spin dependent fragmentation function analysis at belle

Spin dependent fragmentation function analysis at Belle

M. Grosse Perdekamp (University of Illinois and RBRC)

A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC)

Spin 2006

October 5, 京都 , 日本

Measurement of the Collins fragmentation function at BELLE 2 Spin2006, October 6th

KEKB: L>1.6x1034cm-2s-1 !!

• Asymmetric collider• 8GeV e- + 3.5GeV e+

• s = 10.58GeV ((4S))• e+e-S• Off-resonance: 10.52 GeV• e+e-qq (u,d,s,c)• Integrated Luminosity: >600 fb-1

• >60fb-1 => off-resonance

Belle detectorKEKB

Measurement of the Collins fragmentation function at BELLE 3 Spin2006, October 6th

Good tracking and particle identification!

Measurement of the Collins fragmentation function at BELLE 4 Spin2006, October 6th

Collins fragmentation in e+e- : Angles and Cross section cos() method

1hP

2hP

2

21

111

121221

21

sin4

1

cosq

cm

T

B

zHzHBddzdzd

Xhheedσ

2-hadron inclusive transverse momentum dependent cross section:

Net (anti-)alignment oftransverse quark spins

e+e- CMS frame:

e-

e+

GeV 5210ss

E2z h .,

[D.Boer: PhD thesis(1998)]

First |kT| moments of

Collins Function H1⊥

thrustaxis

Measurement of the Collins fragmentation function at BELLE 5 Spin2006, October 6th

Collins fragmentation in e+e- : Angles and Cross section cos(2) method

1hP

2hP

2

21

11TTTT02

21

21

sin4

1

pkphkh2I2cosq

cm

T

B

MM

HHB

ddzdzd

Xhheedσ

2-hadron inclusive transverse momentum dependent cross section:

Net (anti-)alignment oftransverse 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]

Measurement of the Collins fragmentation function at BELLE 6 Spin2006, October 6th

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 < cosi < 0.9 • Event selection:

– Ntrack 3– Thrust > 0.8 – Z1, Z2>0.2

• Hemisphere cut

• QT < 3.5 GeV• Pion PID selection

(Ph 2 ˆ n ) ˆ n (Ph1ˆ n ) ˆ n 0

Measurement of the Collins fragmentation function at BELLE 7 Spin2006, October 6th

Examples of fits to azimuthal asymmetries

D1 : spin averaged fragmentation function,

H1: Collins fragmentation function

N()/N0

No change in cosine moments when including sine and higher harmonics

Cosine modulationsclearly visible

2 )

Measurement of the Collins fragmentation function at BELLE 8 Spin2006, October 6th

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

)(

)(

)(

)(

)(cos1

)(sin:

2

2

2

2

2

2

FavUnfUnfFav

q

FavUnfUnfFav

q

UnfUnfFavFav

q

UnfUnfFavFav

q

DDDDe

HHHHe

DDDDe

HHHHeFA

2 methods give very small difference in the result

))(()(),(1)(

)(

: 2,1

,1

0

0T

disfavoredfavored

Like

Like

Unlike

Unlike

QFOzHzHF

NN

NN

R

)(),()()(

: ,1

,1

00

zHzHFN

N

N

NS disfavoredfavored

Like

Like

Unlike

Unlike

Measurement of the Collins fragmentation function at BELLE 9 Spin2006, October 6th

Other Favored/Unfavored Combinations charged pions or

• 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)

• P.Schweitzer([hep-ph/0603054]): charged pairs are similar (and easier to handle) (C):

(favored + unfavored) x (favored + unfavored)

Challenge: current double ratios not very sensitive to favored to disfavored Collins function ratio Examine other combinations:

Favored = u,d,cc.

Unfavored = d,u,cc.

Build new double ratios:

Unlike-sign/ charged pairs (UC)

UL

UC

Measurement of the Collins fragmentation function at BELLE 10

Spin2006, October 6th

Why is it possible to include on_resonance data?Different Thrust distributions

ii

ii

p

npthrust

ˆ

• 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

9.44 9.46

e+e- Center-of-Mass Energy (GeV)

0

5

10

15

20

25

(e+

e-

had

ron

s)(n

b)

(1S)10.0010.02

0

5

10

15

20

25

(2S)10.34 10.37

0

5

10

15

20

25

(3S)10.54 10.58 10.62

0

5

10

15

20

25

(4S)9.44 9.46

e+e- Center-of-Mass Energy (GeV)

0

5

10

15

20

25

(e+

e-

had

ron

s)(n

b)

(1S)10.0010.02

0

5

10

15

20

25

(2S)10.34 10.37

0

5

10

15

20

25

5

10

15

20

25

(2S)10.34 10.37

0

5

10

15

20

25

(3S)10.54 10.58 10.62

0

5

10

15

20

(3S)10.54 10.58 10.62

0

5

10

15

20

25

(4S)BB00 BB

e+e-qq, q∈uds

e+e-cc

Measurement of the Collins fragmentation function at BELLE 11

Spin2006, October 6th

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 1.21Correlation studies:statistical errrors rescaled by 1.02 (UL) and 0.55 (UC)Beam polarization studiesconsistent with zero

A0 (cos(2)) moments

A12 (cos()) moments

Measurement of the Collins fragmentation function at BELLE 12

Spin2006, October 6th

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

Measurement of the Collins fragmentation function at BELLE 13

Spin2006, October 6th

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

Measurement of the Collins fragmentation function at BELLE 14

Spin2006, October 6th

• e+e- (+-)jet1(-+)jet2X• Stay in the mass region around -mass• Find pion pairs in opposite

hemispheres• Observe angles 12

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 and Artru,Collins

• Early work by Collins, Heppelman, Ladinski

Interference Fragmentation – thrust method

21221111 m,zHm,zHA cos

2

1

1hP

2hP

2h1h PP

Measurement of the Collins fragmentation function at BELLE 15

Spin2006, October 6th

Unpolarized FFs

MC simulation, ~1.4 fb-1

2.

• Performed Systematic studies:– Smearing– Tracking efficiency– Acceptance– Energy scale

• Particle ID study not yet finished

• AKK: Try flavor tagged/enhanced analysis?

• How about 2 hadron analysis favored,disfavored FF 1.4 fb-1, 4.5·106 events

2.5 % of off_resonance data

Measurement of the Collins fragmentation function at BELLE 16

Spin2006, October 6th

Summary and outlook

• Double ratios:double ratios from datamost systematic errors cancel

• Analysis procedure passes all null tests

• Systematic uncertainties understood

• Statistics increased from 29 547 fb-1

Significant nonzero asymmetry with double ratios are observed

• UL/C about half as large UL/L double ratios

• Data can be used for more sophisticated analysis

• Paper with 29 fb-1 U/L double ratios published (PRL96:232002,2006)

• Analysis almost finalized,smalller additions planned (kt dependence of Collins effect, parameterizations)

• Interference fragmentation function analysis started

• Many more QCD/Spin related studies possible (unpol FFs, timelike DVCS, Polarimetry)

Measurement of the Collins fragmentation function at BELLE 17

Spin2006, October 6th

Backup Slides

Measurement of the Collins fragmentation function at BELLE 18

Spin2006, October 6th

Why correction factors of 1.2 and 0.55?

• Charged pion pairs are the sum of U and L

Errors are correlated when building double ratios UC or LC

• Division of histograms takes correlation not into account

• Proper error calculation confirms correction factors found in correlation studies and distributions

Measurement of the Collins fragmentation function at BELLE 19

Spin2006, October 6th

Collins asymmetries IIa: sin2 /(1+cos2 ) binning (UC)

• Nozeron 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)

• Similar behavior, smaller magnitude as UL asymmetries

thrustz

PRELIMINARY

Measurement of the Collins fragmentation function at BELLE 20

Spin2006, October 6th

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 similarThrust>0.8

Thrust<0.8 (not corrected for heavy quark contributions)

PRELIMINARY

Measurement of the Collins fragmentation function at BELLE 21

Spin2006, October 6th

Collins asymmetries IIIa: QT binning (UC)

• Reduced asymmetries in low thrust sample

• At low thrust significant heavy quark contribution

• High QT (>3.5 GeV) asymmetries from beam related BG

• similar behavior, but smaller magnitude as UL asymmetries

Thrust>0.8

Thrust<0.8 (not corrected for heavy quark contributions)

PRELIMINARY

Measurement of the Collins fragmentation function at BELLE 22

Spin2006, October 6th

Final charm corrected results for e+ e- X (29fb-1 of continuum

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 publishedIntegrated results:

A0(UL/L) (3.06 ± 0.57 ± 0.55)%

A12(UL/L) (4.26 ± 0.68 ± 0.68)%

A0(UL/C) (1.27 ± 0.49 ± 0.35)%

A12(UL/C) (1.75 ± 0.59 ± 0.41)%

Final results

Preliminary results

Measurement of the Collins fragmentation function at BELLE 23

Spin2006, October 6th

Final charm corrected results for e+ e- X (547 fb-1)

• Significance largely increased

• Behavior unchanged• Reduced systematics• Precise measurements of

the Collins function

Integrated results:

A0(UL/L) (2.67 ± 0.10 ± 0.26)%

A12(UL/L) (3.55 ± 0.08 ± 0.15)%

A0(UL/C) (1.11 ± 0.11 ± 0.22)%

A12(UL/C) (1.46 ± 0.09 ± 0.13)%

Measurement of the Collins fragmentation function at BELLE 24

Spin2006, October 6th

B, charm and uds contributions in the data

uds quarkscharm quarksCharged B-mesonsNetral B-mesons

Open symbols: charm enhanced data sample used for charm correctionFull symbols: main data sample

thrust>0.8 thrust<0.8

Measurement of the Collins fragmentation function at BELLE 25

Spin2006, October 6th

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

q

momentum hadron relative : 2

z

momentum hadron e transvers:

momentum hadron :

spinquark :

momentumquark :

h

sE

EE

p

p

s

k

h

qh

h

h

q

qs

k

hph

,

Collins Effect:Fragmentation with of a quark q with spin sq into a spinless hadron h carries anazimuthal dependence:

hp

sin

qh spk

Collins effect in quark fragmentation