# Presentation: 273303

## Measurements of chiral-odd fragmentation functions at Belle

**D. Gabbert (University of Illinois and RBRC)**
**M. Grosse Perdekamp (University of Illinois and RBRC)**
**  ****K. Hasuko (RIKEN/RBRC) **
**S. Lange (Frankfurt University)                   **
**A. Ogawa (BNL/RBRC)**
** **_**R. Seidl**_** (University of Illinois and RBRC) **
**V. Siegle (RBRC)**
**for the Belle Collaboration**

- SSA workshop
- June1st – 3rd, BNL, NY

## Outline

- Motivation
- Global transversity analysis
- Feasibility  LEP analysis
- 	[hep-ph/9901216]
- The BELLE detector
- Collins analysis
- Angular definitions and cross sections
- Double Ratios to eliminate radiative/momentum correlation effects
- An experimentalist’s interpretation
- Summary

## Motivation: Global Transversity Analysis

- SIDIS experiments (HERMES and COMPASS) measure q(x) together with either Collins Fragmentation function    or  Interference Fragmentation function

- RHIC measures the same combinations of quark Distribution (DF) and Fragmentation Functions (FF) plus unpolarized DF q(x)

- There are always 2 unknown functions involved which cannot be measured independently

- The Spin dependent Fragmentation function analysis yields information on
- the Collins and the Interference Fragmentation function !

- Universality appears to be proven
- in LO  by Collins and Metz:
- [**PRL93:(****2004)252001** ]

## KEKB:   L>1.5x1034cm-2s-1  !!

- 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: >400 fb****-1**
**        ****>30fb****-1**** =>  off-resonance**

## 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 additional complication from Z interference
 Sensitivity = A2sqrt(N) ~ x19 (60) compared to LEP
    ABelle / ALEP  ~   x2 (A scales as ln Q2)
    LBelle / LLEP  ~ x23 (230) 

- 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 additional complication from Z interference
-  Sensitivity = *A**2**sqrt(N)* ~ **x19 ***(60)* compared to LEP
*    **A*Belle / *A*LEP  ~   **x2** (*A* scales as* ln Q**2*)
*    **L*Belle / *L*LEP  ~ **x23 ***(230) *

- Belle is well suited for FF measurements:

## 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 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+

## 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**]

## Applied cuts, binning

- Off-resonance data
- 	(in the future also resonance)
- 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

- Light quark selection
- Hemisphere cut
- 				<0
- Opening angule cuts:
- - cos(2) method:  
- - cos() method:

- z-binning:    0.2 0.3 0.5 0.7 1.0

## Examples of fitting the azimuthal asymmetries

- Cosine modulations clearly visible
- No change in cosine moments when including higher harmonics (even though double ratios will contain them)

- D1 :  spin averaged fragmentation function,
- H1:  Collins fragmentation function

- N()/N0

## Raw asymmetries vs QT

- Raw asymmetries vs QT

- 

- 

- 

-  QT describes transverse momentum of virtual photon in  CMS system
- Significant nonzero Asymmetries visible in MC (w/o Collins)
- Acceptance, radiative and momentum correlation effects similar for like and unlike sign pairs

- uds MC () Unlike sign pairs
- uds MC ()  Like sign pairs

## Methods to eliminate gluon contributions: Double ratios and subtractions

- _Double ratio method:_

- _Subtraction 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

## Testing the double ratios with MC

- Asymmetries do cancel out for MC
- Double ratios of   compatible to zero
- Mixed events also show zero result
- Asymmetry reconstruction works well for MC
- 	(weak decays)
- Single hemisphere analysis yields zero
- Double ratios are safe to use

- uds MC       (pairs)
- charm MC   pairs
- Data     ()

## Results for -pairs for 30fb-1

- Results for -pairs for 30fb-1

- Significant non-zero asymmetries
- Rising behaviour vs. z
- cosdouble ratios only marginally larger
- First direct measurement of the Collins function

- z1

- z2

## Systematics: charm contribution?

- Weak (parity violating) decays could also create asymmetries
- 	(seen in 
- 	 overall  dilution 5%)
- Especially low dilution in combined
- 	z-bins with large pion asymmetry
- Double ratios from charm MC compatible to zero
- Charm decays cannot explain large double ratios seen in the data
-  Systematic errors from charm are preliminary

- Charm fraction N(charm)/N(all)

## Take unpolarized parameterizations (Kretzer at Q2=2.5GeV2)
Assume 

	(PDF-like behaviour)
Assume

Sensitivity studies in progress

- Assume
- 	(PDF-like behaviour)
- Assume
- Sensitivity studies in progress

- An experimentalist’s interpretation: fitting parameterizations of the Collins function(s)

## Favored/Disfavored  contribution Sensitivity 

- Favored/Disfavored  contribution Sensitivity

- c

- b

## Summary and outlook

- Double ratios:
- double ratios from data
- most systematic errors cancel
- Analysis procedure passes zero tests
- Main systematic uncertainties understood
- Significant nonzero double ratios
-  Naïve LO analysis shows significant Collins effect

- Finalize analysis
- On resonance 10 x statistics
- Include into analysis:
- Better distinction between  favored and disfavored  Collins function
- Include VMs into analysis:
-  Possibility to test string    fragmentation models used to  describe Collins effect
- Expansion of analysis to Interference fragmentation function straightforward

- _Summary:_

- _Outlook:_

## What is the transverse momentum QT of the virtual photon?

- What is the transverse momentum QT of the virtual photon?

- In the lepton CMS frame
- 	**e****-**=-**e****+** and the virtual photon is only time-like:
- 	q=(e-+p+)=(Q,0,0,0)
- Radiative (=significant BG) effects are theoretically best described in the hadron CMS frame where
- 	**P**h1+**P**h2=**0**
**	**q’=(q’0,**q’**)
- Inclusive Cross section for radiative events (acc. to D.Boer):

**P**h1

**e****+**

**e****-**

**P**h2

**e****-****’**

**e****+****’**

**q’**

**P’**h1

**P’**h2

**q****T**

- Lepton-CMS

- Hadron-CMS

## Different charge combinations additional information

- Unlike sign pairs contain either only favored or only unfavored fragmentation functions on quark and antiquark side:
- Like sign pairs contain one
- 	favored and one unfavored fragmentation function each:

- Favored	= u,d,cc.
- Unfavored	= d,u,cc.

## Raw asymmetries vs transverse photon momentum QT

- Raw asymmetries vs transverse photon momentum QT

- 

- 

- 

- 

- 

- Already MC contains large asymmetries
- Strong dependence against transverse photon Momentum QT
- Expected to be due to radiative effects
- Difference of DATA and MC is signal
- not so easy to determine

- DATA ()   fiducial cut
- DATA (KK)  fiducial cut
- UDS-MC      fiducial cut
- CHARM-MC fiducial cut

- Unlike sign
- pairs

- Like sign
- pairs