# Presentation: 849373

## Azimuthal asymmetries 

**in hadron production at e+e- collider **
**and **
**chiral odd fragmentation function**

_**Ogawa Akio**_     	    Penn State Univ. / BNL (STAR)
- Daniel Boer      	    Riken BNL Research Center (Theorist)
- Matthias G. Perdekamp  Riken BNL Research Center(PHENIX)
- 		 From RHIC Spin Collaboration

## Outline

- Introduction
- What is Collins Fragmentation Function
- What is Interference Fragmentation Function(IFF)
- Measurement at e+e-
- Applications
- Transversity
- Single spin asymmetries
- Conclusion

## 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*

## Collins Fragmentation Function : H

- 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 : F

- 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

## jet1

- jet2

- Spin of quarks
- are 100% correlated!

- n

## In  e+e-

- In  e+e-

- Jet production from light quark		Off resonance data
- 						Exclude b fragments
- High enough energy to produce jet		Finding jet
- 		          to apply pQCD		s~100GeV2
- But not too high energy
-       FF decreases as energy increases		s(Belle) << s(LEP)
- 			       Observing Q2 evolution is interesting
-       Avoid extra complication from Z pole	 √s(Belle) < Mz
- Requires good detector:
-    Wide acceptance
-    Momentum/mass resolution 			great
-    PID capability
- The beauty of e+e- is H*H and F*F can be measurd!

- At Belle

## -

- 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?

##  The transversity function             

-  The transversity function

- Helicity flip amplitude =  Chiral odd function
- 					not accessible in (inclusive) DIS
- Naively                   for non-relativistic quarks
-                                   Relativity breaks rotation symmetry.
- Soffer’s bound:
- 			    Need not to be small!  Possibly
- Gluon (spin1) cannot flip proton (spin1/2) helicity
- 	   	   does not mix with gluons under evolution
- 	Non-relativistic                        Relativistic
- First Lattice QCD result

- S. Aoki, M. Doui, T. Hatsuda and Y. Kuramashi  Phys.Rev. D56 (1997)433
- More recently: S. Capitani et.al. Nucl. Phys. B (Proc. Suppl.) 79 (1999) 548

## 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

## The Relativistic Heavy Ion Collider

-  at Brookhaven National Laboratory

**RHIC** accelerates
- heavy ion (Au)
- up to 100 A GeV
- and
**polarized proton**
**up to 250 GeV****  **

**PHENIX**

**STAR**

- 2000 run was successful!

## STAR detector

- L3 Event Display    June 25, 2000.

- Heavy Ion physics
- Spin physics
- Photon/pomeron physics

## The PHENIX Detector 

- Muon ID
- Panels

- Central
- Arms

- North Muon
- Arm

- South Muon
- Arm

**Ring Imaging**
**Cerenkov**

- Muon Tracking
- Chambers

- Beam-Beam
- Counter

- Multiplicity/Vertex
- Detector

**Time Expansion**
**Chamber**

**Drift Chambers**

- Pad Chambers

- Time of Flight
- Panels

- EM Calorimeter

- The PHENIX Detector

## Inclusive pion single spin asymmetry at p  p ( p  C) 

- xF

- xF

- Fermi Lab E704 200GeV

- BNL E925 22GeV

- There is not fully satisfactory explanation
- Collins effect? Twist 3?
- RHIC STAR (BRAHMS?) will measure at

## Future Transversity Measurements at Polarized pp & polarized DIS 

- Future Transversity Measurements at Polarized pp & polarized DIS

- BNL - Star/Phoenix/Phobos

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

- Requires H*H & F*F measurement from e+e-

## Conclusion

- There are interesting and currently unknown fragmentation functions : Collins FF and IFF
- We propose to analyze existing Belle data to extract these FF.
- Large interests
- CERN-LEP-DELPHI analysis on the same FF at different energy
- BNL-STAR & PHENIX Experiments  (BRHAMS & PHOBOS)
- CERN-SPS-COMPASS, DESY-HERMES
- (BNL eRHIC,  DESY Tesla-N)
- “Workshop on transverse spin physics”
-                         at DESY-Zeuthen, Germany  2001 July 9-11th

## Helicity Amplitudes

**Proton Proton Scattering**

- Three  independent
- helicity amplitudes:

- Proton helicity

- quark helicity

- helicity flip!

**Deep Inelastic Scattering**