HERMES の偏極深非弾性散乱による核子構造の研究
田中 秀和
東京工業大学
基礎物理学専攻

核子スピン構造 ～スピン危機～
深非弾性散乱 （ DIS ）HERMES 実験と最近の結果- クォーク偏極度- クォークの新たな分布関数- Sivers & Transversity
まとめHidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 1

Spin Puzzle
Gluon spin distribution

Quark helicity distribution  ≡u d  u  d  s  sG

1
1=   G  Lq  L g
2
2
Orbital angular momentaof quark and gluon

L q L g
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 2

Deep Inelastic Scattering (DIS)
Inclusive(Only scattered lepton
is measured)

lepton*FragmentationQ , q q  xnucleon
P  M , 0UnmeasuredDz

x : Quark momentum fraction(Bjorken scaling parameter)z : Fractional energy of produced

Semi-inclusive(Hadron coincidence
measurement with thescattered lepton)

M : Target mass
Q : Virtual photon 4-momentum
 : Virtual photon energy

hadronHidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 3

Polarized DIS
virtual photone

Beam spinvirtual photon

qf+(x)
Polarized Quark Distribution

Target spinΔqf (x) ≡ qf+(x) - qf-(x)qf-(x)eBeam spin

Target spin

Unpolarized Quark Distribution

qf (x) ≡ qf+(x) + qf-(x)Inclusive/Simi-inclusive Spin Asymmetry A12 =σ e/h - σ e/h
A1 (x,Q )+e/h
σσ e/he/h

g1~F1g 1 ~  q : Polarized structure function
F 1 ~ q : Unpolarized structure function
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 4

DIS with NC and CCCC

NC±γ/Z12g 1 = x ∑q e q  q q21Z
22g 1 = ∑q  g V  g A q  q q
2WggW+1W1−= u  d  s = u d  s NC process : Includes all quark flavors
CC process : Sensitive to sea-quarks
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 5

Deep Inelastic Scattering (DIS)
Inclusive(Only scattered lepton
is measured)

lepton*Q , q 

Structure Function
F i  x ,Q 2  : Unpolarizedg i  x ,Q 2 nucleon
P  M , 0

M : Target mass
Q : Virtual boson 4-momentum
 : Virtual boson energy: Polarized

Parton Distribution
2q  x , Q  : Unpolarized2

 q  x , Q  : Polarizedx : Quark momentum fraction(Bjorken scaling parameter)

Q2
x=
2M 

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 6

The HERMES Experiment

The HERMES experiment have been running since 1995
to investigatie the nucleon spin structure.
- 27.6 GeV longitudinally polarized electron(positron) beampolarization: up to ~ 60 %- Polarized Internal Gas Target
longitudinally polarized atoms: H, D,3He
polarization : ~ 90%
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 7

The HERMES Experiment
HERMES ＠ ドイツ・ハンブルグの DESY 研究所

HERA:e+ : 27.6 GeV
p : 820 GeV

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 8

Polarized e+ Beam

• Self-polarization by emission of synchrotron
radiation• Average beam polarization <pb> ~ 55 %Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 9

HERMES Spectrometer

Side view

Preshower counter

Magnet(Hodoscope)

E.M. Calorimetere+~5 m

Target Cell

RICH~10 m
Filled in red : Tracking detector , in blue : PID detectors
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 10

Internal Gas Target
Open-ended storage cell

40 cm
•Atomic Beam Source (Stern-Gerlach separation)•Undiluted internal targets :–H,D,3He longitudinally polarized atoms•Polarized target polarized H/D (1996 ~ 1999) :~1014 N/cm2–PT~ 90 %, •Unpolarized gases :–H,D,3He,14N,83Kr…, 1015 ~ 1017 N/cm2
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 11

HERMES Spectrometer

Side view

Preshower counter

Magnet(Hodoscope)

E.M. Calorimetere+~5 mTarget Cell

RICH~10 m
Filled in red : Tracking detector , in blue : PID detectors
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 12

Ring Imaging Cherenkov Detector
1998 ~ 2000 dataΘ ｃ (rad)Cherencov angle(Θ ｃ ) vsPMT Plane

Momentum (GeV/c)

Aerogel Tiles

Mirror
C4F10 Gas
Aerogel Tilesa ckrtcl eitrpa

C4F10 Gas

•P (GeV/c)••Radiator– C4F10 Gas n=1.0014– Aerogel Tiles n=1.0303
PMT– 3/4 inch 1934 PMTs
Momentum region– 2 ~ 15 GeV/cHidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 13

Ring Imaging Cherenkov Detector

3.1 GeVpion

4.5 GeV
electron

Ring fromaerogel

Ring fromgas

1934
PMTs

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 14

Double Spin Asymmetry A1
lepton*InclusiveQ  , q

q  x

virtual photoneDzBeam spinvirtual photon

Simi-inclusive

Target spinenucleon
P  M , 0Beam spin

Target spin

Inclusive/Simi-inclusive Spin Asymmetry A1e/hA12 =σ e/h - σ e/h(x,Q )σe/h+Polarized Quark Distribution

Δqf (x) ≡ qf+(x) - qf-(x)σ e/hHidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 15

π+/-

Inclusive

Measured Spin Asymmetry A1h+/-

Data :
Proton target (1996 ~ 1997)
Particle Identification :“Threshold Cherenkov Detector”

A1 =

 −



−

−

 ~ 0.6

−

 :  =4 : 1

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 16

π+/K+/-h+/-Inclusive

Measured Spin Asymmetry A1

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 17

Extracting Quark Polarization
Measured Spin Asymmetry for hadron h in Quark Parton
Model ( QPM )d  h −d  h−

 q  xA  x==∑q P  x⋅
−q  xd  h d  hh1hq

Purity Matrix Method
Extract the quark polarizations Δq/q(x)A = P Q
 A ｈ１（） 1 ｘ
A=  ｈｍ A1 （ｘ）
MeasuredAsymmetries(Input)

 P ｈ１（）
 f１ ｘP = ｈm
Pf （ｘ）
 １hP ｈ１（ｘ）
fn

P fｈm（ｘ）
n（ｘ）
Δ ｑ１/ ｑ１
Q=Δ ｑ/ ｑ（）

nn ｘPurity Matrix

Extracted Quark
Polarizations
Δq/q : polarization

hadron “h” and quark “q”.

Δq : pol. Distribution

Pq ： Correlation between

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.(Output)

p. 18

Purity Matrix_｜ K ＋＞＝｜_u s ＞｜ K ー＞＝｜ u s ＞

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 19

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 20

Extracting Quark Polarization
Measured Spin Asymmetry for hadron h in Quark Parton
Model ( QPM )d  h −d  h−

 q  xA  x==∑q P  x⋅
−q  xd  h d  hh1hq

Purity Matrix Method
Extract the quark polarizations Δq/q(x)A = P Q
 A ｈ１（） 1 ｘ

A=  ｈｍ
 A1 （ｘ）
MeasuredAsymmetries(Input)

 P ｈ１（） f１ ｘ
P =
 ｈm
Pf （ｘ）
 １hP ｈ１（ｘ）
fn

P fｈm（ｘ）
n（ｘ）
Δ ｑ１/ ｑ１Q=Δ ｑ/ ｑ（）
nn ｘ

Purity Matrix

Extracted Quark
Polarizations
Δq/q : polarization

hadron “h” and quark “q”.

Δq : pol. Distribution

Pq ： Correlation between

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.(Output)

p. 21

Extracted Quark Polarization
Positive contribution to nucleon spin in
the measured region.

Negative contribution.

Sea quark contribution almost zero.

  ~ 0.2−0.3  ≡u d  u  d  s  s 
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 22

ここまでをまとめると ...
HERMES 実験では縦偏極 e+ ビームと縦偏極標的を使って偏極核子内でのクォーク偏極度を測定した。
その結果、- u-quark は核子の偏極方向に平行- d-quark は''
反平行- sea-quark は偏極していない ( 核子ないで平均すると )クォークスピンの核子スピンへの寄与はSea-quark を考慮したとしても 20-30 % 程度にしかならない。
核子内には まだ unknown な「構造」が存在している .....
何か手掛かりはあるか ?

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 23

Spin Puzzle
Quark helicity distribution

Gluon spin distribution  ≡u d  u  d  s  s  ~ 0.2−0.3G
now in measuring

Known

11=   G  Lq  L g
22Orbital angular momentaof quark and gluon

L q L g
Unknown ....
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 24

Other Spin-related PDFs
q

qf

⊥
1T

L

Helicity
distribution

Transversity

Sivers function

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 25

What's Transversity ?
Transversity δq describes transverse quark polarization in thetransversely polarized nucleon.

qi??

=q
quark polarizationin the long. pol.
nucleonqquark polarizationin the trans. pol.
nucleonio q −  q = ??
Non-realtivestic limit ;  q− q = 0

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 26

What's Sivers Function ?
⊥1T .

Other quark distribution is “Sivers function” f
The Sivers function describes unpolarized quark in the transverselypolarized nucleon.
??

q x
quark momentum
distributionin unpol. nucleon

Lf⊥
1T x

quark momentum
distributionin trans. pol. nucleon

f⊥
1T

 x

The Sivers function is related toquark orbital angular momentum.

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 27

How do we measure them ?
Inclusive(Only scattered lepton
is measured)

lepton*FragmentationQ , q q  xnucleonP  M , 0UnmeasuredDz

x : Quark momentum fraction(Bjorken scaling parameter)z : Fractional energy of produced

Semi-inclusive(Hadron coincidence
measurement with thescattered lepton)

M : Target massQ : Virtual photon 4-momentum
 : Virtual photon energy

hadronHidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 28

Transversely Polarized DIS
Lepton Scatt.
Plane

Two Azimuthal angles

 S : Angle between S and L.P.
⊥ : Angle between L.P. and H.P.

Hadron Prod.
Planek , k' : Lepton momentum: Virtual photon momentumqphad : Hadron momentum
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 29

Single Target-Spin Asymmetry (SSA)e

Unpolarizede

A UT ≡d∗A

AUT =Transverselyddsin  S  A⊥1∝  q  x H  z Transversity

Ad  −d π production
cross-section

SiversUTsin − S 

Sivers asymmetry

Collins asymmetry
Collins
UT, d  d polarized∗Collins
UT

A

SiversUT∝ f⊥
1T x D 1  z Sivers function

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 30

Contents of the SSA
A UT ≡A

Collins
UTsin  S  Collins Asymmetry

ACollins
UT⊥
1∝  q  x H  z A

SiversUTsin − S 

Sivers Asymmetry
Sivers

AUT⊥∝ f 1 T  x D 1  z Transversity(Polarized PDF)

Sivers function(Unpolarized PDF)&↓

Collins FF(Polarized FF)

Orbital angularmomenta

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 31

1. Collins Asymmetry
AUT =A

Collins
UTsin  S   A

SiversUTsin − S 

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 32

Collins Asymmetry
AUT ≡ACollinssin  S  UTSivers
AUTsin − S 

Collins asymmetry
CollinsAUT⊥∝  q  x H 1  z Transversity(Polarized PDF)  q

h 1 describes transverse quark

polarization in the transversely
polarized nucleon.

H⊥
1Collins FF(Polarized FF)⊥

H 1 describes fragmentationof pol. quark into unpol hadron.

πqProvides information about
relativistic nature of the nucleon.

Collins effects generates singlespin azimuthal asymmetry.

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 33

Measured Collins Asymmetries
ACollins
UT⊥
1∝  q  x H  z π+
Averaged Asymmetries(0.023 < x < 0.4, 0.2 < z < 0.7)π-〈 ACollins〉  0UT〈Aπ0Collins
UT− 〉  00
〈 ACollins
〉 ~ 0UTxz

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 34

Interpretation of Collins Results
well-knownunpol. quantities

Collins asymmetries have
two unknown components.

∑q e q  q  x H 1  z 2ACollins
UT≈q⊥∑q e q q  x D  z 2

Define favored (ex. u→π+) and disfavored (ex. u→π-) FFHfav≡Hu 1

=Hd 
1−= ...

disH ≡Hu  −
1=Hd 
1= ...

π+, π- and π0 asymmetries;
fa v
dis 4  u  d  H   d  4  u  H
A =,favdis
4 u  d  D  4 u  d  D

disfa v

4u

d

H

d

4u

H

A =,
dis
fav
d  4 u  D  4 u  d  D−

0A =Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

....
....
p. 35

Interpretation of Collins Results  r
4HA≡ r4DA
−

Solution space populated according
to statistical error4   r 1  H A≡4  r 1  DA0

Likelihood distribution insolution space ofdis

Hdis / H fav

H
H ≡ fa v
H d  4  ur ≡ u  1 /4 dr

Well-known objects
dis ≡ D
DD favr≡

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

d  4 uu  1 /4 dp. 36

Interpretation of Collins Results  r4HA≡ r4DA−

4   r 1  H A≡4  r 1  DA0

Hdis / H fav solution at CQSM valueδr = - 0.93 (Q2=2.5 GeV2)

r[1] M. Wakamatsu et al., Phys. Rev. D60, 034020

Hdis / H

Hdis / H fav- Chiral Quark Soliton Model (CQSM)[1]- String Model [2][2] X. Artru, hep-ph/9310323

favCollins FF has opposite sign for favored and disfavored(neglecting VM contamination)

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 37

2. Sivers Asymmetry
AUT = ACollins
UTsin  S  ASivers
UTsin − S 

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 38

Sivers Asymmetry
AUT ≡Collins

AUT

sin  S  Sivers

AUT

sin − S Sivers asymmetry
Sivers

AUTUnpol. FF⊥∝ f 1 T  x D 1  z Sivers function

The Sivers function describes unpolarized quark in thetransversely polarized nucleon.

fL⊥
1T x

Non-zero Sivers function
requires quark orbital angularmomentum.

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 39

Measured Sivers Asymmetries
Aπ+Sivers
UT∝ f⊥
1T x D 1  z 

Averaged Asymmetries(0.023 < x < 0.4, 0.2 < z < 0.7)

πSivers〈 AUT  〉  0

3σ away from zero.
Sivers〈 AUT − 〉 ~ 0

π0〈AxzSivers
UT0 〉 ~ 0

Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 40

Interpretation Sivers Results
ASivers
UT∑q e f  x D  z ≈2∑q e q q  x D  z Only one unknown⊥
1T2q

well-known
unpol. objects

Combine π+ and π- asymmetries
⊥u
1T⊥d
1T= f

 1 /4 f

C 3 A  C 4 A − = f

 4 f 1⊥Tu

C1 A

C 2 A−⊥ d
1T

Experimental results indicate;1 ⊥ f 1 T  d  04⊥⊥
f 1 T d   4 f 1 T  u  0⊥f 1 T  u - Non-zero Sivers function.
- Sivers function of u-quark has positive sign.
- Quark angular momentum could contributeto theTANAKA
nucleon
Hidekazu(Tokyospin.
Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 41

Conclusion
Single-spin asymmetry have been measured using
27.6 GeV positron beam and transversely polarizedhydrogen target at the HERMES experiment.
Collins asymmetry;〈A〈ACollins
UTCollinsUT 〉  0
 − 〉  0- Favored and disfavored Collis FF have opposite sign.
Sivers asymmetry;
Sivers〈 AUT  〉  0- First observation of non-zero Sivers effect.
- Sivers function for u-quark is positive.
More data are coming soon (about factor 4 by end of 2004).
Hidekazu TANAKA (Tokyo Tech), 2004 Apr. 30 @ Kyoto Univ.

p. 42