Nucleon Structure Longitudinal Spin of the

HUGS Summer School Jefferson National Laboratory June 1, 2011 Lecture 2

Abhay Deshpande Wednesday, June 1, 2011 Introduction & Overview (I)

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 2 Wednesday, June 1, 2011 Introduction & Overview (I)

• Lecture 1: Introduction & importance to “spin” – What is the spin crisis?

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 2 Wednesday, June 1, 2011 Introduction & Overview (I)

• Lecture 1: Introduction & importance to “spin” – What is the spin crisis?

• Lecture 2 & Lecture 3 – Experimental method : Fixed Target Polarized Deep Inelastic Scattering (pDIS): early investigations – Spin Crisis, and the insights it enabled…. – Latest on pDIS experiments: result summaries – Principle limitations of fixed target experiments

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 2 Wednesday, June 1, 2011 Introduction & Overview (II)

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 3 Wednesday, June 1, 2011 Introduction & Overview (II)

• Lecture 4 & Lecture 5 – Relativistic Heavy Ion Collider as a Polarized Collider – Comments experimental techniques – Review of results – Principle limitations

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 3 Wednesday, June 1, 2011 Introduction & Overview (II)

• Lecture 4 & Lecture 5 – Relativistic Heavy Ion Collider as a Polarized Collider – Comments experimental techniques – Review of results – Principle limitations

• Lecture 6: Future studies in nucleon spin – Review of all experimental limitations – Non-Longitudinal spin structure of the proton – Status and possibilities at an Electron Ion Collider (EIC)

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 3 Wednesday, June 1, 2011 Deep Inelastic Scattering: Kinematics

Inclusive DIS: only measure the scattered electron Semi-Inclusive DIS: Inclusive + Current Jet remnants Exclusive DIS: Semi-Inclusive + Target Jet remnants

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 4 Wednesday, June 1, 2011 Perspective on x,Q2, Center of Mass

Fixed target e-N experiments (center of mass < 30 GeV) Hadron-Hadron Collider: CM ~2 TeV

Typically accessible By e-N collider experiments CM ~ 300 GeV

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 5 Wednesday, June 1, 2011 Deep Inelastic Scattering: Kinematics with spin

k’

s k

S K

No transverse component/ “Deep Inelasc” : Q2 >> 1 GeV2 projecons of spin on parton or “Scaling Limit” : Q2 à proton momentum

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 6 Wednesday, June 1, 2011 • Lepton Nucleon Cross Section Nucleon spin

Lepton spin

• Lepton tensor Lµν affects the kinematics (QED) • Ηadronic tenosr Wµν has information about the hadron structure

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 7 Wednesday, June 1, 2011 • Lepton Nucleon Cross Section Nucleon spin

Lepton spin

• Lepton tensor Lµν affects the kinematics (QED) • Ηadronic tenosr Wµν has information about the hadron structure

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 7 Wednesday, June 1, 2011 • Lepton Nucleon Cross Section Nucleon spin

Lepton spin

• Lepton tensor Lµν affects the kinematics (QED) • Ηadronic tenosr Wµν has information about the hadron structure

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 7 Wednesday, June 1, 2011 Structure Functions & PDFs

• The F1 and F2 are unpolarized structure functions or momentum distributions

• The g1 and g2 are polarized structure functions or spin distributions • In QPM

– F2(x) = 2xF1 (Calan Gross relation)

– g2 = 0 (Twist 3 correlations)

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 8 Wednesday, June 1, 2011 Measurement of Glue at HERA

9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA

2 • Scaling violations of F2(x,Q )

9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA

2 • Scaling violations of F2(x,Q )

9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA

2 • Scaling violations of F2(x,Q )

9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA

2 • Scaling violations of F2(x,Q )

• NLO pQCD analyses: fits with linear DGLAP* equations

9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA

2 • Scaling violations of F2(x,Q )

• NLO pQCD analyses: fits with linear DGLAP* equations

9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA

2 • Scaling violations of F2(x,Q )

• NLO pQCD analyses: fits with linear DGLAP* equations

*Dokshitzer, Gribov, Lipatov, Altarelli, Parisi 9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Measurement of Glue at HERA

2 • Scaling violations of F2(x,Q )

• NLO pQCD analyses: fits with linear DGLAP* equations

Gluon dominates

*Dokshitzer, Gribov, Lipatov, Altarelli, Parisi 9 Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 Wednesday, June 1, 2011 Nucleon spin & Quark Probabilities

• Define

– With q+ and q- probabilities of quark & anti-quark with spin parallel and anti-parallel to the nucleon spin

• Total quark contribution then can be written as:

• The nucleon spin composition

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 10 Wednesday, June 1, 2011 Nucleon’s Spin: Naïve Quark Parton Model

• and are spin 1/2 particles • that constitute them are also spin 1/2 particles – And there are three of them in the nucleons: Proton: u u d : u d d

S proton = Sum of all quark spins!

? 1/2 = 1/2 + 1/2 + 1/2

1/2 = 1/2 - 1/2 + 1/2

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 11 Wednesday, June 1, 2011 How was the Quark Spin measured?

• Deep Inelastic polarized electron or scattering

µ Spin 1/2 quarks Spin 1 γ∗

µ

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 12 Wednesday, June 1, 2011 Lepton-nucleon Cross Section

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 13 Wednesday, June 1, 2011 Polarized lepton-nucleon cross section…

For high energy γ is small

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 14 Wednesday, June 1, 2011 Cross section asymmetries….

• Δσ|| = anti-parallel – parallel spin cross sections

• Δσperp= lepton-nucleon spins orthogonal • Instead of measuring cross sections, it is prudent to measure the differences: Asymmetries in which many measurement imperfections might cancel:

which are related to virtual photon-proton asymmetries A1,A2:

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 15 Wednesday, June 1, 2011 d, η, ξ are kinematic factors

D = Depolarization factor: how much polarization of the incoming electron is taken by the virtual photon, calculable in QED

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 16 Wednesday, June 1, 2011 • A|| could be written down in terms of spin structure function

g1, and A2 along with kinematic factors:

Where A1 is bounded by 1, and A2 by sqrt(R=σΤ/σL), when

terms related A2 can be neglected, and γ is small,

• Where: and

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 17 Wednesday, June 1, 2011 Relation to spin structure function g1

Quark and an-quark with spin orientaon along and against the proton spin.

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 18 Wednesday, June 1, 2011 Relation to spin structure function g1

Quark and an-quark with spin orientaon along and against the proton spin.

• In QCD quarks interact with each other through , which gives rise to a weak Q2 dependence of structure functions

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 18 Wednesday, June 1, 2011 Relation to spin structure function g1

Quark and an-quark with spin orientaon along and against the proton spin.

• In QCD quarks interact with each other through gluons, which gives rise to a weak Q2 dependence of structure functions

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 18 Wednesday, June 1, 2011 Relation to spin structure function g1

Quark and an-quark with spin orientaon along and against the proton spin.

• In QCD quarks interact with each other through gluons, which gives rise to a weak Q2 dependence of structure functions

• At any given Q2 the spin structure function is related to

polarized quark & gluon distributions by coefficients Cq and Cg

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 18 Wednesday, June 1, 2011 Composition & Q2 or t dependence of Structure Functions

In this equaon: t = ln(Q2/Λ2)

αS = strong interacon constant S & NS stand for flavor singlet & flavor non-singlet

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 19 Wednesday, June 1, 2011 Composition & Q2 or t dependence of Structure Functions

In this equaon: t = ln(Q2/Λ2)

αS = strong interacon constant S & NS stand for flavor singlet & flavor non-singlet

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 19 Wednesday, June 1, 2011 Composition & Q2 or t dependence of Structure Functions

In this equaon: t = ln(Q2/Λ2)

αS = strong interacon constant S & NS stand for flavor singlet & flavor non-singlet

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 19 Wednesday, June 1, 2011 Composition & Q2 or t dependence of Structure Functions

Singlet quark distribuon And its t dependence

(Singlet) Gluon distribuon And its t dependence

Non-Singlet quark distribuon And its t dependence

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 20 Wednesday, June 1, 2011 At leading order g1 decouples with ΔG

Beyond the leading order coefficient & splitting functions are not uniquely defined: There are some favorite schemes of theorists, each with distinct calculation advantage. – Most are now available at – More comments on this in various theory talks

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 21 Wednesday, June 1, 2011 At leading order g1 decouples with ΔG Whenever you hear Analysis done at “Leading order” --This means quark- gluon interacons are dropped from consideraon

Beyond the leading order coefficient & splitting functions are not uniquely defined: There are some favorite schemes of theorists, each with distinct calculation advantage. – Most are now available at – More comments on this in various theory talks

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 21 Wednesday, June 1, 2011 2 • In QCD, the ratio A1~ g1/F1 is Q dependent because the

splitting functions (with the exception for Pqq) are different for polarized and un-polarized parton distributions.

• The difference comes from “soft gluon singularity” at x=0 which is “only present in the un-polarized case!” – Low x rise in un-polarized gluon distribution

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 22 Wednesday, June 1, 2011 Measurement of Gluons at HERA

• Inclusive e-p scattering at 300 GeV center of mass • Low x gluon distribution measured up to x = 10-4 • Evolved to a high value of Q2 using the Altarelli Parisi equation • Gluon distribution keeps on rising: “the Low x singularity”

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 23 Wednesday, June 1, 2011 Measurement of Gluons at HERA

• Inclusive e-p scattering at 300 GeV center of mass • Low x gluon distribution measured up to x = 10-4 • Evolved to a high value of Q2 using the Altarelli Parisi equation • Gluon distribution keeps on rising: “the Low x singularity”

What this means to our understanding of QCD: in Lecture 6

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 23 Wednesday, June 1, 2011 2 • In QCD, the ratio A1~ g1/F1 is Q dependent because the

splitting functions (with the exception for Pqq) are different for polarized and un-polarized parton distributions.

• The difference comes from “soft gluon singularity” at x=0 which is “only present in the un-polarized case!” – Low x rise in un-polarized gluon distribution

• However in the region of x dominated by the valence quarks, the gluon’s effects are expected to be small, and an

indication of this is the ratio: g1/F1 is anticipated to be approximately constant. – And it is indeed observed.

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 24 Wednesday, June 1, 2011 Measurements of spin structure functions: What issues we need to worry about? Design of experiments Operational issues

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 25 Wednesday, June 1, 2011 The most important theoretical predictions for the polarized deep inelastic scattering are the sum rules for the nucleon structure function g1.

Due to experimental limitations, accessibility of x range is limited, and extrapolations to x= 0 and x = 1 are unavoidable.

Extrapolations to x = 1, are somewhat less problematic: Small contribution to the integral Future precisions studies at JLab 12GeV of great interest

Low x behavior of g1(x) is theoretically not well established hence of significant debate and excitement in the community

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 26 Wednesday, June 1, 2011 Low x behavior of g1

• Regge models (mostly used until mid 1990s):

Where α is the intercept of the lowest contributing Regge trajectories

• Other model dependent expectations (non-QCD based):

• QCD based calculations: Resummation of AP: Resum of leading power of ln(1/x) gives:

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 27 Wednesday, June 1, 2011 A collection of low x behaviors:

• Low x behavior all over the place

• No theoretical guidance for which one is correct

• Only logical path is though measurements. – Not easy – But planned in future

Deshpande, Hughes, Lichtenstadt, HERA low x WS (1999) – (lecture 6) Simulated data for polarized e-p scaering shown in the figure. Polarized HERA was not realize!

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 28 Wednesday, June 1, 2011 Experimental Basics for Measurements with

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 29 Wednesday, June 1, 2011 Experimental Needs in DIS

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam • Polarized targets: hydrogen (p), deuteron (pn), helium (3He: 2p+n)

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam • Polarized targets: hydrogen (p), deuteron (pn), helium (3He: 2p+n) • Polarized beams: electron,muon used in DIS experiments

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam • Polarized targets: hydrogen (p), deuteron (pn), helium (3He: 2p+n) • Polarized beams: electron,muon used in DIS experiments

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam • Polarized targets: hydrogen (p), deuteron (pn), helium (3He: 2p+n) • Polarized beams: electron,muon used in DIS experiments

Determine the kinematics: measure with high accuracy:

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam • Polarized targets: hydrogen (p), deuteron (pn), helium (3He: 2p+n) • Polarized beams: electron,muon used in DIS experiments

Determine the kinematics: measure with high accuracy: • Energy of incoming lepton

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam • Polarized targets: hydrogen (p), deuteron (pn), helium (3He: 2p+n) • Polarized beams: electron,muon used in DIS experiments

Determine the kinematics: measure with high accuracy: • Energy of incoming lepton • Energy, direction of scattered lepton: energy, direction

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam • Polarized targets: hydrogen (p), deuteron (pn), helium (3He: 2p+n) • Polarized beams: electron,muon used in DIS experiments

Determine the kinematics: measure with high accuracy: • Energy of incoming lepton • Energy, direction of scattered lepton: energy, direction • Good identification of scattered lepton

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam • Polarized targets: hydrogen (p), deuteron (pn), helium (3He: 2p+n) • Polarized beams: electron,muon used in DIS experiments

Determine the kinematics: measure with high accuracy: • Energy of incoming lepton • Energy, direction of scattered lepton: energy, direction • Good identification of scattered lepton

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam • Polarized targets: hydrogen (p), deuteron (pn), helium (3He: 2p+n) • Polarized beams: electron,muon used in DIS experiments

Determine the kinematics: measure with high accuracy: • Energy of incoming lepton • Energy, direction of scattered lepton: energy, direction • Good identification of scattered lepton

Control of false asymmetries:

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental Needs in DIS

Polarized target, polarized beam • Polarized targets: hydrogen (p), deuteron (pn), helium (3He: 2p+n) • Polarized beams: electron,muon used in DIS experiments

Determine the kinematics: measure with high accuracy: • Energy of incoming lepton • Energy, direction of scattered lepton: energy, direction • Good identification of scattered lepton

Control of false asymmetries: • Need excellent understanding and control of false asymmetries (time variation of the detector efficiency etc.)

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 30 Wednesday, June 1, 2011 Experimental issues detector beam target

Possible sources of false asymmetries: • beam flux • target size • detector size • detector efficiency

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 31 Wednesday, June 1, 2011 An Ideal Situation

If all other things are equal, they cancel in the ratio and….

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 32 Wednesday, June 1, 2011 A Typical Setup

• Experiment setup (EMC, SMC, COMPASS@CERN)

• Target polarization direction reversed every 6-8 hrs • Typically experiments try to limit false asymmetries to be about 10 times smaller than the physics asymmetry of interest

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 33 Wednesday, June 1, 2011 Asymmetry Measurement

• f = dilution factor proportional to the polarizable nucleons of

interest in the target “material” used, for example for NH3, f=3/17

• D is the depolarization factor, kinematics, polarization transfer from polarized lepton to photon, D ~ y2

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 34 Wednesday, June 1, 2011 First Moments of SPIN SFs • With

a a a3=ga 8 0 ΔΣ Neutron decay (3F-D)/3 Hyperon Decay

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 35 Wednesday, June 1, 2011 p First moment of g1 (x) : Ellis-Jaffe SR

Assuming SU(3)f & Δs = 0 , Ellis & Jaffe:

Measurements were done at SLAC (E80, E130) Experiments: Low 8-20 GeV electron beam on fixed target -2 Did not reach low enough x à xmin ~ 10 Found consistency of data and E-J sum rule above Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 36 Wednesday, June 1, 2011 European Muon Collaboration at CERN

• 160 GeV muon beam (lower intensity), but significantly higher energy -3 • Significantly LOWER X reach à xmin ~ 10

• Polarized target

• Repeated experiment for A1 and measured g1 of the proton!

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 37 Wednesday, June 1, 2011 (1989)!

ΔΣ = (0.12) +/- (0.17) (EMC, 1989) ΔΣ = 0.58 expected from E-J sum rule….

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 38 Wednesday, June 1, 2011 Evolution: Our Understanding of Nucleon Spin

?

1980s 1990/2000s

ΔΣ = 0.12 +/- 0.17

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 39 Wednesday, June 1, 2011 Evolution: Our Understanding of Nucleon Spin

?

1980s 1990/2000s

ΔΣ = 0.12 +/- 0.17

We have come a long way, but do we understand nucleon spin? Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 39 Wednesday, June 1, 2011 Lesson:

• Every time we explored a physical observable with “spin” as one of the experimental variable, we have learnt something new about nature….

• But was this really a “ spin crisis”? – Experimental uncertainties too large – The assumptions: naïve (constituent) quark model – We needed to examine and improve on both fonts!

This is precisely what was done in the following decade….

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 40 Wednesday, June 1, 2011 How significant is this?

“It could the discovery of the century. Depending, of course on how far below it goes…”

Abhay Deshpande, Nucleon Spin Lecture 2 of 6 at HUGS 2011 6/01/11 41 Wednesday, June 1, 2011