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Spin Physics

Anselm Vossen

Sources:

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Outline• Short Introduction to spin phenomena• Spin structure of the nucleon

– How to probe the nucleon– Existing measurements– Spin program at RHIC– …

• Disclaimer:– This is a highly personal selection– Very incomplete– Focused on RHIC spin physics– Questions are highly encouraged!

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Spin is fascinating…

And leads to unexpected effects….

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In the Beginning there was: The Stern Gerlach Experiment

• Spin is a quantum number

• Angular momentum

5

Spin vs. Angular Momentum

• Classical picture of spinning object has problems:

– Elementary particles are pointlike– On quantum level: 2 Rotations

necessary to ‘come back’

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Measuring spin effects Reveals Structure of the Nucleon

• Magnetic moment of elementary particle with spin ½ is 1 unit, e.g electron

• However: Proton: 2.79 units– First hint at substructure

• MRI

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• Spin effects tell of internal structure• What contributes most of the visible

mass in the universe?

– Not Higgs: Strong force interactions within the nucleon!

• Proton mass is dominated by it

• Proton momentum is half carried by quarks, half by gluons

• SPIN is fundamental quantity:What role does it play in strong interactions? (analogue: Atomic physics)

Nucleon spin still not understood

Confinement Interesting spin effects help

us understand QCD

Motivation for Spin Physics as a Motivation for Spin Physics as a nuclear physicist?nuclear physicist?

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Therefore Spin is integral part of the RHIC ‘Mission’

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γγ**

u,d,u,d,ss

ee-- γγ**

u,d,su,d,s

ee-- XX

polarized deep inelastic scattering (DIS)

polarized pp scattering

u,d,su,d,s,g,g

u,d,su,d,s,g,g

u,d,su,d,s,g,g

XX

polarized semi inclusive DIS

Probes to Study Polarized Proton StructureProbes to Study Polarized Proton Structure

uu 　　　　

uu 　　　　

dddd

/ e

e/W

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Probing the Proton Structure• EM interaction

– Photon• Sensitive to electric charge2

• Insensitive to color charge

• Strong interaction– Gluon

• Sensitive to color charge• Insensitive to flavor

• Weak interaction– Weak Boson

• Sensitive to weak charge ~ flavor• Insensitive to color

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Unpolarized Proton Structure from e-p Unpolarized Proton Structure from e-p ScatteringScattering

→ Structure of the proton

→ 1955 Hofstadter: Radius 0,8 fm

Nobel Prize 1961

→ 1968 Friedman, Kendall, Taylor: quarks in the proton Nobel Prize 1990

→ Highest Q²: quarks, gluons elementary

Q² = negative momentum transfer squared

18/ 10 mp

p, proton

e, electron

, photon

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Spin Decomposition of the ProtonSpin Decomposition of the Proton

v v s

1 1Δu Δd Δq

2 2Σ 1 ???

Naïve quark model – 3 valence quark

CERN, SLAC, DESY, JLAB: 0.30

…and orbital angular momentum…

1

2 q gJ J 1

Σ2

G

q

g

L

L

QCD:..additional contributions from gluons and gluon splitting, sea quarks…

GΣ21

21

ΔG = ?

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Sidenote: How can we measure Polarized Structure?

Inclusive Measurement:Inclusive Measurement: ´

Nucleon

1. Polarized Probe:

2. Count events with different spin setting:

3. Construct Asymmetry: Cancels many systematic effects

2

2i

i

ii

ii

e q

e q

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Flavor decomposition with semi-inclusive

Asymmetries

´

Nukleon

: Fragmentation Function- Probability to produce hadron h from quark q

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The three leading order, collinear PDFs

Parton Distribution Functions

q(x)f1

q (x)

q(x) g1

q(x)

Tq(x)

h1q(x)

chiral odd, poorly known

unpolarized PDFquark with momentum x=pquark/pproton in a nucleon well known – unpolarized DIS

helicity PDFquark with spin parallel to the nucleon spin in a longitudinally polarized nucleon known – polarized DIS

transversity PDF quark with spin parallel to the nucleon spin in a transversely polarized nucleon

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Unpolarized Longitudinally Polarized Transversely Polarized

First part…

Current Status of Distribution Functions

…second part…

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Polarized e + N at EIC

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2008 DSSV Global Fit

anti-u and anti-d distributions small, but not well constrained (positive? negative? nodes?)

How Well do We Know the Longitudinal Polarized Parton Distribution Functions?

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Impact of Fragmentation Functions in SIDIS data

• Kretzer FF favors SU(3) symmetric sea, not so for KKP• DS ~30% in all cases

D. De Florian et al. PRD71:094018,2005 NLO @ Q2=10 GeV2

Kretzer

KKP

DIS

SIDIS uv udv d s g

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RHIC can Answer

• Successful program to determine gluon polarization

• W program in the future

• EIC in the far future

RHIC can ask:

• Transverse Spin Asymmetries

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RHIC: World’s Only Polarized Hadron Collider

BRAHMS & PP2PP

STAR

PHENIX

AGS

LINACBOOSTER

Pol. H- SourceSolenoid Partial Siberian Snake

200 MeV Polarimeter AGS Internal Polarimeter

Rf DipoleStrong AGS Snake

PHOBOS

Spin flipper

Siberian SnakesSiberian Snakes

RHIC Polarimeters

Spin Rotators

Spin Rotators

AGS pC Polarimeter

Warm AGS Snake

Polarized atomic H jet

Siberian snakes: built into

design from the start !

No snakes ~1000 depolarizing resonancesWith snakes no first order resonancesTwo partial AGS snakes (11 and 27 spin rotators)

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Spin Physics Experiments

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PHENIX Detector

04/22/23Swadhin Taneja RHIC AGS User's Meeting

π0, η, γ detection• Electromagnetic Calorimeter (PbSc/PbGl):

• High pT photon trigger to collect π0's, η’s, γ’s • Acceptance: |η|<0.35, φ= 2 x π/2• High granularity (~10*10mrad2)

π+/ π-

• Drift Chamber (DC) for Charged Tracks• Ring Imaging Cherenkov Detector (RICH)

• High pT charged pions (pT>4.7 GeV).

Luminosity (Global) Detectors• Beam Beam Counter (BBC)

• Acceptance: 3.0< η<3.9• Zero Degree Calorimeter (ZDC)

• Acceptance: ±2 mrad about beam axis

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RHIC Performance

04/22/23Swadhin Taneja RHIC AGS User's Meeting

• Data accumulation in longitudinally polarized p+p Runs

• 05’+06’ ~ 200 times increase in FOM than 03’+04’• 09’ run at s = 500 GeV , L *~ 10 pb-1 , P ~ 40%

Years

[GeV]

L [pb-1] (recorded

)Pol. [%]

FOM (P4L)

2003 200 0.35 27 0.0019

2004 200 0.12 40 0.0031

2005 200 3.4 49 0.20

2006 200 7.5 57 0.79

2006 62.4 0.08 48 0.0042

2009 200 14 57 1.2

Longitudinal

0

10

20

30

40

50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Weeks into run

Nuc

leon

pai

r lu

min

osity

L

NN

[pb

-1]

2003P=34%

2005P=46%

2006P=60%

2008P=45%

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Cross section from PHENIX agree with Perturbative QCD Calculations

04/22/23Swadhin Taneja RHIC AGS User's Meeting

• π0 , direct γ cross section– NLO PQCD shows agreement with the data

0 @ 200 GeV (PRD76, 051106) We observe elementary scattering (with corrections that we can compute)

u,d,su,d,s,g,g

u,d,su,d,s,g,g

u,d,su,d,s,g,g

XX

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Measuring the Gluon Polarization at PHENIX

• ….The infamous Delta G measurement with 0’s

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gqgq G

G

q

q

qqqqq

q

q

q

gggg G

G

G

G

Constraints on gluon polariztion w/ 0 Production

• pp 0 X is sensitive to gggg and gqgq

ECAL

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Extracting ΔG from ALL measurements

04/22/23Swadhin Taneja RHIC AGS User's Meeting

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• Theory interpretation of ALL π0,+/-,

– pol. (Δf) and unpol. pdf’s (f ) from DIS (mainly)– pol. (Δσ) and unpol. (σ) hard scattering cross section from NLO

PQCD

– fragmentation functions (Dπ/c ), from e+ e- , Semi Inclusive DIS and pp

• Three processes contribute to ALL π0,+/-,

– Need to make sure pQCD, factorization,

universality in pdf and fragmentation WORK

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Measurement of ALL

04/22/23Swadhin Taneja RHIC AGS User's Meeting

• π0 yield measurement– π0 → γγ BR ~ 98.8 %– Combinatorial BG fraction

wBG = NBG / (NBG + Nπ )

• ALL measurement

– signal ALL is corrected for background ALL,

– PB , PY (~55%) beam pol. , less than 10 % relative error in PB.PY

– R : relative luminosity, δALL = 2 x 10-4 in 2005, 7 x 10-4 in 2006

– N++ (N+- ) π0 yield with same (opposite) helicity of colliding beams

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Present and Future Constraints on Gluon Polarization in the Proton:

1st NLO pQCD analysis incorporating RHIC spin inclusive jet and 0 ALL (2006) data (arXiv:0804.0422) by de Florian, Sassot, Stratmann & Vogelsang

DIS and RHIC spin impose comparable constraints to date on shape & magnitude of gluon polarization vs. x; RHIC spin data should dominate after next long 200 GeV p+p run, with new jet+jet coincidence data significantly constraining x-dependence.

w/ Run 6 RHIC data

w/ projected Run 9 RHIC data

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Sea-Quarks

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A new experimental Approach to Determine Sea Quark Polarization in

p-p

• Accessing sea quark polarization in W productionHigh Q2

No u quark dominanceOnly single spin asymmetriesNo uncertainty due to fragmentationNo nuclear corrections of measurements

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Wud

Wduu u 　　　　

u u 　　　　 dddd

/ e

e/W

))u(x(xd)(xd)u(x

)(xd)Δu(x))u(x(xdΔ

σσ

σσAWL

2121

2121

Similar expression for W- to get Δῡ and Δd…

Since W is maximally parity violating large measured Δu and Δd require large asymmetries.

W Production Basics

No Fragmentation!

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RPCs

μμ+/-+/-

Rapidity: 1.2 < η <2.2 (2.4)Δφ = 2 π

Philosophy (initial design): High rate capability & granularityHigh rate capability & granularity Good mass resolution & particle IDGood mass resolution & particle ID Sacrifice acceptanceSacrifice acceptance

μ +/μ - : Muon Tracking Detector Muon Identifier

500GeVs

Measurement of W Production in W-> in the PHENIX Muon Arms in Polarized pp Collisions

at

~10m

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Need fast dedicated detector stations for momentum

reconstruction and background rejection

Design Luminosity√s = 500 GeV σ=60mb L = 1.6 x1032/cm2/s

Total X-sec rate ＝ 9.6 MHz

MuID LL1 (current trigger) RF=200 ~ 500

DAQ LIMIT=1-2 kHz （ for μ arm ）

Required RF10,000

W signal

W’s in the PHENIX Muon Arms

A bit of development necessary… PYTHIA

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Single Transverse Spin Asymmetries• Fermilab E-704 reported

Large Asymmetries AN • Could be explained as

– Transversity x Spin-dep fragmentation (Collins effect),

– Intrinsic-kT imbalance (Sivers effect) , or

– Twist-3 (Qiu-Sterman, Koike)– Or combination of above

GeV 4.19at sXpp Left Right

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Collins Fragmentation - Modell

http://cerncourier.com/main/article/44/8/19/1

Collins Effekt in String Fragmentation(X. Artru)

K. Bruhwel, TJNAF

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+ }

x

M. Burkardt, PRD, 66, 114005(2002)

Sivers Effect is sensitive to Orbital Angular Momentum of Quarks

x

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Summary

• Spin physics is one of the best tools to learn about nucleon structure

• RHIC experiments are at the forefront in – Determining gluon contribution – Measuring sea quark contribution– Finding the origin of large transverse spin

asymmetries

• In the future with – Possible upgrades– The EIC

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Backups

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Handbag Diagrams

γγ**

u,d,u,d,ss

ee--

Optical Theorem:

=-m(forward scattering)

+

+ +

+

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Transversity is Chiral Odd

_

+1h

_

+↑

↑ ↑

↑ ↓

↑ ↑

↓ _

• Helicity base: chiral odd

Need chiral odd partner => Fragmentation function

Difference in densities for ↑, ↓ quarks in ↑ nucleon

• Transversity base:

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QED and QCD interactions (and SM weak interactions) conserve

helicity:

Cannot measure h1 inclusively

_

+1h

_

+

QED, QCD Preserve Helicity

•Helicity base: chiral odd

Need chiral odd partner => Fragmentation function

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Chiral odd FFs

+

_

+

1h

_

+

_1H

Collins effect

q

N

: Collins FF

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Chiral odd FFs

+

_

+ _

+ q

N

_

Lz-1Lz

1H

Interference Fragmentation Function

( )

1h

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Year Due

# Milestone

2013 HP8 Measure flavor-identified q and q contributions to the spin of the proton via the longitudinal-spin asymmetry of W production.

2013 HP12(update of HP1)

Utilize polarized proton collisions at center of mass energies of 200 and 500 GeV, in combination with global QCD analyses, to determine if gluons have appreciable polarization over any range of momentum fraction between 1 and 30% of the momentum of a polarized proton.

2015 HP13(new)

Test unique QCD predictions for relations between single-transverse spin phenomena in p-p scattering and those observed in deep-inelastic lepton scattering

Near-Term RHIC Spin Program Addresses Three Specific DOE Hadron Physics

Performance Milestones

A few brief comments on the physics goals to follow…

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Tentative RHIC Run Plan Following 2008 PAC Recommendations(assumes 6-month FY09 CR, 2-species runs in FY10-14 & best info on detector upgrade schedules)

Fiscal

Year

Colliding Beam

Species/Energy

Comments

2009 200 GeV p+p~12 physics weeks to complete 200 GeV ALL measurements – could be

swapped with 500 GeV Run 10 if >6-month FY09 CR likely; STAR DAQ1000 fully operational

2010

500 GeV p+p~5-6 physics weeks to commission collisions, work on polarization & luminosity and obtain first W production signal to meet 2011 RIKEN milestone

200 GeV Au+Au

9-10 physics weeks with PHENIX HBD, STAR DAQ1000 & TOF permits low-mass dilepton response map and 1st HI collision test of transverse stochastic cooling (one ring)

2011

Au+Au at assorted low E

1st energy scan for critical point search, using top-off mode for luminosity improvement – energies and focus signals to be decided; commission PHENIX VTX (at least prototype)

200 GeV U+U 1st U+U run with EBIS, to increase energy density coverage

2012

500 GeV p+p1st long 500 GeV p+p run, with PHENIX muon trigger and STAR FGT upgrades, to reach ~100 pb-1 for substantial statistics on W production and G measurements

200 GeV Au+Au

Long run with full stochastic cooling, PHENIX VTX and prototype STAR HFT installed; focus on RHIC-II goals: heavy flavor, -jet, quarkonium, multi-particle correlations

2013

500 GeV p+pReach ~300 pb-1 to address 2013 DOE performance milestone on W production

200 GeV Au+Au or 2nd low-E scan

To be determined from 1st low-E scan and 1st upgraded luminosity runs, progress on low-E e-cooling, and on installation of PHENIX FVTX and NCC and full STAR HFT

2014

200 GeV Au+Au or

2nd low-E scan

Run option not chosen for 2013 run – low-E scan addresses 2015 DOE milestone on critical point, full-E run addresses 2014 (-jet) and 2016 (identified heavy flavor) milestones. Proof of principle test of coherent electron cooling.

200 GeV p+pAddress 2015 DOE milestone on transverse SSA for -jet; reference data with new detector subsystems; test e-lenses for p+p beam-beam tune spread reduction

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• What is spin?

• Spin structure of proton

• Why is this important

• Observables

• Experimental overview

• Spin at RHIC

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• Substructure

• Importance of spin spin, etc coupling (example: atoms)

• Spin important quantum number

• Like little antennas…

• First quantum number, (quantum-relativistic quantum effect)

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• What are the summerstudents doing?

• Spin at rhic?

• Overview over source, polarimetry, …

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• Outline:• Historic perspective

– Spin in stern gerlach, first quantized measurement– Different quantum numbers than orbital angular momentum– Magnetic moment

• Hint to substructure of proton neutron• MRI (is that magnetic moment?)

– Substructure important• Analog of atoms, spin orbit, spin spin interactions

• How to probe substructure– Different probes– Different energies (Q^2)– Pdfs– Hera etc– Spin at Rhic (machine etc…)

• Future of spin at rhic

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• Stern Gerlach

• How does

• Otto stern (nobelpreise, 1933 -> substruktur des protons)

• Different Q2 (pictures)

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Definitionen

y = / : Inelastizität

´

Nukleon

xBj = Q2 / ( 2M) : Impulsbruchteil des getroffenen Quarks

z = Eh / : Exklusivität

= E – E´: Photon Energie

Wirkungsquerschnitt

unpolarisiert: polarisiert:

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0

10

20

30

40

50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Weeks into run

Nuc

leon

pai

r lu

min

osity

L

NN

[pb

-1]

2003P=34%

2005P=46%

2006P=60%

2008P=45%

P L(pb^-1) Results

2002 15% 0.15 first pol. pp collisions!

2003 30% 1.6 pi^0, photon cross section,

A_LL(pi^0)

2004 40% 3.0 absolute beam polarization

with polarized H jet

2005 50% 13 large gluon pol. ruled out

(P^4 x L = 0.8)

2006 60% 46 first long spin run *

(P^4 x L = 6)

2007 no spin running

2008 50% (short) run

* support for 2006 run from Renaissance Tech. crucial for program

Polarized Collision Performance at RHIC

2006, P=60%

2008, P=45%

2005, P=46%

2003, P=34%

Delivered luminosity at s = 200 GeV

Further development ( long runs!) needed to reach “enhanced” design goals: P=70%, L = 6 1031 cm2s1 (or 15 pb1/week) at s = 200 GeV

Absolute beam polarization calibration to better than 5% design goal achieved!

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Introduction

04/22/23Swadhin Taneja RHIC AGS User's Meeting

• Proton spin structure,

– Global analysis, [PRL101:072001,2008]

– ΔG not well constrained by fits to pDIS , g1(x, Q2), at this time

• Polarized p+p collisions for ΔG measurement

– π0, jet , direct photons etc.

– double helicity asymmetry (ALL)

• Inclusive π0 at mid-rapidity (|η| < 0.35) is PHENIX main channel for the determination of ΔG at this time.

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Proton Spin Crisis?• Proton has gone through many crisis

– Mass : mu~5 MeV/c2, md~10 MeV/c2

• Saved by constituent quark model

– Momentum : • Saved by gluon momentum

• Spin – Helicity SR:

– Theory guideline for separation (nf=3) (Ji, Tang, and Hoodboy)

gq

proton

LLg 2

1

2

1

5.0)( q

dxxxq

3.01.0 3.01.0)( q

dxxq

18.0163

3

2

1

2

1

f

fq n

nL 32.0

163

16

2

1

fg nLg

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Precision Data from DIS• Precision Data in

Wide Kinematical Range– Q2 evolution agrees

with pQCD

• Notes ：– Only Fixed Target

Spin Experiments in DIS so far…

– Need a Collider to extend kinematical coverage

Q2 (GeV2)

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Spin Physics Experiments

• COMPASS– Pol.

• HERMES– Pol.e±

• JLab Exp’s– Pol.e-

• RHIC Spin– Pol. pp

• BELLE– e+e-

Pol. Beam:

RICH-1

Pol.Target

SM1

SM2

2-stage spectrometer• LAS (Large angle) K• SAS(Small angle)

SAS

LAS

Ecal1 & Hcal1

filter 1

filter 2Ecal2 & Hcal2

RICH-2