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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