1. Belle Fragmentation activity
RIKEN/RBRC
Illinois
Indiana
Titech
Unpol FFs
e+e-hX,
e+e-(hh)X,
(h)(h)X,hhX
Unpol kT dependence
Neutral hadrons: (p0 ,h0)
John Koster
Charged di-hadrons: Ralf Seidl
Charged hadrons (p,K,P):
Martin Leitgab
Collins FFs
e+e-(h)(h)X
kT dependence
pp0 : John Koster
pr0: Ralf Seidl
pp: Ralf Seidl
pK,KK: new Postdoc?
New postdoc?
pr±: ?
Interference FF:
e+e-(hh)(hh)X
Charged pp : Ralf Seidl
Charged pp: Anselm Vossen
pp0 : Anselm Vossen
Charged pK,
KK:
Nori-aki Kobayashi
Local P :
(polFF,SSA) :
Jet-jet asy:
Anselm Vossen
Black: about to start
Green: ongoing
Grey: finished

2. Backup Slides TMD2010,Trento
R.Seidl: fragmentation functions from Belle

3. Universality understood
Towards a global transversity analysis: Chiral –odd Fragmentation functions
RHIC and SIDIS experiments measure:
Transversity dq(x) X
Collins Fragmentation function
or Interference Fragmentation function (IFF)
2 Unknown Functions measured together
Universality understood
Evolution ?
Transversity
Belle measures:
Collins X Collins - finished for charged pion pairs
or IFF X IFF – charged pions about to be published
TMD2010,Trento
R.Seidl: fragmentation functions from Belle

4. 2-hadron inclusive transverse momentum dependent cross section:
Collins fragmentation in e+e- : Angles and Cross section cos(f1+f2) method
e+e- 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
TMD2010,Trento
R.Seidl: fragmentation functions from Belle

5. Final Collins results First direct measurement of the Collins effect:
(PRL96: )
Nonzero asymmetries
Belle 547 fb-1 data set
(PRD78:032011)
TMD2010,Trento
R.Seidl: fragmentation functions from Belle

6. First global analysis from Collins Hermes, Compass d and Belle data
Phys.Rev.D75:054032,2007,
update in Nucl.Phys.Proc.Suppl.1
91:98-107,2009
First results available, still open questions from evolution of Collins FF and transverse momentum dependence
TMD2010,Trento
R.Seidl: fragmentation functions from Belle

7. 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[PRD 67,(2003)] and Artru,Collins[ZPhysC69(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)]
R.Seidl: fragmentation functions from Belle
TMD2010,Trento

8. Results for 9x9 z1 z2 binning
Preliminary
Preliminary
Preliminary
Preliminary
Preliminary
Preliminary
Preliminary
Preliminary
Preliminary
TMD2010,Trento
R.Seidl: fragmentation functions from Belle

9. Martin Leitgab’s Spin 2010 talk
TMD2010,Trento
R.Seidl: fragmentation functions from Belle

10. Event Structure for hadron pairs in e+e- annihilation
e+e- CMS frame: e-
<Nh+,-> = 6.4 Q e+
Spin averaged cross section:
Jet axis: Thrust
TMD2010,Trento
R.Seidl: fragmentation functions from Belle

11. Unpolarized 2-hadron fragmentation
Favored = up+,dp-,cc.
Unfavored = dp+,up-,cc.
Detect two hadrons simultaneously:
e+e-hhX
If two hadrons in opposite hemispheres one obtains sensitivity to favored/ disfavored fragmentation:
Difficulty: contribution from one quark fragmentation qhhX
measure all three:
(hh)jet1 X
(h) jet1(h) jet2X
hhX,
( ) requires
thrust cut
Unlike-sign pion pairs (U):
(favored x favored + unfavored x unfavored)
Like-sign pion pairs (L):
(favored x unfavored + unfavored x favored)
any charge hadron pairs (C):
(favored + unfavored) x (favored + unfavored)
TMD2010,Trento
R.Seidl: fragmentation functions from Belle