Azimuthal asymmetries in hadron production at e+e- collider and

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Azimuthal asymmetries in hadron production at e+e- collider

and chiral odd fragmentation function

Ogawa Akio Penn State Univ. / BNL (STAR)Daniel Boer Riken BNL Research Center (Theorist)Matthias G. Perdekamp Riken BNL Research Center(PHENIX)

From RHIC Spin Collaboration

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Outline

•Introduction•What is Collins Fragmentation Function•What is Interference Fragmentation Function(IFF)•Measurement at e+e-

•Applications•Transversity•Single spin asymmetries

•Conclusion

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Fragmentation Function(FF) “Probability of a parton to hadronize into a specific final state”

Factorization theorem ensures universality

Collins FF & 2 pion interference FF Initial parton with transverse spin - chiral odd Azimuthal asymmetry in hadron final state

Currently unknownTheoretical Interests : Q2 evolution is as fundamental as PDF

Polarized DIS & pp experiment can measure FF*TransversityUnpolarized e+e- experiment can measure FF*FF

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psr

γθ

⊥ps

r

γθsinpp ssr

=⊥

Non-zero transverse polarization!

θγ ≈150 mrad

HERMES result on azimuthal asymmetry beams

r

psr

π

Results shows thatboth Collins Function andTransversity are non zero, and rather large

l

p

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Collins Fragmentation Function : H

Z = Eh / Eq

angle between S and kT around quark (jet) axis

A∝ H(z)sin(φ) =H(z)r s ⋅(

r q ×

r h )

A =s

q

skT

h

kT

h

φ

q

q

s h)sin(φ∝

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2 pion interference fragmentation function : F

Zpair = (Eπ+ +Eπ- ) / Eq

m = invariant mass of 2 pionsangle between s and r

sq

+π

−π

q

+π

−π

A∝ F(z,m)sin(φ) =F(z,m)r s ⋅(

r π −×

r π +)

s

A = rr

)sin(φ∝φ

q

s +π

−π

−+

+−+

−+−

−=

=

=

ππππ

ππ

ππ

rr

r

r

r

zpz

zpzpair

pair

/

/

The same thing for KK around

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Strong interaction phase shifts

d2Fdzdm2 ∝sinδ0e

iδ0 κ ⋅ ˆ q I (z) +λ ⋅δˆ q I (z)( )sinδ1e−iδ1 +...

ππS- p wave interference around mass

Bin +

Bin -

Non-vanishing “Analyzing power”

above and below mass

and flip sign

Requires mass Resolution Great for systematic study

ρ

P. Estabrooks and A.D. Martin, Nucl. Phys. B79 (1974)301

ˆ q I(z),δˆ q I (z)

A model of Interference Fragmentation Function

ρ−σSpin average,

difference FF

8)2cos()()(

)cos()()(

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2121

φφφ

zHzHzHzHA

=+∝

e+e− → (π +)jet1(π−)jet2 X

+e

−e

+π−π

1φ2φ

+e

−e

+π

φ−π

jet1jet2

Without using jet axis

Spin of quarks are 100% correlated!

n

n

9

€

A∝F(z1,m1)F (z2,m2)cos(φ1 +φ2)

e+e− → (π +π−)jet1(π+π−)jet2 X

+e

−e

+π

−π

1φ2φ

jet1jet2

Spin of quarksare 100% correlated!

+π

−π

n

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In e+e-

Jet production from light quark Off resonance dataExclude b

fragmentsHigh enough energy to produce jet Finding jet

to apply pQCD s~100GeV2

But not too high energy FF decreases as energy increases s(Belle) << s(LEP)

Observing Q2 evolution is interesting Avoid extra complication from Z pole √s(Belle) < Mz

Requires good detector: Wide acceptance Momentum/mass resolution great PID capability

The beauty of e+e- is H*H and F*F can be measurd!

At Belle

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q

qΔ

qδ

g

gΔ L

Helicity average

Helicity difference

RHIC,Compass,Hermes...

-

-

Momentum

Leading twist quark distribution

F =q2

I ×I +Δq2

σ3 ×σ 3 +δq2

(σ+×σ− +σ−×σ+)

Transversity is the last missing piece at leading twist quark distribution

Well measured at DIS,pp

Well measured at pol. DIS

×

×

Helicity flip ?DVCS?

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The transversity function

Helicity flip amplitude = Chiral odd function not accessible in (inclusive) DIS

Naively for non-relativistic quarks Relativity breaks rotation symmetry.

Soffer’s bound:

Need not to be small! Possibly

Gluon (spin1) cannot flip proton (spin1/2) helicity does not mix with gluons under evolution

Non-relativistic Relativistic

First Lattice QCD result

δq=Δq

),(),(),(2 222 QxqQxqQxq iii Δ+≤δδqi ≈ Δqi

),( 2Qxqδ

δΣ =δu+δd+δs=0.56±0.09S. Aoki, M. Doui, T. Hatsuda and Y. Kuramashi Phys.Rev. D56 (1997)433

More recently: S. Capitani et.al. Nucl. Phys. B (Proc. Suppl.) 79 (1999) 548

ΔΣ =1

δΣ =1

δq≠Δq

ΔΣ ~0.6(theory)

ΔΣ ~0.2(exp)

δΣ =?

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2P

iqδ

iq

11Px

22PxijσΔ

1psv

F

σ ρ,

+π−π

Jet

Jet

d6σH pp↑ → π+π −X( )

dx1dx2dtdzdm2dφ∝δq(x1) ⋅q(x2) ⋅

d3σ (q1q2 → q3q4)dx1dx2dt

⋅d3F

dzdm2dφProtonStructure

Hard Scattering Process

InterferenceFragmentation

Jian Tang , Thesis MIT, June 1999

R. Jaffe, X.Jin, J. Tang Phys. Rev. D57 (1999)5920

X. Ji, Phys. Rev. D49 (1994)114J. Collins, S. Heppelmann, G. Ladinsky, Nucl.Phys. B420 (1994)565

Nucleon Transversity at p p

1P

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The Relativistic Heavy Ion Collider at Brookhaven National Laboratory

RHIC acceleratesheavy ion (Au)

up to 100 A GeVand

polarized protonup to 250 GeV

PHENIXSTAR

2000 run was successful!

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Au on Au Event with CM Energy 130 GeV*A

L3 Event Display June 25, 2000.

STAR detector

Heavy Ion physicsSpin physicsPhoton/pomeron physics

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Muon IDPanels

CentralArms

North MuonArm

South MuonArm

Ring ImagingCerenkov

Muon TrackingChambers

Beam-BeamCounter

Multiplicity/VertexDetector

Time ExpansionChamber

Drift Chambers

Pad Chambers

Time of FlightPanels

EM Calorimeter

The PHENIX Detector

π+

K+ p

p−K

0π

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Inclusive pion single spin asymmetry at p p ( p C)

xF xF

Fermi Lab E704 200GeV BNL E925 22GeV

There is not fully satisfactory explanationCollins effect? Twist 3?

RHIC STAR (BRAHMS?) will measure at

€

s=200−500GeV

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π+π − Interference Fragmentation: AT p⊥ +p→ jet(π +,π −)+X( ) ⇔ δq⋅F

Future Transversity Measurements at Polarized pp & polarized DIS

Drell Yan: ATT(p⊥p⊥ → ll)⇔ δq⋅δq

Collins Effect : AT(lp⊥ → l +π +X) ⇔ δq⋅ H

Collins Effect : AT p⊥ +p→ jet(h)+X( ) ⇔ δq⋅H

BNL - Star/Phoenix/Phobos

DESY-Hermes & CERN-Compass (BNL eRHIC, DESY Tesla-N)

Requires H*H & F*F measurement from e+e-

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Conclusion•There are interesting and currently unknown fragmentation functions : Collins FF and IFF

•We propose to analyze existing Belle data to extract these FF.

•Large interests•CERN-LEP-DELPHI analysis on the same FF at different energy•BNL-STAR & PHENIX Experiments (BRHAMS & PHOBOS)•CERN-SPS-COMPASS, DESY-HERMES•(BNL eRHIC, DESY Tesla-N)

•“Workshop on transverse spin physics” at DESY-Zeuthen, Germany 2001 July 9-11th

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Proton Proton Scattering

Three independenthelicity amplitudes:

12

12

→ 12

12

12

- 12

→ 12

- 12

⇒ f1 (helicity average)

g1 (helicity difference)

12

- 12

→ - 12

12

⇒ h1

h H ′H h′

H

h

H ′

h′

…H Proton helicity …h quark helicity

helicity flip!

H

h h′

Deep Inelastic Scattering

H ′

Helicity Amplitudes

function structure twist leading

unmeasured last the remains

functionty transversi The 1h