Jan 12, 2008 KEK研究会 「核子の構造関数2008」

HERMESによる核子のスピン構造測定結果と他の高エネルギ－反応過程へのインパクト
Toshi-Aki ShibataTokyo TechContents:• Deep Inelastic Scattering: lepton scattering and pp collision• Unpolarized and Polarized Gluon Distribution• Quark Helicity Distribution – Flavor Separation• Physics with Transverse Targets• Impact on other high energy reaction processes

Proton Spin from Viewpoint of Quark Flavors
1/2

SU(6) Quark Wave Functions of Baryons
1/2

Sum of Spins of u u d Quarks = Spin of Proton
12-1/2

12+1 ⎞⎛⎜ −⎟2⎝⎠+=1/2++=1
1= ∑ ( Δ u + Δ d + Δ s ) + L q + Δ G + LG
22 q12

HERMES:• Inclusive Deep Inelastic Scattering, A1(x), g1(x)• Semi-inclusive Deep Inelastic Scattering – Hadron Identification
Flavor DecompositionΔu ( x ), Δd ( x ), Δu ( x ), Δd ( x ), Δs ( x )• Large pt hadrons:Δg (x)• Deeply Virtual Compton Scattering andExclusive meson productions:
Generalized Parton Distribution Æ Jq
• Single spin asymmetry, transversely polarized target:
Sivers effect - Lq, orbital angular momentum
Collins effect - New structure function

Impact on RHIC, J-lab, COMPASS, Polarized Drell-Yan,
Neutrino Scattering Experiments etc.

Electron- Nucleon
Deep Inelastic Scattering

Bjorken x

Q2− q2xB ==2q • P 2 MνInclusive measurement, e’ee’σ ( xB ) ∝ F2 ( xB ) = xB ∑ eq2 q( xB )q

Semi-inclusive measurement,e’ and π , K, p, p ...

σ h ( xB , z ) ∝ xB ∑ eq2 q( xB ) Dqh ( z )q

( quark distribution ) x( fragmentation function )z = E h /νFragmentation in e+e- annihilation

pp collisions

ALL ∝ Δg( x1 ) g1 ( x 2 )gg, gq… collisions
measured as a function of pt
xbj, z integrated
two xbj’s involved in each eventｘ ｒｅｓｏｌｕｔｉｏｎ
Lepton scattering (l, l’ h)
l’ detected-- x is determined event by eventl’ undetected, only h is detected -- x is spread and is compared with MC
pp collision
jet – jet coincidence-- x1, x2 are determined event by event
jet – prompt photon coincidence -’’inclusive hadron measurement-- x is spread and is compared with MCpp → π 0 X

Unfold, or assume a functional formand compare to the data

0.01

Log10(x)Gluon Distributions- Unpolarized and PolarizedDURHAM HEP Databases, online plot
http://durpdg.dur.ac.uk/hepdata/pdf3.html

S. Kretzer, H.L. Lai, F.I. Olness, W-K. Tung
Phys.Rev. D69 (2004) 114005

ＣＴＥＱg (x)x g (x)(log x ) = 011∫(log x )=−∞x g ( x) d (log x) = ∫0 x g ( x) x dx = ∫0 g ( x) dx
1Linear momentum
1First moment∫ g ( x) dxx| Δg ( x) | ≤ g ( x)1Second Moment∫ x g ( x) dxx

111Δg ( x ) = N x α (1 − x ) β g ( x )000Δg ( x) ∝ xα g ( x) at x → 0| ∫ Δg ( x) dx | ≤ ∫ | Δg ( x) | dx ≤ ∫ g ( x) dx

Δg (x)
Lepton scattering
hadron pair production
charm-anticharm production

pp collisions
π0 production
prompt photon production (gq → qγ)…

Δg ( x ) / g ( x ) from lepton scattering

pp collision

pp → π 0 X

ＧＲＳＶΔg ( x ) = N x α (1 − x ) β g ( x )Δq( x ) = N ' x α ' (1 − x ) β ' q( x )…
12 parametersχ 2 increase by 1 ↔ one σ
PHENIX’s error evaluationdifferent from AAC’s approachHelicity Distributions of Partons in the Nucleon

Contents:
・ A1 and g1 Measurement• Semi-inclusive Measurement of Hadrons with a precise PID• Flavor Separation of Quark Helicity Distributions

Quark Helicity Distributions,

Flavor Separation

Double-spin asymmetryr r
e + N → e′ + X

Beam and target, both polarized

....

....
Virtual photonNucleon....
→σ→← (x ) − σ → (x )A 1( x , z ) = →σ ← (x ) + σ →→ (x )....

Proton Spin Problem

EMC Experiment (1988)

EMC’s Flavor Decomposition with First Moments
1pg∫ 1 ( xB ) dx
01
1
( Δu + Δd + Δs ) = 0.06 ± 0.047 ± 0.068 ≤22(12 ± 9 ± 14)%
‘Quark spin contribution to the proton spinis small’: Nucleon Spin Problem
SMC, SLAC, … 20 – 30 % of Nucleon Spin

0.01 < xB < 0.6

1
1= ( Δ u + Δ d + Δ s ) + Lq + S g + L g22

Main Features of HERMES：HERa MEasurement of Spin
1995 –2007 at DESY
• Polarized Electron (Positron) Beam of HERA
E = 27.6 GeV, P ≈ 60%• Internal Gas Targets
Longitudinally polarized 3He, D, HP（H） 85%
Transversely polarized H
Unpolarized High Density Targets (H2, D2, He, N2, Ne, Ar,Kr, Xe)• Semi-inclusive Measurement, Hadron Detection with a good
PID of π , K, p
Ring Imaging Cherenkov Counter （RICH)

Flavor Separation of Quark Helicity Distributionsat HERMES

Δu ( x ), Δd ( x ), Δu ( x ), Δd ( x ), Δs ( x )g1(xB) from HERMES and other experiments

pxBdQuark spin contributions to the nucleon spin, 33%

e + N → e′ + π + + X , etc.

Semi-inclusive measurement:
Aπ+Aπ−

AK..

...

+K-Au →π +,

=K+

RICH

ΔuΔdΔsΔuΔuΔdΔd..

Result:ΔuΔdΔsΔu ( xB ) > 0Δd ( xB ) < 0Δq ( xB ) ≈ 0• x bin by bin analysis• First moment from neutron lifetime or hyperon decay,not used• No functional forms as a function of x are assumed• Helicity conservation not assumed ( Δq → 1 when xB → 1)

Conclusions of this part
• HERMES is a Deep Inelastic Scattering Experiment
at HERA-DESY with 27.6 GeV Electron (Positron) Beamand Polarized Internal Gas Targets• π ,K, p Identification with RICH
• A1(x), g1(x), and A1h(x) are measured• Flavor Separation of Quark Helicity Distribution Δq (x )from Semi-Inclusive Measurement with π , K Identification
for the First Time, an Independent Extraction from data of DIS• Positive u, negative d Distributions, Sea Quarks nearly zeroFurther new approaches – Access to total angular momentum of quark Jq

11= ( Δ u + Δ d + Δ s ) + Lq + S g + L g
22Jq
Ji’s sum ruleJg

PRL 78 (1997) 610

11J q = lim ∫ dx x [H q ( x , ξ , t ) + E q ( x , ξ , t )],2 t →0 −1
J g = ...

Generalized Parton
Distributions (GPD)
Structure Functions
Form Factors

How to measure
Deeply Virtual Compton Scattering(DVCS)and exclusive meson productions
Cross section of DVCS ismeasured at H1 and ZEUS
Interference with Bethe-Heitler ismeasured at HERMESeγ∗γ (π , ρ )x +ξx −ξH,E,…

Interference between

Deeply Virtual Compton Scattering
HERMES

Bethe-Heitler

CLAS at JLabALUφφBeam Spin Asymmetry: ALU
Beam Charge Asymmetry: Ac
Longitudinal Target Spin Asymmetry: AUL
Transverse Target Spin Asymmetry: AUT

ＪuＪｄExclusive meson productions also give access to GPD.

11126 GeV CEBAF
Upgrade magnets
and power
supplies

CHL-2

Enhanced capabilities
in existing Halls

Lower pass beam energies
still available

Access to the DIS Regime @ 12 GeVwith enough luminosity to reach the high-Q2, high-x
region!

Counts/hour/(100 MeV)2 (100 MeV2)
for L=1035 cm-2 sec-1

Extending DIS to High x
The Neutron to Proton
Structure Function Ratio< Projection >The Neutron Asymmetry A1(similar precision for p and d)

Hall C: 3H/3He
CLAS: tagging
spectator proton

12 GeV will access the valencequark regime (x > 0.3)
A. Brull, Pacific-Spin07

3He(e,e’)Single Spin Asymmetry with a Transversely Polarized
Hydrogen Target at HERMES- Separation of Collins Effect and Sivers EffectFourier Amplitude< sin(φ + φS ) > UTis expectedfrom the Transversity h1(xB)
h1(xB) is coupled with fragmentation function
which is measured in fragmentation at e+e- collider
Belle at KEK.

γ∗
1.

F2 ( x B ) = x B ∑ e q2 q ( x B )
q

γ∗
2.

g1 ( x B ) = 2 ∑ e q2 Δ q ( x B )qhelicity3.

h1 ( x B ) ∝ ∑ e q2 δ q ( x B )qtransversity

Why Are Quark Transversity Distributions δ q (x ) Interesting?

δ q ( x ) ≠ Δq ( x ) ⇒ proves Quark’s Relativistic Nature in theNucleon
Because of Lack of Transversity of Gluon, Q2 Evolution
Should Be Different From That of q (x ) and Δq (x ) .
Collins Effect: Chiral Odd. So Far Never Measured
2T⊥
12Th1 ( x , p ) H (z , k )Sivers Effect:
⊥1T

2
T

pT initial quark transverse momentum
kT final quark transverse momentum

could be related to orbital motion of quarks
2
Tf ( x , p ) D1 (z , k )The separation of the two effects was carried out for the first time.

Access to orbital angular momentum of quarks:Lq Sivers mechanism

11= ( Δ u + Δ d + Δ s ) + Lq + S g + L g
22Two azimuthal angles φ s , φin semi-inclusive measurement of π , K with a transversely
polarized targete’erS⊥rS⊥reaction planeφ − φspTπ

Fourier Amplitude

Target polarization
P = 0.78 ± 0.04

< sin(φ − φS ) > UT
expectedAzimuthal Single Spin Asymmetry
Asymmetry around the virtual photon direction

Fit in 2-dimension(φ ,φ s ) in each x bin

AUT (φ ,φs ) = 2 < sin(φ + φs ) >1UT sin ( φ + φs )Collins+ 2 < sin(φ − φs ) >1UT sin(φ − φs )SiversFourier Component

π ,KSivers Amplitudes for

non-zero orbital angularmomentum

π +, K+ amplitudes significantly positive
π −, K− amplitudes consistent with 0Conclusions of this part
• The separation of Collins effect and Sivers effect was carriedout for the first time.
• Non-zero asymmetry is observed for Collins asymmetry.
Positive π + asymmetry, negative π − asymmetry are compatible
with helicity distribution Δq (x ). But the amplitude of π −asymmetry is large.
• πasymmetry is positive, and π − asymmetry is nearly 0for Sivers asymmetry.
+Spin Structure of The Nucleon and Related Topics
Q2 = 0, Real Photon: (GDH Integral)

Q2 > 0, Lepton Scattering:Mainz, Bonn, JLab,
SPring8, LEGS at BNLHERMES at DESY-HERACOMPASS at CERNJLab (CEBAF) Æ 12 GeVSLAC

Hadron Reaction : RHIC SPIN

J-PARC, GSI
e+e- Collider: Belle

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Over 500 experimental physicists

SummaryGluon distribution, Unpolarized and polarized
Several approaches with lepton scattering and pp collisions
Quark helicity distributions, quark flavor separation
Physics with transversely polarized proton
Collins effect
Sivers effect - Orbital angular momentum
Generarized Parton Distributions -- Jq
Fragmentation processes – Fragmentation functions
Impact on programs of COMPASS, J-lab, RHIC, polarized Drell-Yan,
Neutrino Scattering Experiments etc.