Transverse Spin dependent Fragmentation Functions at

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)

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 pp and SIDIS

• Summary & Outlook

RL

RLN P

A

1

Transverse Spin Asymmetries at RHIC

• QCD: : very small

• Single transverse spin asymmetries pick up:– Sivers Effect: kT in quark

distribution– Quark transverse

polarization x Collins fragmentation function: kT in fragmentation function

δq x CFF3

Transversity

PHENIX, forward at s = 62 GeV, nucl-ex/0701031

21

222xx

s

px L

F

smA qN /

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

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: New COMPASS results for Collins Asymmetries on proton target (consistent with previous HERMES results)

Collins Effect in Quark Fragmentation

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

hp

sin

qh spk

6

General Form of Fragmentation Functions

h

qhh

hqhqh

h

q 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 !

8

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>1.96 x 1034cm-2s-1 !!• Asymmetric collider• 8GeV e- + 3.5GeV e+

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

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

• >60fb-1 => continuum

9

Belle detectorKEKB

Collins Asymmetries in Belle 10 May 28th Large acceptance, good tracking and particle identification!

11

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

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

0.5 0.8 1.0

4s“off”

12

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

1hP

2hP

2

21

111

121221

21

sin4

11

cosq

cm

T

yyyB

zHzHyBddzdzd

Xhheedσ

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

13

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

1hP2hP

2

21

11TTTT02

21

21

sin4

11

pkphkh22cosq

cm

T

yyyB

MM

HHyB

ddzdzd

XhheedσI

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

14

D1 : spin averaged fragmentation function,

H1: Collins fragmentation function

N()/N0

2 )

• Cosine modulations

• clearly visible

• P1 contains information on Collins function

15

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 FavUnfUnfFav

q

FavUnfUnfFav

qUnfUnfFavFav

q

UnfUnfFavFav

q

DDDDe

HHHHe

DDDDe

HHHHeFA

2 methods give very small difference in the result

16

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

Final Collins results

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

17

Combined Analysis: Extract Transversity Distributions

Transversity, δq(x)Tensor Charge

Lattice QCD: Tensor Charge

Factorization + Evolution

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)

19

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

HERMES SIDIS (p)

+ COMPASS SIDIS (d)

+ 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

20

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

dkxqkddde

AhqhS

qq

hShqSqhS

qq

CollinsUT

tra

nsversity

Collins F

F

Collins Extraction of Transversity:unknown Transverse Momentum Dependences!

Interference Fragmentation–thrust method

• e+e- (+-)jet1()jet2X• Find pion pairs in opposite hemispheres• Observe angles 1+2 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)collinear factorization

• Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)]

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

• Independent Measurement• Favourable in pp: no Sivers

21

21221111 m,zHm,zHA cos

2

1

1hP

2hP

2h1h PP

Model predictions by:

•Jaffe et al. [PRL 80,(1998)]

•Radici et al. [PRD 65,(2002)]

Expected sensitivities for ~580 fb-1 () ()

Minv<0.4 GeV 0.4 GeV<Minv<0.55 GeV 0.55 GeV<Minv<0.77 GeV

0.77 GeV <Minv< 1.2 GeV 1.2 GeV Minv< 2.0 GeV

A A A

A A

() () A

A AA AMinv<0.4 GeV

0.4 GeV<Minv<0.55 GeV 0.55 GeV<Minv<0.77 GeV

0.77 GeV <Minv< 1.2 GeV 1.2 GeV Minv< 2.0 GeV

() (K)

Minv<0.7 GeV 0.7 GeV<Minv<0.85 GeV

0.85 GeV<Minv<1.0 GeV1.0 GeV<Minv

A A

A

A

A

25

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

BELLE kT dep. Pol. & upol FF, pol. Lambda FF

26

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 planeR : from polarization vector

to scattering plane S

Bacchetta and Radici, PRD70, 094032 (2004)

2 CR..............

Models

• Main contribution: interference of hadron pairs produced in relative s and p wave

• P wave from Vector meson decay

• S wave from non-resonant background

• Signal around vector meson mass

Jaffe, Jin and Tang, PRL 80 (1998) 1166Bacchetta and Radici, Phys. Rev. D 74, 114007 (2006)

• Two different theoretical models gave different prediction of mass dependence

• Sign change is not observed in HERMES/COMPASS results

SSA from di-hadron production

See Talk R. Yang

IFF in SIDISIFF in SIDIS

R defined by:

R = (z1p

2 – z

2p

1)/(z

1+z

2)

(X. Artru, hep-ph/0207309)

R

Di-Hadron SSA in SIDIS

Summary & Outlook

• Collins FF at Belle final ->global analysis• 2H Interference FF Analysis underway

• Plans for kT dependent Pol. & Upol. FFs

– Necessary for global analysis w/o model assumptions

• Polarized Lambda FF• 2H Interference FF Measurements at Phenix, HERMES and

COMPASS– Non vanishing effect at HERMES and COMPASS– Together with Belle results -> Independent extraction of

transversity

Proposed Transverse Spin Sum rule

Bakker, Leader, TruemanPhys.Rev.D70:114001,2004

xx L+δΣ=S=2

1

2

1

Gluon contribution is Small (Phenix, Compass results)