03/03/31 日本物理学会 1 hermes による横偏極水素標的を用いた quark transversity...

03/03/31 日本物理学会 1

HERMES による横偏極水素標的を用いた quark transversity の測定

　大須賀弘 , 田中秀和 , 宮地義之 , 柴田利明 , 　他 HERMES Collaboration

東京工業大学柴田研究室

03/03/31 日本物理学会 2

OutlineOutline

•Transversity - What is the Transversity? - Motivation of the Transversity Measurement - How to Access the Transversity

• HERMES Experiment

( 27.6 GeV e+ + N Deep Inelastic Scattering)

• AUL(φ) Single-Spin Asymmetry and Transversity (analyzed)

• AUT(φ) Single-Spin Asymmetry and Transversity (in progress)

• Conclusion

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NotationNotation

Quark Number Density: q(x) F⇒ 1(x)

Quark Helicity: Δq(x) g⇒ 1(x)

Quark Transversity: δq(x) h⇒ 1(x)

introduced by Jaffe and Ji in their classificationPhys. Rev. Lett. 71 (1993) 2547

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What is the Transversity?What is the Transversity?

Quark Number Density: q(x)

q q xqexF )(

2

1)( 2

1

Quark Helicity: Δq(x)

q q xqexg )(

2

1)( 2

1

Quark Transversity: δq(x)

q q xqexh )(

2

1)( 2

1

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MotivationMotivation

The difference between helicity distribution Δq and transversity distribution δq ⇒ measure of the relativistic effects for quarks inside the nucleon

Relativistic Effects for Quarks inside the Nucleon

)()( xqxq for non-relativistic quarks

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Characteristics of TransversityCharacteristics of Transversity

• for relativistic quarks :

• transversity distribution CHIRAL ODD

• Bounds:

　　　　　　　　　　　　　　 ( Soffer Bound )

• q and q contribute with opposite sign to the transversity ⇒ predominantly sensitive to valence quark polarization

)()( xqxq )()(

2

1)( xqxqxq

)()( xqxq

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How to Access TransversityHow to Access Transversity

Collins Effect with Transverse Target

- Cleanest method is

- effect already visible using a longitudinally polarized target

1sin qHAUT

dAA UTUT )(sinsin sinφ moment :

)(UTAAzimuthal Asymmetry with Transversely Polarized Target :

U: Unpolarized BeamT: Transversely Polarized Target along Beam Direction

Azimuthal Angle :

the angle between lepton scattering plane and hadron production plane

)(1 zH : Collins Fragmentation Function (T-odd, Chiral odd)

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HERMES at DESY-HERAHERMES at DESY-HERA

• target: gas target in internal storage cell • PID: RICH, TRD, Preshower, Calorimeter

8 m

e+ beam

27.6 GeV

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Transversity Measurement at HERMESTransversity Measurement at HERMES

HERMES 1995-2000

HERMES 2002-

Longitudinally Polarized Target

Transversely Polarized Target

⇒ Quark Helicity Distribution: Δq ⇒ Glimpse on Quark Transversity Distribution: δq

⇒ Quark Transverse Distribution: δq

(analyzed)

(in progress)

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Azimuthal Asymmetry withAzimuthal Asymmetry withLongitudinal Longitudinal Polarized Target (analyzed)Polarized Target (analyzed)

Longitudinal Target Spin Asymmetry:

)()(

)()(1)(

NN

NN

PA

tUL

• significant sinφ dependence observed for π+ and π0

• sin 2φ moment consistent with zero for all pions

π0

π-

π+

π0 : Phys. Rev. D64 (2001) 097101π± : Phys. Rev. Lett. 84 (2000) 4047-4051

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Sinφ Moment of the Azimuthal Asymmetry (analyzed)Sinφ Moment of the Azimuthal Asymmetry (analyzed)

HERMES: Phys. Rev. D64 (2001) 097101

SL (T) : component of the longitudinal (transverse) target polarization in the virtual photon frame

q q

qqT

qqLqLUL zHxqxeySzHxxhe

yQ

ySA )()()1()()(

1

)2(2 ,1

2,1

2sin

z x p ⊥ (GeV)

sinφ moment of the azimuthal asymmetry: sin

ULA

π0

π+

π-

15.012

yQ

MxST

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Transversity Measurement at HERMESTransversity Measurement at HERMES

HERMES 1995-2000

HERMES 2002-



⇒ Quark Helicity Distribution: Δq ⇒ Glimpse on Quark Transversity Distribution: δq

⇒ Quark Transverse Distribution: δq

(analyzed)

(in progress)

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Target MagnetTarget Magnet

• Transverse target ( B = 0.295 T )• Transversely polarized hydrogen• Target polarization above 80%

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Azimuthal Asymmetries with Transversely Polarized Target(unpolarized beam)

q

qq

q

qq

UT zDxqe

zHxqeA

)()(

)()(

12

,1

2

sin

ls : Collins Angle

ls : Angle between Target Spin Vector

and Scattering Plane

)(1 zH : Collins Fragmentation Function

Azimuthal Asymmetry withAzimuthal Asymmetry withTransversely Transversely Polarized Target (in progress)Polarized Target (in progress)

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Integrated Deep Inelastic Scattering eventsIntegrated Deep Inelastic Scattering events

0 100 200 300

Total DIS : 512K

Day of Year (2002)

5000

4000

3000

2000

1000

0

×102

Nu

mb

er o

f D

IS

even

ts • 2002: 512 K DIS events

(accumulated)

• Up to Spring 2003: 1.3 M DIS events

(in progress)

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ConclusionConclusion

• HERMES is a deep inelastic scattering experiment using HERA 27.6 GeV positron beam　• Transversity is the distribution of the quark’s transverse spin in a transversely polarized nucleon• The transversity measurement can provide a measure of the relativistic effects for quarks inside the nucleon•HERMES　　　　 suggests both δq and significantly non-zero• HERMES is taking data with transversely polarized hydrogen target• Spring 2003: 1.3 Million DIS events expected• HERMES will do the first determination of transverse u-quark distribution

sinULA

1H

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How to Access TransversityHow to Access Transversity

• Drell - Yan Process

•Λ-hyperon Semi-Inclusive Deep Inelastic Scattering

• Collins Effect with Transverse Target



11sin HhAUT

AdAUT sinsinsinφ moment

UTAAzimuthal Asymmetry with Transversely Polarized Target

U: Unpolarized BeamT: Transversely Polarized Target along Beam Direction

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q q

qqT

qqLqLUL zHxqxeySzHxxhe

yQ

ySA )()()1()()(

1

)2(2 ,1

2,1

2sin

　

Sinφ Moment of the Single Spin AsymmetrySinφ Moment of the Single Spin Asymmetry

HERMES, Phys. Rev. D64 (2001) 097101

• Larger for π+,π0 than π-

⇒ u-quark dominance in case of proton target• Peak around x=0.3 ⇒ valence quark dominance

SL (T) : component of the longitudinal (transverse) target polarization in the virtual photon frame

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Deep Inelastic Scattering (DIS)Deep Inelastic Scattering (DIS)

lepton

nucleon

γ

hadron

)(E,k k

) (M,P 0

),(E'k' k'

)(ν,q q

θ

)p,(Ep hhhadronization

fragmentation

2MνQ

x

, 2θ

sin 4EE'qQ

2

222

νE

z h

Inclusive

Semi-inclusive

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SSA with Longitudinal Polarized TargetSSA with Longitudinal Polarized Target

Longitudinally polarized in experiment(along beam direction) L/T polarized in theory

(along virtual gamma direction)

UTTULLUL SSA sinsinsin ～

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quark (u,d,s)gluon

Sz

gqZ LGLS 2

1

2

1

Spin Structure of the Nucleon

Contribution from the quark spin

1988: EMC

1988-2000: SLAC, CERN, DESY

17.012.0

4.0...2.0

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HERMES 1995-2000

HERMES 2002-



⇒ Quark Helicity Distribution: Δq

⇒ Remaining Quark Transverse Distribution: δq

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History of TransversityHistory of Transversity

The concept was Introduced by Ralston and Soper (1979) via Drell - Yan Production with polarized beams

LO anomalous dimensions were first calculatedby Baldracchini et al. (1981)

Also calculated (for g2 evolution) - Kodaira et al. (1979) - Antoniadis and Kounnas (1981) - Bukhvostov et al. (1985) - PGR (1986)

Re-calculated by Artru and Mekhfi (1990)

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Twist-2 Quark Distribution FunctionsTwist-2 Quark Distribution Functions

・　

• Functions Surviving on Integration over Transverse Momenta• The others are sensitive to intrinsic < kt > in the nucleon and in the fragmentation process

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How Access TransversityHow Access Transversity

• Collins Effect with Transverse Target

• Λ-hyperon SIDIS

• Drell - Yan Process



11sin HhAUT

11)()(

)()(hh

XllPPdXllPPd

XllPPdXllPPdADYTT

- Method requires significant spin transfer from quark to Λ in fragmentation process…

- low rate of quark fragmentation into Λ-particle ( ～ 2%)

03/03/31 日本物理学会 1 hermes による横偏極水素標的を 用いた quark transversity...

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03/03/31 日本物理学会 1 hermes による横偏極水素標的を用いた quark transversity...