At lower CMS energies very little data available
• 3-jet fragmentation to access gluon FF
  theoretically difficult
• Gluon fragmentation from evolution not yet well
  constrained
• Higher z FFs (gt0.7) hardly available

6
Systematic studies Particle identification

• Particle identification
• create PID efficiency matrix for K,p,p,e,m
• PID responses from MC not reliable, use well
  identified decays from data
• Use D?pslow D0?pslowpfastK for K,p
  identification
• Use L ?pp for p,p identification
• ? Unfolding

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D analysis

• Measure signal Ni and yield contributions in Fit
  of
• Dm(D-m(K,pfast)) distribution to obtain real K,
  p yields
• Repeat Fits for particular particle likelihood
  selection to obtain Ni?j
• Ratio of signals gives efficiency

8
L analysis, leptons

• Similarly calculate efficiencies from
• m(Pp) distribution
• Most kinematic
• regions well covered
• So far lepton efficiencies from MC,
• in the future extract efficiencies form J/y
  decays
• Perform inversion of efficiency matrix, keep
  stable inverse matrices

9
Acceptance correction, status

• Correction from MC for missing acceptance in
  forward/backward regions and empty PID matrix
  elements in (qLab,pLab)
• Status
• p and K FFs in intermediate z-region close to
  being able to be released
• P and higher z (gt0.75) data need more studies
  (PID efficiency matrix)

p
K
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Further FF measurements

• Additional FF measurements planned
• p0 ( cross check with completely different
  systematics)
• h (PHENIX ALL measurement available, higher
  strange content??)
• Other decaying particles
• (KS,f0,?)
• kt dependent FFs

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Event Structure for Hadron pairs
ee- CMS frame
Near-side Hemisphere hi , i1,Nn with zi

e-
ltNh,-gt 6.4
Q
e
Spin averaged cross section
Far-side hj , j1,Nf with zj
Jet axis Thrust
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Unpolarized 2-hadron fragmentation
Favored u?p,d?p-,cc. Unfavored d?p,u?p-,cc.

• Detect two hadrons simultaneously
• If two hadrons in opposite hemispheres one
  obtains sensitivity to favored/disfavored
  fragmentation

• Problems
• Either need to ensure two-jet topology (thrust
  cut)
• Or contribution from one quark fragmentation q?hhX

• Unlike-sign pion pairs (U)
• (favored x favored unfavored x unfavored)
• Like-sign pion pairs (L)
• (favored x unfavored unfavored x favored)
• pp0 or any charge hadron pairs (C)
• (favored unfavored) x (favored unfavored)

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Collins fragmentation in ee- Angles and Cross
section cos(f1f2) method
ee- CMS frame
j2-p
e-
Q
j1
j2
j1
D.Boer PhD thesis(1998)
e
2-hadron inclusive transverse momentum dependent
cross section
Net (anti-)alignment of transverse quark spins
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Examples of fits to azimuthal asymmetries

• Cosine modulations
• clearly visible
• P1 contains information on Collins function

N(f)/N0
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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What about the data under the resonance?

• More than 540 fb-1 of on_resonance data
• U(4S) is just small resonance
• More than 75 of hadronic cross section
• from open quark-antiquark production

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Why is it possible to include on_resonance data?
Different Thrust distributions
ee-?qq, q?uds
ee-?cc

• e e- ? q ?q (u d s) MC
• U(4S) ?B B- MC
• U(4S) ?B0 ?B0 MC

• Charm-tagged Data sample (used
• for charm correction) also increases
• with statistics
• Largest systematic errors reduce with
• more statistics

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Improved systematic errors (UC)

• Tau contribution (not shown)
• Quark axis correction
• PID systematics
• MC uncertainties
• Charged ratios (pp /p-p- )
• higher moments in Fit (not shown)
• difference double ratio-subtraction method

• Beam polarization studies
• ?consistent with zero
• Correction for charm events

19
Final Collins results

• Belle 547 fb-1 data set (submitted to PRD
  arXiv0805.2975)

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Towards a global transversity analysis
SIDIS experiments (HERMES and COMPASS, eRHIC)
measure dq(x) together with either Collins
Fragmentation function or
Interference Fragmentation function
There are always 2 unknown functions involved
which cannot be measured independently
RHIC measures the same combinations of quark
Distribution (DF) and Fragmentation Functions
(FF) plus unpolarized DF q(x)

• Universality understood
• Evolution ?

Spin dependent Fragmentation function analysis
in ee- Annihilation yields information on the
Collins and the Interference Fragmentation
function !
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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,RadiciPRD 67,(2003) and
  Artru,CollinsZPhysC69(1996)
• Early work by Collins, Heppelmann, Ladinsky
  NPB420(1994)

j2-p
p-j1

• Model predictions by
• Jaffe et al. PRL 80,(1998)
• Radici et al. PRD 65,(2002)

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Interference Fragmentation f0 method
jR2

• Similar to previous method
• Observe angles j1Rj2R
• between the event-plane (beam, two-pion-axis)
  and the two two-pion planes.
• Theoretical guidance by Boer, Jakob, Radici

p-jR1
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Summary and outlook

• Continue to measure precise spin dependent
  fragmentation functions at Belle
• kT dependence of Collins function
• Artru model test with Vector meson Collins
• Interference Fragmentation function measurements
  (started)
• Measure other interesting QCD-related quantities
  at Belle
• Chiral-odd L-fragmentation function
• L single spin asymmetry
• Event shapes
• R-ratio with ISR

• Measure precise unpolarized fragmentation
  functions of many final states
• ? Important input for general QCD physics and
  helicity structure measurements
• Analysis progressing
• PID studies
• Acceptance correction
• Belle Collins data largely improved from 29 ? 547
  fb -1
• Significant, nonzero asymmetries ? Collins
  function is large
• Long Collins paper submitted

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Backup Slides
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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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Interference Fragmentation f0 method

• Similar to previous method
• Observe angles j1Rj2R
• between the event-plane (beam,
  two-pion-axis) and the two two-pion planes.
• Theoretical guidance by Boer,Jakob,Radici

jR2
p-jR1
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Applied cuts, binning

• Hemisphere cut
• QT lt 3.5 GeV

• Off-resonance data
• 60 MeV below U(4S) resonance
• 29.1 fb-1
• ? Later also on-resonance data 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

z1
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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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What would we see in ee-?

• Simply modeled the shapes of these predictions in
  an equidistant Mass1 x Mass2 binning

m2pp
m2pp
m1pp
m1pp
Jaffe
Radici