collins asymmetries in belle measurement of collins asymmetries in e + e - annihilation at the kek...

Collins Asymmetries in Belle

Measurement of Collins Asymmetries in e+e- Annihilation at the KEK B-Factory

XII Workshop on High Energy Spin 2007Joint Institute for Nuclear Research, Dubna, September 6th

M. Grosse Perdekamp. Illinois

D. Gabbert Illinois and RBRCM. Grosse Perdekamp Illinois and RBRCK. Hasuko RIKEN and RBRCS. Lange Frankfurt M. Leitgab IllinoisD. Mertens Illinois A. Ogawa BNL and RBRCR. Seidl Illinois and RBRC V. Siegle RBRC

for the Belle Collaboration

Collins Asymmetries in Belle 2 September 6th

----------- Outline ------------

o Motivation Collins FF for global QCD analysis of single transverse asymmetries in pp and SIDIS

o Collins Asymmetries from e+e- LEP first work on Delphi data in the 90s: Bonivento, Matteuzzi, Kotzinian, (DELPHI note,1995), Efremov, Smirnova, Tkachev (Nucl. Phys. Proc. Suppl. 74,

1999) Experimental technique Results

o Future Plans• Spin dependent observables• Precision measurement of spin averaged

hadron fragmentation functions


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 δq(x) fromCollins- (CFF) and Interference-Fragmentation (IFF)

Collins- and IFF- asymmetriesin semi-inclusive deep inelastic scattering (SIDIS) and pp measure ~ δq(x) x CFF(z) ~ δq(x) x IFF(z)

Collins- and IFF- asymmetriesin e+e- annihilation are of the form ~ CFF(z1) x CFF(z2)

~ IFF(z1) x IFF(z2)

global QCD analysis

Latest HERMES results for Collins Asym-Metries, M. Diefenthaler, DIS 2007, Munich


Global Analysis: Extract Transversity Distributions

Transversity, δq(x)Tensor Charge

Lattice QCD: Tensor Charge

Factorization + Universality ?!

Theo

ry

RBRC Transversity Workshop 2000

SIDIS~ δq(x) x CFF(z)~ δq(x) x IFF(z)

e+e-

~ CFF(z1) x CFF(z2)~ IFF(z1) x IFF(z2)

pp jets~ G(x1)xδq(x2) x CFF(z)

pp h+ + h- + X~ G(x1)xδq(x2) x IFF(z)

pp l+ + l- + X~ δq(x1) x δq(x2)


First QCD Analysis of SIDIS + e+e- !

Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, TurkPhys. Rev. D75:05032,2007

HERMES SIDIS+ COMPASS SIDIS+ Belle e+e-

transversity dist. + Collins FF

Fit includes:


The Preliminary DELPHI Collins Result

1

1

6.2 1.7 (stat. error)H ppmD

Efremov, Smirnova, Tkachev (Nucl. Phys. Proc. Suppl. 74, 1999)

1

1

12.9 1.4 (stat. error)H ppmD

Sample: 3.5 x 106 events at √s=MZ0Analysis: di-hadron correlation for leading hadrons

35<θ2<135

15< θ2 <175

endc

aps

endc

aps

First result on Collins Asymmetries in e+e- Monte Carlo for acceptance corrections Un-estimated (large) systematic errors DELPHI result e+e- compatible with HERMES+ BELLE (Efremov, Goeke, Schweitzer)

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

q

momentum hadron relative : 2

zmomentum hadron e transvers:

momentum hadron :

spinquark : momentumquark :

h

sE

EEpp

sk

h

qh

h

h

q

qs

k

hph ,

Collins Effect:Fragmentation of a transversely polarizedquark q into spin-less hadron h carries anazimuthal dependence:

hp

sin

qh spk

Collins Asymmetries in Belle 10

September 6th

General Form of Fragmentation Functions

h

qhh

hqhqh

hq zM

spkpzHzDpzD

ˆ ),()(),( 2,

1,

1

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

unpolarized FF Collins FF


September 6th

o Quark spin direction unknown: measurement of Collins function in one hemisphere is not possible sin φ modulation will average out.

o Correlation between two hemispheres with sin φi Collins single spin asymmetries results in cos(φ1+φ2) 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- : NeedCorrelation between Hemispheres !


September 6th

q1

quark-1 spin

Collins effect in e+e-

quark fragmentation will lead to azimuthalasymmetries in di-hadron correlation measurements!

Experimental requirements: Small asymmetries very large data sample! Good particle ID to high moments. Hermetic detector

Collins Effect in di-Hadron CorrelationsIn e+e- Annihilation into Quarks!

electron

positron

q2

quark-2 spin

z2 z1

z1,2 relative pion momenta


September 6th

KEKB– Asymmetric collider– 8 GeV e- + 3.5 GeV e+

– s = 10.58 GeV , e+e- ϒS– Off-resonance: 10.52 GeV e+e- qq (u,d,s,c)– Integrated Luminosity: 547 fb-1 (on resonance) 60 fb-1 (off-resonance)

Belle detectorKEKB

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

Average Trigger rates:(4S)BB 11.5Hzqq 28 Hz 16 HzBhabha 4.4 Hz2 35 Hz

1.5 x 109 hadronic events in analysis ~ 430 x DELPHI …


September 6th

Luminosity vs time for 24 hours at KEKB Continuous Injection Constant Collision

Rate

24 hours

high energy ring - beam current

low energy ring - beam current

HER lifetime

LER lifetime

∫Ldt vs day time

∫Ldt =1fb-1/day


September 6th Large acceptance, good tracking and particle identification!


September 6th

Hadronic Events observed with Belle

ii

ii

p

npthrust

particles

ˆThrust ~ 1 ~ 0.5

1.5 x 109 hadronic events in analysis

Off resonance: 29fb-1 , √s=10.52 GeV (published)

On resonance: 547fb-1 , √s=10.58 GeV (preliminary)


September 6th

Measuring Light Quark Fragmentation Functions on the ϒ(4S) Resonance

ii

ii

p

npthrust

ˆ

• small B contribution (<1%) in high thrust sample • >75% of X-section continuum under ϒ(4S) resonance• 29 fb-1 547 fb-1 • several 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

- ha

dron

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

- ha

dron

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-qq̅, q∈uds

e+e-cc̅

0.5 0.8 1.0


September 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 (Ph1 ˆ n ) ˆ n 0

z2

0 1 2 3

4 5 6

7 8

9

0.2

0.3

0.5

0.7

1.0

0.2 0.3 0.5 0.7 1.0

5

86

1

2

3

z1


September 6th

e-

e+ Jet axis: Thrust

<Nh+,-> = 6.4

GeV 5210ss

E2z h ., Near-side Hemisphere: hi , i=1,Nn with zi

far-side hemisphere: hj , j=1,Nf with zj

Event Structure at Belle

22

21112

2

2

21

21

141

21

3

cos

,

cm

aaa

yyyA

zDzDeyAQdzdzd

Xhheed

e+e- CMS frame:

Spin averaged cross section:


September 6th

Collins Fragmentation: Angles and CrossSection: cos() Method (e+e- CMS

frame)

1hP

2hP

2cm

21

111

121T

221

21

41y1yyB

zHzHyBddzdzd

Xhheedσ

sin

cos q

2-hadron inclusive transverse momentum dependent cross section:

Net anti-alignment oftransverse quark spins

e-

e+

Observable: yield, N12(φ1+φ2) of π+π- pairs


September 6th

Collins Fragmentation: Angles and Cross Section cos(2) Method (CMS

Frame)

1hP2hP

2cm

21

110

T2

21

21

41y1yyB

MMHH22yB

ddzdzdXhheedσ

sin

ˆˆcos TTTT pkphkhq

I

2-hadron inclusive transverse momentum dependent cross section:

Net anti-alignment oftransverse quark spins

Independent of thrust-axis

Convolution integral I over transverse momenta

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

e-

e+

Observable: yield,N0(2φ0) of π+π- pairs


September 6th

z2

QTe- e+

21110

222

2

21

)2cos(sin ... before as... zDzDQQ

qdQdzdzd

dN

T

T

T

z1 21 pp Frame:

Complication: Radiative Contribution to the Di-Hadron Cross Section

same cos(2Φ0)dependence asCollins effect …


September 6th

Examples of Fits to Azimuthal Asymmetries

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

N0()/<N0>

2 )

2a0R0 R1

2

2a12

N12(Φ1+Φ2)/<N12>

)2cos()2cos()2(

00011

1111011

0

000 ab

DaDDcDHbHDaD

NNR

a0 and a12 contain Collins + radiative effects+ acceptance effects


September 6th

Large Radiative and Acceptance Effects !

Example:a0 for unlike-sign pion pairs: a0

U

generated uds-MCvs reconstructed uds-MCvs data (Difference MC-data: charm contribution)

a0 for like-sign pion pairs: a0L

generated uds-MCvs reconstructed uds-MCvs data (Difference MC-data: charm contribution)

generated uds-MC

reconstructed uds-MCdata

data

reconstructed uds-MC

generated uds-MC


September 6th

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

pions

),()cos(411

)()(

21/

1221

12

2112

12

2112

12

12

zzA

NN

NN

RR

R

LUL

LUL

signLike

signUnLike

(I) radiative effects are charge independent and cancel.

(II) Acceptance effects cancel.

(III) RUL and RL depend depend on Hfav and Hdis differently.

A12 retains sensitivity for the Collins effect!

Cross checked againstsubtraction RUL-RL withidentical results.

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


September 6th

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: A12(UL), A12(UC) A0(UL) , A0(UC)

published and input tofit by Anselmino et al.


September 6th

Consistency Checks for Double Ratio

(0) Check that Monte Carlo Double asymmetries are 0.(1) Calibrate with “known” physics asymmetry: Weak decays produce azimuthal asymmetries. Showed that double ratio method give correct asymmetry for tau-sample.(2) Comparison of Double Ratio with Subtraction Method leads to identical results.(3) Observe polar angle dependence

(4) Smaller asymmetry for lower thrust sample

(5) Null tests:

(a) mixed events give 0 asymmetry (b) single side asymmetries average to 0

)cos1(sin~ 2

2

0

A


September 6th

Double Ratios From Monte Carlo

Monte Carlo knowsRadiative and accep-tance effects!

Do they cancel in the final double ratio?

Assign largest observedaverage MC double ratio + statistical error as systematic error

<A0UL>=0.0013∓0.0009

0.0022


September 6th

Collins Asymmetries: 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


September 6th

Other Experimental Issues

• Beam Polarization zero? cos(2) asymmetries for jets or • False asymmetries from weak decays estimate charm contribution through D tagging• False asymmetries from misidentified hemispheres

QT or polar angle cut• False asymmetries from acceptance Cancels in double ratios, can be estimated in

charge ratios from data, fiducial cuts• Correlations from decays

lower z cut


September 6th

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

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)%

Phys.Rev.Lett.96:232002,2006


September 6th

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

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)%

Preliminary


September 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)

A0 (cos(2)) moments

A12 (cos()) moments


September 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


September 6th

First QCD Analysis of SIDIS + e+e- !

Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, TurkPhys. Rev. D75:05032,2007

HERMES SIDIS+ COMPASS SIDIS+ Belle e+e-

transversity dist. + Collins FF

Fit includes:


September 6th

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.


September 6th

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

PHENIX π0 cross section a |η|<0.35 Phys.Rev.Lett.91:241803,2003

Deviation connected to uncertaintiesin FFs gluon FF!

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


September 6th

What is Known Experimentally in e+e- ?

Hirai, Kumano,Nagai, Sudohep-ph/0612009(including errors!)

Earlier work:KretzerBinnewies, Potter, AlbinoKniehl, Kramer, PotterAlbino, Kniehl, Kramer

Most recent work:De Florian, Sassot,Stratmann


September 6th

Belle MC

<1% of data sample work in progress

Belle Impact on the Knowledge of FFs

2/

sEz

h

2/

sEz

h

FF

FF

Compilation of dataavailable 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.


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

PRELIMINARY

collins asymmetries in belle measurement of collins asymmetries in e + e - annihilation at the kek...

Documents