# Presentation: 030736

## Chiral odd fragmentation function

**At Belle**

_**Ogawa Akio**_
- Penn State Univ. / BNL / RBRC (STAR/Belle)
- Matthias Grosse Perdekamp
- BRBC (Phenix/Belle)
- Special thanks to
- Soeren Lange
- Frankfurt (Belle / STAR)

## -

- Helicity average

- Helicity difference

- RHIC,Compass,Hermes...

- Momentum

**Leading twist quark distribution**

- Transversity is the last missing piece
-                     at leading twist quark distribution

- Well measured at DIS,pp

- Well measured at pol. DIS

- Helicity flip

- DVCS?

## Nucleon Transversity at p  p

- F

*Jet*

*Jet*

- Proton
- Structure

- Hard Scattering
-              Process

- Interference
- Fragmentation

- Jian Tang , Thesis MIT, June 1999

- R. Jaffe, X.Jin, J. Tang Phys. Rev. D57 (1999)5920

- X. Ji, Phys. Rev. D49 (1994)114

- J. Collins, S. Heppelmann, G. Ladinsky, Nucl.Phys. B420 (1994)565

## Fragmentation Function(FF)

-      “Probability of a parton to hadronize into a specific final state”
- Factorization theorem  ensures  universality
- Collins FF & 2 pion interference FF
- 	Initial parton with transverse spin   -   chiral odd
- 	Azimuthal asymmetry in hadron final state
- 	Currently unknown
- 	Theoretical Interests : Q2 evolution is as fundamental as PDF
- 	Polarized DIS & pp experiment can measure FF*Transversity
- 	Unpolarized  e+e-  experiment can measure FF*FF

## HERMES result on azimuthal asymmetry  

- Non-zero
- transverse
- polarization!

- HERMES result on azimuthal asymmetry

- Results shows that
- both Collins Function and
- Transversity are non zero,
- and rather large

*l*

*p*

## “Complete” Measurements

- “Complete” Measurements

- BNL - Star/Phoenix/Phobos

- DESY-Hermes & CERN-Compass  (BNL eRHIC,  DESY Tesla-N)

- e+e- collider

## Collins Fragmentation Function : C

- Z = Eh / Eq
- angle between S and kT  around quark (jet) axis

- A =

- s

- q

- s

- kT

- h

- kT

- h

- q

- q

- s

- h

## 2 pion interference fragmentation function :

- Zpair = (E+ +E- ) / Eq
- m =  invariant mass of 2 pions
- angle between s and r

- s

- q

- q

- s

- A =

- r

- r

- q

- s

- The same thing for KK around 

## A model of Interference Fragmentation Function

- S- p wave interference around            mass

- Bin +

- Bin -

-  Non-vanishing
-      “Analyzing power” above and below
-        mass
- and flip sign
- Requires mass Resolution
-  Great for systematic study

- P. Estabrooks and A.D. Martin, Nucl. Phys. B79 (1974)301

**A model of Interference Fragmentation Function**

- Spin average, difference FF

## jet1

- jet2

- Without
-   using
-  jet axis

- Spin of quarks are
-   100% correlated!

- n

- n

- Gluon emission can
- cause same cos(2)
-    But calculable

## jet1

- jet2

- Spin of quarks
- are 100% correlated!

- n

- Gluon emission does NOT fake this asymmetry

## In  e+e-

- In  e+e-

- High enough energy to produce jet		                5GeV jets
- 		          to apply pQCD		              s~100GeV2
- But not too high energy
-       FF decreases as energy increases		    s(BF) << s(LEP)
- 			       Observing Q2 evolution is interesting
-       Extra complication from Z pole	                    √s(BF) < Mz
- Jet production from light quark		  Off resonance data
- 					         Exclude heavy flavors
- Requires good detector:
-    Wide acceptance			             86% of 4 Belle)
-    Momentum/mass resolution  Great, they even can do b physics
-    PID capability		  PID covers full momentum range
- Requires many events	            They are designed for high statistic

- At B factories

## Some basic numbersfrom PYTHIA:

- Eparton

- # of charged pion
-  in hadronic events
-  average ~ 6.5
- (for 4pi detector)

- d    s     b

- u    c

- e    

- u/d fragments
- s/c/b fragments

- E charged pion

- Simulation (pythia) at sqrt(s) = 10.52GeV gives:
-                      6.6 nb ( 30% ud, 23% sc, 2% b, 45% leptons)

## Z distributions

- Charged Hadrons for Collins

- Pairs for

- E ~ 5*Z

- All
- Pion    85%
- Kaon   10%
- Proton   5%

-  10K total / 5K hadronic Event ~ **Belle has 1000 times more data**
-  This is projection to one side :  asymmetry depends on average of “the other side”

- Unidentifed @ m=0.5-1GeV
- 2 Pion    @  m=0.5-1GeV
- 2 Kaon   @ m<1.1GeV

- 200

## Statistics estimate 

- CC	0-0.2	0.2-0.4   0.4-0.6  0.6-0.8   0.8-1.0  (z1)
- 0-0.2 	0.00031  0.00068  0.0014   0.0032   0.0072
- 0.2-0.4	0.00068  0.0015    0.0031   0.0070   0.016
- 0.4-0.6	0.0014    0.0030    0.0063   0.014     0.032
- 0.6-0.8	0.0032    0.0070    0.014     0.033     0.073
- 0.8-1.0	0.0072    0.016      0.032     0.073     0.16
- Cq
- 0-0.2 	0.0014   0.00063   0.0012    0.0027   0.0060
- 0.2-0.4 	0.0029   0.0014     0.0027    0.0058   0.013
- 0.4-0.6 	0.0061   0.0028     0.0055    0.012     0.027
- 0.6-0.8 	0.014     0.0064     0.013      0.027     0.062
- 0.8-1.0 	0.030     0.014       0.028      0.061     0.14
- qq
- 0-0.2 	0.0058   0.0027    0.0053   0.012      0.026
- 0.2-0.4 	0.0027   0.0013    0.0025   0.0053    0.012
- 0.4-0.6 	0.0053   0.0025    0.0048   0.010      0.024
- 0.6-0.8 	0.012     0.0053    0.010     0.023      0.051
- 0.8-1.0 	0.026     0.012      0.024     0.051      0.12
- (Z2)

- Estimate of
-   F*F) = /cos()
- For ~2.3/fb ~ 6M Events
-    Belle already have it
-    ~2 weeks of off resonance
-    data taking at Belle
- For example:
-    2pions + 2 pions
-  	4 C*C
-  	4 C*q
- 	1 q*q
- total 9 independent
-    measurements
-    in a event

## Belle off resonance data first look 

- for fragmentation function analysis
-     by J.S.Lange (Frankfurt)

- DST for a run
-    ~ 1 hour 40min, 7.6/pb, 23K events
-    ~5min for micro DST analysis

- Average ~5 charged pions / event

##     Some comments:

- Understanding jets production at sqrt(s) at ~10GeV
- Effects of heavy flavours and weak decay background
- Identified Pions, kaons & unidentified hadrons
- 	Study dilution of analyzing power due to lack of PID at STAR (PHENIX’s)
- Extracting FFs from
-                        with gluon emission effects subtraction in Collins
- Q2 evolution     LEP analysis on the same FF at different energy  (100GeV)
-     B factories ~ 10.5GeV
-     Other older & existing data   10 - 50GeV
- More “Off resonance” data expected, more data in “On resonance data”....

## Fragmented experiments and people:

- Belle      A small group of RHIC spinners joined Belle
- 		 Matthias G. Perdekamp (RBRC)
- 		 Ogawa Akio (Penn State Univ)
- 		 + ...
- 	Belle collaborators:
- 		Soeren Lange    (Frankfurt  - STAR & Belle)
- 		Bruce Yabsley  (Sidney / KEK - Belle)
- 	Theoretical aspects:
- 		Daniel Boer (RBRC / Free University)
- 		Robert Jaffe (MIT)
- Delphi		Oliver Passon   (Wuppertal Univ)
- 		Klaus Hamacher  (Wuppertal Univ)
- Opal                     Albert de Roeck  (CERN)
- Babar		?
- Cleo		???

## B factories : Belle, Babar, Cleo...

- Belle
- 	8GeV+3.5GeV
- 	1.3/fb/week
- Babar
- 	9GeV+3.1GeV
- 	~1/fb/week
- Cleo
- 	4.7GeV+5.6GeV
- 	~0.35/fb/week
- All have almost  hermetic
- collider detector with
- good PID

##                   Belle Data    Number provided by J.S.Lange(Frankfurt) 

- On-Resonance
-    10.58GeV
-    bb cross section = 1.19nb
-    ~32/fb on tape
-    ~240/pb/day
-    peak L = 4.44 1033/cm/cm/s
-            World Record!
-   design L = 10.0 1033/cm/cm/s
-     (Babar = 3.3 1033)

- Off-Resonance
-   10.52GeV
-   cross section = 3.08nb
-   Motivation : Background study
-   2.3/fb = 6.4 106 Events on tape
-   DST processing speed ~850/pb/day
-   Analysis ~50 events/sec on i686 450MHz

## Conclusion

-  Collins FF and Interference FF  are needed
-  to extract transversity from DIS/pp
-  to understand AN for inclusive pion productions
-  FF itself  is as fundamental as PDF
-  e+e- can measure these FF
- B factories are the places to measure it
- Luminosity, detector with PID, energy, etc
- Comparison with LEP data will be interesting
- Belle accepted RBRC group (Matthias & me & some more)
- RHIC Spinners will be on task