Fragmentation Functions at Belle

Anselm Vossen (University of Illinois)Matthias Grosse Perdekamp

(University of Illinois)Martin Leitgab (University of Illinois)

Akio Ogawa (BNL/RBRC) Ralf Seidl (RBRC)

Kieran Boyle (RBRC)

for the Belle collaboration

SPIN2008, University of Virginia

Outline

• Motivation– Collins FF for transversity extraction in global QCD Analysis

of single transverse spin asymmetries in pp and SIDIS• Measuring Fragmentation Functions at Belle

– Experimental techniques– Collins FF results

• Interference Fragmentation Functions– Planned measurements of IFF at Belle– Recent results from PHENIX

• Summary & Outlook

Motivation: Transversity Quark Distributions δq(x) fromTransverse Single Spin Asymmetries in Semi Inclusive Deep Inelastic Scattering

Collins- and IFF- asymmetriesin semi-inclusive deep inelastic scattering (SIDIS) and pp measure

~ δq(x) x CFF(z) combined analysis with CFF from e+e- annihilation

Example: COMPASS results for Collins Asymmetries on proton target (see talk by H. Wollny)

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

5

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

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 !

7

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 momenta. 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

KEKB: L>1.7x1034cm-2s-1 !!• Asymmetric collider• 8GeV e- + 3.5GeV e+

• √s = 10.58GeV (U(4S))• e+e-U(4S)BB• Continuum production:

10.52 GeV• e+e-qq (u,d,s,c)• Integrated Luminosity: >700 fb-1

• >60fb-1 => continuum

8

Belle detectorKEKB

Collins Asymmetries in Belle 9 May 28th Large acceptance, good tracking and particle identification!

10

Collins Fragmentation: Angles and CrossSection: cos(12) Method (e+e- CMS frame)

j1

1hP

2hPj2

j1j

2

2

21

111

121221

21

sin411

cosq

cm

T

yyyB

zHzHyBddzdzd

Xhheedσ jj

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

11

Collins Fragmentation: Angles and Cross Section cos(20) Method (CMS Frame)

j0

1hP2hP

2

21

11TTTT02

21

21

sin411

pkphkh22cosq

cm

T

yyyB

MMHHyB

ddzdzdXhheedσ Ij

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

Examples of fits to azimuthal asymmetries

12

D1 : spin averaged fragmentation function,

H1: Collins fragmentation function

N()/N0

No change in cosine moments when including sine and higher harmonics

20 12)

• Cosine modulations

• clearly visible

• P1 contains information on Collins function

13

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)2cos(:

2

2

2

2

2

2

0 FavUnfUnfFavq

FavUnfUnfFavq

UnfUnfFavFavq

UnfUnfFavFavq

DDDDe

HHHHe

DDDDe

HHHHeFA

j

2 methods give very small difference in the result

14

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

ii

ii

p

npTThrust

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-qq, q uds∈

e+e-cc

0.5 0.8 1.0

4s“off”

15

Applied Cuts, Binning• Two data sets: off-resonance data ( 29.1 fb-1 ) on-resonance data ( 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

0ˆ)ˆ(ˆ)ˆ( 12 nnPnnP hh

z2

0 1 2 3

4 5 6

7 8

9

0.20.3

0.5

0.7

1.0

0.2 0.3 0.5 0.7 1.0

5

86

1

2

3

z1

(z1, z2)-binning

16

Final Collins results

Belle 547 fb-1 data set (Phys.Rev.D78:032011,2008.)

Combined Analysis: Extract Transversity Distributions

Transversity, δq(x)Tensor Charge

Lattice QCD: Tensor Charge

Factorization + Universality ?!

Theo

rySIDIS

~ 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) x δq(x2) x CFF(z)

pp h+ + h- + X~ G(x1) x δq(x2) x IFF(z)

pp l+ + l- + X~ δq(x1) x δq(x2)

18

Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, Turkand Melis at Transversity 2008,Ferrara. Previously:Phys. Rev. D75:05032,2007

HERMES SIDIS

+ COMPASS SIDIS

+ Belle e+e-

transversity dist.

+ Collins FF

Fit includes:

Extraction of Quark Transversity Distributionsand Collins Fragmentation Functions SIDIS + e+e-

Soffer Bound

Old fit New fit

New fit

Old fit

19

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

k┴ transverse quark momentum in nucleonp┴ transverse hadron momentum in fragmentation

hadron FF

quark pdf

The transverse momentum dependencies are unknown and veryDifficult to obtain experimentally!

),()(),(

)sin()sin(),()(),(

22

,122

pzDdy

dkxqkddde

pzHdy

dkxqkdddeA

hqhS

qq

hShqSqhS

qq

CollinsUT

transversit

y

Collins F

F

Collins Extraction of Transversity:unknown Transverse Momentum Dependences!

20

Why di-hadron SSA in SIDIS & p+p

• Di-hadron vs single hadron– Collinear factorization– No model uncertainties due to kT dependence of FF and PDF– Doesn’t need quark momentum– No need to separate effects like Sivers/Collins effects in single

hadron measurement– Completely independent measurement

• Di-hadron measurement in fixed target vs collider– At higher scale

• sub-leading twist effects suppressed• factorization assumption better justified

Interference Fragmentation–thrust method

• e+e- (+-)jet1()jet2X• Stay in the mass region around r-mass• Find pion pairs in opposite hemispheres• Observe angles j1+j2 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[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)]

• Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)]

21 21221111 m,zHm,zHA jj cos

j2

j1

1hP

2hP

2h1h PP

Model predictions by:•Jaffe et al. [PRL 80,(1998)]•Radici et al. [PRD 65,(2002)]

Expected sensitivities for 60 fb-1

• () () pairs as a function of the invariant mass m,1 x m,2

• Similar distributions to be shown as a function of z,1 x z,2

• Other hadron combinations

22

23

Measurements of quark transversity

p+p

SIDIS

e++e-

E704, 1991Large forward SSA

STAR, PHENIX, BRAHMS, 2004~2005Inclusive AN

HERMES 2005, COMPASS 2006AUT

BELLE 2006Collins FF

BELLEIFF

RHICIFF asym.

RHICCollins asym.

JParc, RHIC, FAIRDrell-Yan

COMPASSp target

JLab 3He and 12 GeV

Underway Future1991 2005

CourtesyRuizhe Yang

24

Definition of Vectors and Angles

1 2

1 2

1 2

p+p c.m.s. = lab frame

, : momenta of protons

, : momenta of hadrons

( ) / 2

: proton spin orientation

A B

h h

C h h

C h h

B

P P

P P

P P P

R P P

S

1hP

2hP

100 GeVAP

100 GeVBP

CP

BS

pp hhX

1 2hadron plane: ,

scattering plane: ,

h h

C B

P P

P P

: from scattering plane to hadron plane

R : from polarization vector to scattering plane

S

Bacchetta and Radici, PRD70, 094032 (2004)

2 CR

25

vs invariant mass of the pairsinUTA

Consistent with 0, despite the second bin of 0h- pairs and the last bin of h+h- pairs are 2 from 0.

Systematic errors

Polarization 5%

Relative lumi. 5x10-4

No systematic effects detected from bunch shuffling

Ruizhe Yang, U of I,PKU RBRC Workshop2008

26

Future• Prospects from future large transverse spin

data sample from PHENIX• Sub-percent sensitivity possible

Summary & Outlook

• Collins FF at Belle final ->global analysis• 2H Interference FF Analysis underway• Plans for k_T dependent Upol FFs

– Necessary for global analysis w/o model assumptions

• 2H Interference FF at Phenix– First measurement of IFF at p-p collider– Analysis of 2008 data underway