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Experimental Data on Spin Structure Function

For 原子核特論講義資料

Yasuhiro SAKEMI (RCNP)E-mail : sakemi@rcnp.osaka-u.ac.jp

講義内容の追加資料等は、http://www.rcnp.osaka-u.ac.jp/~sakemi/lecture.htmlに随時掲載しますので、そちらも必要に応じて確認してください。

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核子スピンの起源

The spin structure of the proton :

Sz = = ΔΣ +ΔG +LZ

whereΔΣ≡Δu+Δd+Δs

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12

u u

dd

ss

du

u

• Quark spin contribution (ΔΣ ) to the nucleon spin is found to be small in inclusive DIS experiments (EMC,SMC,SLAC,HERMES)

– ΔΣ≡Σ q(Δq + Δq ) ～ 0.2 ... 0.4

• What are the contributions of the different quark flavors ? – The answer is only partially known. – e.g. Strange sea polarization Δs has not yet been measured.

• Further Study !– Hadron coincidence measurement in the polarized DIS– Particle identification with Ring Imaging Cherenkov Counter

(RICH) – Flavor tagging with the final state produced hadrons

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Quark Polarization (Inclusive)

Proton Spin Structure Function g1p(x)

≃≃≃

– g1h(x,Q2) Σf ef

2Δqf(x,Q2)– F1

h(x,Q2) Σf ef2 qf(x,Q2)

A1≃ =

x

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Quark Polarization (Inclusive)

Neutron Spin Structure Function g1n(x)

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Quark Polarization (Semi-Inclusive)

Hadron Asymmetries

• Statistics of proton data ~ high • Data given at mean Q2 of each x• Error :

– Error bars of HERMES : statistical uncertainties– Bands are HERMES systematic error– Error bars of SLAC and SMC : total uncertainties

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Quark Polarization (Semi-Inclusive)

Flavor decomposition of PDF

• Flavor decomposition of quark polarizations as a function of x at measured Q2

• Sea assumption (flavor independent polarization) : – Δqs Δus Δds Δs Δu Δd Δs– qs us ds s u d s

• Result insensitive to sea assumption – another assumption : flavor symmetric sea : checked

≡ = = = = =

Flavor Decomposition of the Polarized Quark Distributions in the Nucleon fromInclusive and Semi-Inclusive Deep-inelastic ScatteringK. Ackerstaff et al, Phys. Lett. B464 (1999) 123-134

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Quark Polarization (Semi-Inclusive)

Polarized Quark Distributions

• Polarized valence and sea quark distributions atQ2 = 2.5 GeV2

• Dotted line : Gehrmann and Stirling (Gluon A, LO)• Sea assumptions :

– HERMES : flavor independent polarization– SLAC : flavor symmetric

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Quark Polarization (Semi-Inclusive)

Comparison to Parametrizations

• Polarized quark distributions at Q2 = 2.5 GeV2 compared to parametrizations

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Quark Polarization (Sum Rule)

xΔqNS and Bjorken Sum Rule

• Non-singlet contribution ΔqNS = (Δu+Δu-Δd-Δd) is directly related to the spin structure functions according to ΔqNS = 6(g1

p(x)-g1n(x)) .

• ΔqNS at Q2=2.5 GeV2 compared to paramerizations extracted from inclusive data

• Bjorken Sum Rule : model independent – ∫0

1ΔqNS (x) dx = |ga/gv|×CQCD

– (experiment) 0.84±0.07±0.06– (prediction:Bjorken) 1.01±0.05– consistent

• Nucleon

integral

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Quark Polarization (Sum Rule)

xΔq8

• Octet combination xΔq8=x(Δu+Δu+Δd+Δd-2(Δs+Δs))at Q2=2.5GeV2 assuming a flavor symmetric sea (open circle) or a flavor independent sea (full circle)

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Quark Polarization (Moment)

Integrals over measured range

• Integral over measured range is obtained as

– Δq = Σi ( |i∫xixi+1 q(x) dx )

– where (Δq/q)|i is constant within each bin [xi, xi+1]

» HERMES SMC– Δuv 0.52±0.05 ±0.08 0.59±0.08 ±0.07– Δdv -0.18 ±0.10 ±0.13 -0.33±0.11 ±0.09– Δu -0.01 ±0.02 ±0.03 0.02±0.03 ±0.02– Δd -0.02 ±0.03 ±0.04 0.02±0.03 ±0.02– Δs -0.01 ±0.02 ±0.02 0.01±0.03 ±0.02

• Comparison of HERMES and SMC integrals in the HERMES x-range of 0.023 ≤ x ≤ 0.6 . All values given at Q2=2.5 GeV2

• Agreement of HERMES and SMC results

Δｑｑ

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Quark Polarization (Moment)

Moments

• Flavor decomposition (Q2=2.5 GeV2)– comparison with SU(3) prediction

(J.Ellis and M.Karliner, Phys.Lett.B341(1995)397) » total integral prediction

– Δu+Δu 0.57±0.02±0.03 0.66±0.03– Δd+Δd -0.25±0.06±0.05 -0.35±0.03– Δs+Δs -0.01±0.03±0.04 -0.08±0.02

• Comparison with Lattice calculation (Q2=2.5 GeV2)– M.Gockeler, Phys.Lett. B414 (1997) 81

» total integral prediction– Δuv 0.57±0.05±0.08 0.84±0.05 (Q2=5)– Δdv -0.22±0.11±0.13 -0.25±0.02 (Q2=5)

• Singlet (Δq0), Triplet(Δq3), and Octet(Δq8) (Q2=2.5 GeV2)» total integral prediction

– Δq0 0.30±0.04±0.09 0.23±0.04 (SU(3))– Δq3 0.84±0.07±0.06 1.01±0.05 (Bjorken)– Δq8 0.32±0.09±0.10 0.35±0.07 (non-SU(3))– Δq8

* 0.33±0.10±0.11 0.46±0.03 ((3F-D)×CQCD)– where Δq8 : use flavor asymmetric polarized sea

Δq8*:use flavor symmetric polarized sea

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Gluon Polarization

Measured Asymmetry A//(pTh+,pT

h-)

• systematic error ~ 8 % • checks that have been performed on the data

– e+ - h+ misidentification– particle identification cut variation– momentum (~z) cut variation– consistent result obtained using identified pions only

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Gluon Polarization

Region of interest

• Systematic error ~ 8 %

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Gluon Polarization

MC data comparison

• Comparisons of measured cross sections with predictions of model implemented in PYTHIA

– solid black: total– solid red: PGF– dashed blue: QCDC– dotted black: soft VMD

• data are compared in a region where PYTHIA model is independent of pT

min cut-off parameter• Other comparisons:

– other distributions: e.g. Δφ…– other regions of phase space: e.g. in regions

dominated by soft VMD

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Gluon Polarization

Fraction of subprocesses

• The unpolarized model of the data is used to extract the unpolarized fi’s :

• The negative asymmetry is observed where PGF is expected to dominate.

• Significant uncertainty from contribution due to hadronic structure of the photon.

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Gluon Polarization

Gluon polarization

• ΔG/G = 0.41 ±0.18 (stat.) ±0.03 (exp.syst.)at <xG> = 0.17 and <pT

2> = 2.1 GeV2

• Large uncertainty from contribution and unknown spin asymmetry of hadronic photon. If only a dilution, value of ΔG/G will increase but significance will not change.

ΔG/G=-1

ΔG/G=0.41

ΔG/G=0

ΔG/G= +1

Measurement of the Spin Asymmetry in the Photoproduction of Pairs of High-pTHadrons at HERMESA. Airapetian et al, Phys. Rev. Lett. 84 (2000) 2584-2588

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Flavor Asymmetry

フレーバー非対称性：d-u 分布

• 核子中のseaクォーク分布の非対称性– (d-u)/(u-d) > 0 : 反ダウンクォーク分布が excess

• meson cloud model による実験データの解釈– p -> n + π+ : d の分布が多くなっている。

• ストレンジクォークの分布は？

– s(x) と s(x) の分布が非対称の可能性がある。– Meson cloud model : p -> Λ + K – RICHを用いてストレンジクォーク分布の測定

＝ ＋p nπの雲

(uud) (udd) (ud)

The Flavor Asymmetry of the Light Quark Sea from Semi-inclusive Deep-inelasticScatteringK. Ackerstaff et al, Phys. Rev. Lett.25, vol. 81 (1998) 5519-5523

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Experiment (Polarized Electron Beam)

The polarized electron beam at HERA

• Self-polarization by emission of synchrotron radiation– pb(t) = Pb

max[1-exp(-t/τ)]• Spin rotators longitudinal polarization at HERMES IP• 2 Compton polarimeters• Average beam polarization <pb> ~ 55 %

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Experiment (Spectrometer)

The HERMES experiment

• 27.5 GeV longitudinally polarized e-beam– polarization: Pbeam ~ 55 %

• Internal Target– longitudinally polarized atoms: H, D, 3He

• Kinematic range– 0.02 < x < 0.8 for Q2 > 1 GeV2 and W > 2 GeV

• Track reconstruction: 57 tracking chamber planes– δP/P = 0.7 % ~1.3 % , δθ < 0.6 mrad

• Particle Identification– 4 PID detectors : electron-hadron separation

The HERMES SpectrometerK. Ackerstaff et al., NIM A417 (1998) 230-265

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Experiment (Polarized Target)

Polarized target

• 40 cm long open-ended storage cell • Undiluted internal targets :

– H,D,3He longitudinally polarized atoms• Laser driven polarized 3He (1995) :

– PT=46 %, =1015 N/cm2, Δtflip ~ 10 min• Atmic beam source for polarized H/D (1996 ~ 1999) :

– PT=92 %, =7 ×1013 N/cm2, Δtflip ~ 1 min• Unpolarized gases :

– H,D,3He,14N,83Kr…, 1015 ~ 1017 N/cm2

Beam-Induced Nuclear Depolarisation in a Gaseous Polarised Hydrogen TargetK. Ackerstaff et al., Phys. Rev. Lett. 82 (1999) 1164-1168

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Experiment Event reconstruction at HERMES

トラック再構成

Vertexchamber

内部標的

Frontchamber

MagnetMagnetchamber

Backchamber

Cherenkov

Hodoscope

TRDCalorimeter

e+

π+

π‐

PID: step1:positron / hadron separation• Calorimeter, Preshower, TRD, Cerenkov• 99 % positron identification efficiency with 1 % hadron contamination

PID: step2:Hadron ID :RICH(π,K,p)• Method1: Inverse Ray Tracing (IRT):Reconstruction of the cherenkov angle by IRT using PMT hits and tracking info.

• Method2: Direct Ray Tracing (DRT):Construction of the expected hitprobability densities for a giving track and given particle type hypotheses by DRT

Detail : reported at JPS meeting on 25-Sep,1999

粒子識別

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Experiment (Particle Identification : PID)

Ring Imaging Cherenkov 検出器(RICH)

• 1998年6月に完成

エアロジェル発光体：エアロジェルタイル

１７×５×５＝４２５枚ひとつのタイルのサイズは 11 cm×11 cm×1 cm

200 cm

60 cm

5 cm

120 cm

150 cm

300 cm

Photon Detector反射鏡

外観図

側面図

Photons

Aerogel Tiles

Mirror

C4F10

PMTs plane

Aluminium

エアロジェル発光体の内部構造

Charged particle

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• RICH：チェレンコフ放射角度から速度測定(v)：

• 磁気スペクトロメータ：運動量測定(p)：

粒子の質量 (m) 決定：粒子識別

Experiment (PID)

RICHによる粒子識別

チェレンコフ放射角度と運動量の関係

Aerogeln=1.03

C4F10n=1.0014

e

π K

p

e

πK

p0

0.05

0.1

0.15

0.2

0.25

0 4 8 12 16 20

π

Kp

(1) エアロジェルとC4F10に

よるチェレンコフ放射角度の情報を用いる(2) threshold type cherenkov counter としての情報を用いる

この２つの方法を組み合わせて粒子識別

P (GeV/c)

粒子識別方法

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Experiment (PID) RICHの特徴

• シリカ･エアロジェルとC4F10ガスを用いた2重発光体RICH

• シリカ･エアロジェルを世界で初めてRICHの発光体として実

際の実験に用いた

• 2 GeV/c から20 GeV/c の広い運動量領域にわたってπ,K,ｐのハドロンを識別

ハドロン運動量分布

Even

ts

1

10

10

10

2

3

0 10 20Momentum(GeV/c)

Target: proton

K, p

p

π

π, K

3.8 GeV/c 13.6 GeV/c

(threshold type cherenkov)

RICH PID

Beam Energy27.5 GeV/c

(1)HERMESで発生するハドロンのほぼ全運動量領域をcover(2)測定されるハドロンのYield：増加：πのYield～RICH以前の閾値型チェレンコフ検出器に比べて約2倍増加

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Experiment (PID)

エアロジェル発光体の外観

• タイル 5×17列×5層からなる発光体

Optical characterization of n=1.03 silica aerogel used as radiator in the RICH of HERMESNIM A440 (2000) 338

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Experiment (PID)Photon Detector

Photon detector• Hexagonal grid of 1934 PMTs per detector half • PMT Type: Philips XP1911/UV • 3/4 inch PMT diameter• Active area increased to 91 % by reflective funnel cones

Photo cathode

funnel

23.3 mm

Front view Side view

Readout• 3864 PMT channels (top and bottom together)• No analog information: use LeCroy PCOS4 system• 1024 PMTs -> 64 preamp cards -> 4 back planes with

FPGA -> 1 VME module

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Experiment (PID)

RICHの全体写真

• エアロジェル発光体をインストールする直前

• 反射鏡に光電子倍増管が映っているのが見える

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Experiment (PID)

RICHにより得られる情報

• Photon Detector がヒットした位置• 2種類の発光体（エアロジェルとC4F10）により2種類のチェレンコフリングが生じる

• リングの半径の違いが粒子の速度－種類を反映

典型的なイベント(e+P -> e’ + π X)の RICH によるリングイメージ

Top Detector

Bottom Detector

Side View

3.1 GeV/c π 中間子

4.5 GeV/c 電子

－

‐

RICH

C4F10ガスからのチェレンコフ光子によるリング

エアロジェルからのチェレンコフ光子によるリング

1934本の光電子倍増管で構成された検出面

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• RICH：チェレンコフ放射角度から速度測定(v)：

• 磁気スペクトロメータ：運動量測定(p)：

粒子の質量 (m) 決定：粒子識別

Experiment (PID)

RICHによる粒子識別

質量2乗分布によるπ、K分離

00 0.4Mass (GeV )2 2

2<P<3 GeV/c

π

K

6000

Yie

ldEventselection

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Experiment (PID)

RICHの解析結果

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Experiment (Δq) Δq extraction

電子

仮想光子

核子

Targetfragment

Currentfragment

ee’

Nh

X’

X

ΔS(x) , Δu(x)-Δd(x) , Δq(x)

ef2･qf(x)･Df

h(z) Δqf(x)Σf’ ef’

2･qf’(x)･Df’h(z) qf(x)A1

h (x,z) = Σf Ａ＝Ｐ･Ｑ

Purity FragmentationFunction

Parton densityfunction

Δq/q = P-1 ･A

Statistical error :Systematic error:(1) Ambiguity of experiment : RICH PID etc… many things(2) Δq extraction method : purity method / analytic method(3) unpol parton distribution function : GRV/CTEQ/…(4) Fragmentation Function :

- Experimental Data : EMC/HERMES/…- Theoretical Model :

F.F/Lund/Cluster/Spectator/UCLA …(5) others…

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Experiment (Δq)

Monte Carlo Projection

Projection based on 8 × 106 DIS events with semi-inclusive K± asymmetries.

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Nuclear Transparency

実験結果

• lc > R14N において Hadronic ISI により T14N は減少

• 様々な原子核標的を用いて lc依存性を測定する必要がある

• Glauber 近似によるモデルの予想– γ*N →ρ0N の散乱振幅がρ0Nの弾性散乱に比例するとする

– lc≫ RA における effective ISI が自然に導入できる• 原子核

＝λ

γ* ρ ρ’ρ

N N N’N’