# Presentation: 571938

##  Measurement of Collins Asymmetries in e+e- Annihilation at Belle

**D. Gabbert****	****	****Illinois and RBRC**
**M. G.Perdekamp****	****Illinois and RBRC**
**K. Hasuko****	****	****RIKEN and RBRC**
**S. Lange****	****	****Frankfurt  **
**M. Leitgab****	****	****Illinois**
**D. Mertens****	****	****Illinois                 **
**A. Ogawa****	****	****BNL and RBRC**
**R. Seidl****	****	****Illinois and RBRC **
**V. Siegle****	****	****RBRC**
***                             ******for the Belle Collaboration***

**AGS&RHIC Users’ Meeting**
***June 19******th****** , Brookhaven National Laboratory***

## -----------   Outline   ------------

- Motivation
- Collins FF for global QCD analysis of single
-      transverse asymmetries in  pp and SIDIS
- Collins Asymmetries from e+e-
- LEP  first work on Delphi data in the 90s:
*              **Efremov, Smirnova, Tkatchev and*
-             *Bonivento, Matteuzzi, Kotzinian*
- Experimental technique
- Results

- o Very basic QCD process: Fundamental test
-    case for any approach to solve QCD at soft scales.
- o Tests of universality and factorization between
-     e+e-, DIS and p-p collisions
- o Symmetry properties
- o Evolution is fundamental QCD prediction
- o Connection between microscopic and
-    macroscopic observables:
-            Probe/analyzer for transverse quark spin
-                critical input for transverse proton spin program
-                at DESY, CERN, JLab and RHIC

**Why is the Collins Fragmentation **
**          ****Function Interesting?**

## Motivation  Transversity Quark Distributions

**Motivation**  Transversity Quark Distributions
- from Collins- and Interference-Fragmentation

- Collins- and IFF- asymmetries
- in SIDIS and pp are of the form
*  **~ Transversity (x) x CFF(z)*
*   *
*  **~ Transversity (x) x IFF(z)*
- Collins- and IFF- asymmetries
- in e+e- are of the form
-     ~ CFF(z1) x CFF(z2)
-     ~  IFF(z1) x IFF(z2)
-  global QCD analysis

**New HERMES results for Collins Asymmetries**
**M. Diefenthaler, DIS 2007, Munich**

## Global Analysis:              Extract Transversity Distributions

- Global Analysis:              Extract Transversity Distributions

- Transversity
- Tensor Charge

-  Lattice QCD: Tensor Charge

- Factorization
-          +
-  Universality ?!

**Belle**

**RHIC / GSI**

- Theory

**RBRC Transversity Workshop 2000**

## First QCD Analysis   of SIDIS + e+e-  !

**Anselmino, Boglione, D’Alesio,**
**Kotzinian, Murgia, Prokudin, Turk**
**Phys. Rev. D75:05032,2007**

**HERMES SIDIS**

**+ COMPASS SIDIS**

**+ Belle e****+****e****-**

****** ****transversity dist.**

**   ****+ ****Collins FF**

**Fit includes:**

## Measurement of Collins Asymmetries

- In e+e- at KEK B with the Belle
**Phys.Rev.Lett.96:232002,2006 **
**and update at Spin 2006 in Kyoto **

##    Collins Effect in Quark Fragmentation

- J.C. Collins, Nucl. Phys. B396, 161(1993)

- q

***Collins Effect:***
- Fragmentation of a
- transversely polarized
- quark *q* into spin-less
- hadron *h*  carries an
- azimuthal dependence:

## General Form of Fragmentation Functions

- Number density for finding
- hadron *h* from a transversely
- polarized quark, *q*:

**unpolarized FF**

**Collins FF**

## Event Structure at Belle

- e-

- e+

- Jet axis: Thrust

- <Nh+,-> = 6.4

- Near-side Hemisphere:
- hi ,  i=1,Nn  with zi

-  Far-side:
-              hj , j=1,Nf with zj

- 

- _e__+__e__- __ CMS frame:_

_**Spin averaged cross section:**_

##         Collins FF in e+e- : Need

-     Collins function in one hemisphere is not possible
-     *sin **φ* modulation will average out.
-   Correlation between two hemispheres with
-     *sin **φ**i* Collins single spin asymmetries results in
-     *cos(**φ**1**+**φ**2**)* modulation of the observed di-hadron
-     yield.
*        *Measurement of azimuthal correlations for pion pairs
-         around the jet axis in two-jet events!

-         Collins FF in e+e- : Need
- Correlation between Hemispheres !

## Collins Fragmentation: Angles and Cross Section cos() Method

- Collins Fragmentation: Angles and Cross Section cos() Method

- 

- 

- 

- 

- _2-hadron inclusive transverse momentum dependent cross section:_

- Net anti-alignment of
- transverse quark spins

- 

- _e__+__e__- __ CMS frame:_

- e-

- e+

**Observables: N****12****(****φ****1****+****φ****2****), ****A****12****(z****1****,z****2****)**

## Collins Fragmentation: Angles and Cross Section cos(2) Method

- Collins Fragmentation: Angles and Cross Section cos(2) Method

- 

- _2-hadron inclusive transverse momentum dependent cross section:_

- Net anti-alignment of
- transverse quark spins

- 

- Independent of thrust-axis
- Convolution integral I  over transverse momenta involved

- _e__+__e__- __ CMS frame:_

- e-

- e+

- [Boer,Jakob,Mulders: **NPB504(1997)345**]

**A****0**

**Observables: N****0****(****φ****0****), ****A****12****(z****1****,z****2****)**

## Hadronic Events observed with Belle

**~ 1**

**~ 0.5**

****** ****1.5 x 10****9 ****hadronic events in analysis**

**On  resonance: 547fb****-1**** , √s=10.52 GeV ***(published)*
**Off  resonance: 29fb****-1    ****, √s=10.58 GeV ***(preliminary)*

## Gluon Emission

- z2

- QT

- e-

- e+

- z1

- Frame:

##      Examples of Fits to                      Azimuthal Asymmetries

**D****1 ****:  spin averaged fragmentation function, **
**H****1****:  Collins fragmentation function**

- N0()/<N0>

- 2

- )

**2a****0**

**R****0**

**R****12**

**2a****12**

- N12()/<N12>

**Notes:**
Radiativen Term schon einfuehren, proportional zu 1

## Method to eliminate gluon contributions: Double ratios for unlike- and like sign pions

- (I) radiative effects are
-     charge independent
-     and cancel.
- (II) RUL and RL depend
-      depend on Hfav and
-      Hdis differently.
-  A12 retains sensitivity
-     for the Collins effect!

**Form double ratios for unlike and like-sign pion pairs:**

## Two Double Ratios 

- Unlike-sign pion pairs (U):
- 		(favored x favored + unfavored x unfavored)
- Like-sign pion pairs (L):
- 		(favored x unfavored + unfavored x favored)
-  ± pairs
- 		(favored + unfavored) x (favored + unfavored)
- A. Efremov et al. (**[hep-ph/0603054]**): charged  pairs are similar
- 	(and easier to handle) (C):
- 		(favored + unfavored) x (favored + unfavored)

- Double ratios unlike/like-sign not very sensitive in separating favored and disfavored Collins functions   look at unlike-sign/charge-sum

- UL

- UC

**Observables:**
**                         ****A****12****(UL),  A****12****(UC)**
**                         ****A****0****(UL) ,  A****0****(UC)**

- published and input to
- fit by Anselmino et al.

## Final Charm Corrected Results for e+ e- X (29fb-1, off-resonance 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

**Phys.Rev.Lett.96:232002,2006**

## Preliminary Charm Corrected Results for e+ e- X (547 fb-1 ,on-resonance)

- Significance largely increased
- Behavior unchanged
- Reduced systematics
- Precise measurements of the Collins function

**Preliminary **

## Summary     &       Outlook

- Observation of large azimuthal asymmetries in light quark frag-mentation. Updated statistics:
-        ∫Ldt = 29 fb-1  547 fb-1
- Double ratios reliably cancel contributions from detector acceptance and gluon radiation.
- Important input for the transverse spin physics programs at RHIC, HERMES, COMPASS and JLab.
- Fundamental test case for
-      QCD at soft scales!

- Future spin dependent FFs:
-            update Collins FF
-            measure pT dependence
-            interference fragmentation
-            Collins FF for VMs
-            Lambdas
- Precision measurement of spin
-      averaged fragmentation func-tions as input to RHIC program
-      with inclusive hadrons and future
-      precision measurements in SIDIS.

## Motivation ∆G from QCD Analysis of  ALL for inclusive hadrons: π0,+,-, η, K+,-

**Motivation **∆G from QCD Analysis of  ALL for inclusive hadrons: *π**0,+,-**, **η**, K**+,-*

**PHENIX ****π****0**** cross section a |****η****|<0.35**
*   **Phys.Rev.Lett.91:241803,2003*

**Deviation connected to uncertainties**
**in FFs ******** gluon FF!**

- Idea: QCD analysis of
- LEP and Belle data will
- fix uncertainty in know-
- ledge of FFs (gluon FF,
- flavor separation)

## What is Known Experimentally in e+e- ?

**Hirai, Kumano,**
**Nagai, Sudo**
**hep-ph/0612009**
- (including errors!)

**Earlier work:**
**Kretzer**
**Binnewies, Potter, Albino**
**Kniehl, Kramer, Potter**
**Albino, Kniehl, Kramer**
**Most recent work:**
**De Florian, Sassot,**
**Stratmann**

## Belle Impact on the Knowledge of FFs 

- Belle MC

- <1% of data sample           work in progress

- Belle Impact on the Knowledge of FFs

- FF

- FF

- Compilation of data
- available for the char-
- ged hadron FF

- Belle: Charged h+/-, pions, kaons, protons

- precision
- at high z!

-   h+,-
-   pions
-   kaons
-   protons

-  Input also for precision
-  measurements of quark
-  helicity distributions in
-  SIDIS, in particular at
-  a possible future electron-
-  polarized proton collider.

- o Very basic QCD process: Fundamental test
-    case for any approach to solve QCD at soft scales.
- o Tests of universality and factorization between
-     e+e-, DIS and p-p collisions
- o Symmetry properties
- o Evolution is fundamental QCD prediction
- o Connection between microscopic and
-    macroscopic observables:
-            Probe/analyzer for transverse quark spin
-                critical input for transverse proton spin program
-                at DESY, CERN, JLab and RHIC

**Why is the Collins Fragmentation **
**          ****Function Interesting?**

## KEKB
Asymmetric collider
8GeV e- + 3.5GeV e+
 s = 10.58GeV ((4S))
	e+e-S
Off-resonance: 10.52 GeV
	e+e-qq  (u,d,s,c)
Integrated Luminosity: > 600 fb-1
        > 60fb-1 =>  off-resonance

- Asymmetric collider
- 8GeV e- + 3.5GeV e+
* ****s* = 10.58GeV ((4S))
- 	e+e-S
- Off-resonance: 10.52 GeV
- 	e+e-qq  (u,d,s,c)
**Integrated Luminosity: > 600 fb****-1**
**        ****> 60fb****-1**** =>  off-resonance**

- KEKB:   L>1.6 x 1034cm-2s-1  !!

- Average Trigger rates:
- (4S)BB		11.5Hz
- qq			28   Hz
- 		16   Hz
*Bhabha**	**	** 4.4 Hz*
*2****	**	**	**35   Hz*

****** ****1.5 x 10****9 ****hadronic events in analysis**

## Good tracking and particle identification!

**Good tracking and particle identification!**

## 
Good detector performance (acceptance, momentum resolution, pid)
Jet production from light quarks
	 off-resonance (60 MeV below resonance) 
           (~10% of all data)
Intermediate Energy
	Sufficiently high scale (Q2 ~ 110 GeV2)
		- can apply pQCD
	Not too high energy (Q2 << MZ2)
		-avoids complication from Z interference
 Sensitivity = A2sqrt(N) ~ x 25 (100) compared to LEP
    ABelle / ALEP  ~   x 2 (A  scales as ln Q2)
    ∫LBelle dt / ∫LLEP dt ~ x 46 (600) 

Total number of hadronic events ~ 1.5 x 109

- Good detector performance (acceptance, momentum resolution, pid)
- Jet production from light quarks
- 	 off-resonance (60 MeV below resonance)
-            (~10% of all data)
- Intermediate Energy
- 	Sufficiently high scale (*Q**2** ~ 110 GeV**2*)
- 		- can apply pQCD
- 	Not too high energy (*Q**2** << M**Z**2*)
- 		-avoids complication from Z interference
-  Sensitivity = *A**2**sqrt(N)* ~ **x 25 ***(100)* compared to LEP
*    **A*Belle / *A*LEP  ~   **x 2** (*A * scales as* ln Q**2*)
*    **∫**L*Belle dt / ∫*L*LEP dt ~ **x 46 ***(600) *
- Total number of hadronic events ~ 1.5 x 109

- Belle is Well Suited for FF Measurements:

## Applied Cuts, Binning

- Originally off_resonance data, now also on_resonance data (29.1  547 fb-1)
-  Track selection:
- pT > 0.1GeV
- vertex cut:dr<2cm, |dz|<4cm
- Acceptance cut
- -0.6 < cosi < 0.9
- Event selection**:**
- Ntrack  3
- Thrust > 0.8
- Z1, Z2>0.2

- Hemisphere cut
- QT < 3.5 GeV
- Pion PID selection

## Experimental Issues

- Cos2 moments have two contributions:
- Collins		Can be isolated either by subtraction or double ratio method
- Radiative effects	Cancels exactly in subtraction method, and in LO of double 			     	     ratios
- Beam Polarization
- 	zero?		*cos(2****)* asymmetries for jets or 
- False asymmetries
- 	from weak decays	 Study effect in  decays, constrain through D tagging
- False asymmetries
- 	from misidentified
- 	hemispheres		 *Q**T* or polar angle cut
- False asymmetries
- 	from acceptance	Cancels in double ratios, can be estimated in charge ratios,
- 				     fiducial cuts
- Decaying particles	lower z cut

## Why is it Possible to Include Data on Resonance?Different Thrust Distributions

- Why is it Possible to Include Data on Resonance?Different Thrust Distributions

-  small B contribution (<1%) in high thrust sample
- >75% of X-section continuum under
-    (4S) resonance
- 29 fb-1  547 fb-1
- many systematic errors reduce with more
-  statistics
-  Charm-tagged Data sample also increases

- e+e-qq̅, q∈uds

- e+e-cc̅

## Collins Asymmetries I:  4x4 z1, z2 binning

- Collins Asymmetries I:  4x4 z1, z2 binning

- 547 fb-1 charm corrected data sample,
- UL and UC double ratios

- PRELIMINARY

- PRELIMINARY

- A0 (cos(2)) moments

- A12 (cos()) moments

## Collins Asymmetries II: sin2 /(1+cos2 ) Binning (UL)

- Collins Asymmetries II: sin2 /(1+cos2 ) Binning (UL)

- Nonzero quark polarization ~ sin2 
- Unpolarized de-nominator ~ 1+cos2 
- 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

- thrustz
- 

- PRELIMINARY

## Collins Asymmetries III: QT  Binning (UL)

- Collins Asymmetries III: QT  Binning (UL)

- Reduced asymmetries in low thrust sample
- At low thrust significant B contribution
- 	(for t<0.8  ~20 % B
- 	 for t>0.8  < 1 % B)
- A12 thrust axis dependent
- High QT (>3.5 GeV) asymmetries from beam related BG
- UC plots similar

- Thrust>0.8
- Thrust<0.8 (not corrected for heavy quark contributions)

- PRELIMINARY

## Improved Systematic Errors (UC)

- Tau contributions
- PID systematics
- MC double ratios
- Charged ratios (
- Higher order terms
- Double ratio-subtraction method

- Reweighting  asymmetries: underestimation of cos asymmetries rescaled by 1.21
- Correlation studies:
- statistical errrors rescaled by 1.02 (UL) and 0.55 (UC)
- Beam polarization studies
- consistent with zero

- A0 (cos(2)) moments

- A12 (cos()) moments