spin: some answers many questions the issues raised by the “spin crisis” of the 1990’s have...

Spin: Spin: Some AnswersSome Answers

Many QuestionsMany QuestionsThe issues raised by the “spin crisis” of the The issues raised by the “spin crisis” of the 1990’s have been around for nearly two 1990’s have been around for nearly two decades. decades.

R. L. Jaffe R. L. Jaffe Workshop RHIC Physics in the Context Workshop RHIC Physics in the Context

of the Standard Model, RBRC, BNL, of the Standard Model, RBRC, BNL, June 2006June 2006

Much has been learnedMuch has been learnedSome conclusions can (tentatively) be drawnSome conclusions can (tentatively) be drawnSome old questions (for both theorists and Some old questions (for both theorists and

experimenters) persistexperimenters) persistSome new questions come to the foreSome new questions come to the fore

R. L. Jaffe, RHIC Physics in the Context of the Standard Model, BNL, June 2006R. L. Jaffe, RHIC Physics in the Context of the Standard Model, BNL, June 2006

Why not string theory?Why not string theory?The perfect The perfect theorytheory•• No parametersNo parameters

•• All interactions dictated by symmetriesAll interactions dictated by symmetries

•• Highly non-trivial ground state that is Highly non-trivial ground state that is

responsible for all the structure in the responsible for all the structure in the

multiversemultiverse

•• A warm up for the “Theory of Everything”A warm up for the “Theory of Everything”

•• Emergent phenomenaEmergent phenomena: Confinement, chiral : Confinement, chiral symmetry breaking, hadrons!symmetry breaking, hadrons!

--- at least for light quarks--- at least for light quarks

Why not QCD!!Why not QCD!!

visible universevisible universe

The perfect The perfect theorytheory


•• Basic QCD dynamics at the scale where the hadrons form is Basic QCD dynamics at the scale where the hadrons form is not understood.not understood.

•• We don’t understand the mechanism of confinement or of We don’t understand the mechanism of confinement or of chiral symmetry breaking in quantitative terms.chiral symmetry breaking in quantitative terms.

•• We don’t understand why quarks are the quasiparticles of We don’t understand why quarks are the quasiparticles of QCD, even after running through regions of such strong QCD, even after running through regions of such strong renormalization. All the more reason to look for other renormalization. All the more reason to look for other quasiparticles: quasiparticles: pseudoscalar bosons, diquarks(!)pseudoscalar bosons, diquarks(!)

•• We don’t have a satisfactory description of the confined We don’t have a satisfactory description of the confined relativistic bound state to enable us to predict and/or relativistic bound state to enable us to predict and/or interpret information like angular momentum content, interpret information like angular momentum content, magnetic moments, excited state spectra, and flavor magnetic moments, excited state spectra, and flavor mixing via OZI rule violation.mixing via OZI rule violation.

•• We don’t know how to connect the precise information We don’t know how to connect the precise information obtained with short distance probes at high energies to the obtained with short distance probes at high energies to the properties we would like to understand at hadronic scales properties we would like to understand at hadronic scales --- sum rules, duality, “inclusive-exclusive connection”...--- sum rules, duality, “inclusive-exclusive connection”...

(Light quark (Light quark dynamics)dynamics)


•• Does the strange quark carry a small, significant, negative fraction of Does the strange quark carry a small, significant, negative fraction of the nucleon spin? the nucleon spin? Yes, Yes, but?but?•• Does the quark spin carry a mere 30% of the nucleon spin?Does the quark spin carry a mere 30% of the nucleon spin?

Yes,Yes, but? but?•• Can single particle inclusive DIS unravel flavor/spin correlations?Can single particle inclusive DIS unravel flavor/spin correlations?

We’ll see We’ll see Sum rules and SIDIS disagree at this point...Sum rules and SIDIS disagree at this point... •• Is there significant SU(3)-flavor symmetry violation in the axial charges? Is there significant SU(3)-flavor symmetry violation in the axial charges? Perhaps??Perhaps??

•• Can this question be answered on the lattice?Can this question be answered on the lattice?Yes, Yes, Now!Now!

•• Is the OZI rule badly violated --- do strange quarks play a significant role in the Is the OZI rule badly violated --- do strange quarks play a significant role in the nucleon?nucleon?

NONO

•• Is there a gauge invariant description of Is there a gauge invariant description of all the componentsall the components of the nucleon of the nucleon spin in terms of (in principle) observables?spin in terms of (in principle) observables?

Not one, but two! And neither is experimentally Not one, but two! And neither is experimentally accessible.accessible.

RLJ & Manohar, Ji, Hoodbhoy RLJ & Manohar, Ji, Hoodbhoy & Ji& Ji Bashinsky & RLJ, Hagler & SchaferBashinsky & RLJ, Hagler & Schafer

Harindranath & KunduHarindranath & Kundu

DISDIS

DISDIS DISDIS

DVCSDVCS DVCS ?DVCS ?

?????? ??????

SAMPLE, HAPPEX, A4, G0 @ JLabSAMPLE, HAPPEX, A4, G0 @ JLab


•• Is the gluon spin associated with a well-defined, gauge invariant operator?Is the gluon spin associated with a well-defined, gauge invariant operator?YesYes

•• Can the gluon spin contribution to the nucleon spin be computed on the lattice? Can the gluon spin contribution to the nucleon spin be computed on the lattice? No ~ not without major breakthroughsNo ~ not without major breakthroughs

•• Is the gluon spin operator related to the axial anomaly?Is the gluon spin operator related to the axial anomaly? No!No!

•• What about the old assertion that an anomalously large gluon spin could What about the old assertion that an anomalously large gluon spin could somehow restore the quark spin content of the nucleon to ~100%?somehow restore the quark spin content of the nucleon to ~100%?

It’s dead theoreticallyIt’s dead theoretically and on life support experimentally and on life support experimentally

Not as complicated as it looks!Not as complicated as it looks!


•• What is the leading twist physics of transverse spin?What is the leading twist physics of transverse spin?TransversityTransversityCollins fragmentation functionCollins fragmentation functionSivers distribution functionSivers distribution function

Collins & Soper; RLJ & Ji, Artru & Mekhfi, Ralston & Collins & Soper; RLJ & Ji, Artru & Mekhfi, Ralston & PirePire

CollinsCollinsSiversSivers

•• Can transversity be measured?Can transversity be measured?Yes,Yes, with the aid of the Collins function, or in with the aid of the Collins function, or in

transverse Drell-Yantransverse Drell-Yan•• But is the Collins function non-zero? Is there any transverse resolving But is the Collins function non-zero? Is there any transverse resolving

power in fragmentation?power in fragmentation?YesYes

Ogawa, Gabbert, Gross-Ogawa, Gabbert, Gross-Perdekamp, Seidl & Hasuko Perdekamp, Seidl & Hasuko

@ BELLE@ BELLE

•• But I thought the Sivers function is zero by time-reversal invariance?But I thought the Sivers function is zero by time-reversal invariance?NONO the gluon field of the nucleon dresses the initial the gluon field of the nucleon dresses the initial

state with a phase “borrowed” from the final state.state with a phase “borrowed” from the final state. SiversSiversBrodsky, Hwang, and SchmidtBrodsky, Hwang, and Schmidt

•• What does all this have to do with single transverse spin asymmetries What does all this have to do with single transverse spin asymmetries in DIS?in DIS?

We don’t yet know for sure!We don’t yet know for sure!


•• What is the relation among all the effects in DIS that vanish for on-shell, What is the relation among all the effects in DIS that vanish for on-shell, collinear, NRQM quarks?collinear, NRQM quarks?

Transversity and the tensor chargeTransversity and the tensor chargeOrbital angular momentumOrbital angular momentumSivers distribution functionSivers distribution function

No one knows!No one knows!


•• Neutron beta decay + Exact SU(2) Neutron beta decay + Exact SU(2)

Axial chargesAxial charges

SourcesSources

•• Hyperon beta decay + Hyperon beta decay + Exact SU(3) !Exact SU(3) !Remember Remember

this!this!

•• The quest for the nucleon spin: find The quest for the nucleon spin: find access to another linear combination of access to another linear combination of

•• 1973 1973 J. Ellis & RLJ 1973J. Ellis & RLJ 1973

WEAK DECAYS But only flavor changing axial charges are measured in beta-WEAK DECAYS But only flavor changing axial charges are measured in beta-decay, so flavor symmetry must be used to “rotate” the information to the decay, so flavor symmetry must be used to “rotate” the information to the flavor diagonal charges.flavor diagonal charges.


•• Hyperon beta decay + Hyperon beta decay + Exact Exact SU(3) !SU(3) !

•• Why not ? That would require Why not ? That would require

•• What were the choices in 1973?What were the choices in 1973?

1.1. and , and something and , and something else must account for 40% of the nucleon’s spin.else must account for 40% of the nucleon’s spin.

Eg. orbital angular momentum in a relativistic quark Eg. orbital angular momentum in a relativistic quark bag modelbag model

L. Sehgal 1974L. Sehgal 1974

2.2. and the OZI rule is violated. Suggests a and the OZI rule is violated. Suggests a program:program:

3.3. SU(3) violation could be significant, altering SU(3) violation could be significant, altering

•• Enter experiment!Enter experiment!


(doesn’t yet include new

COMPASS results)


Result of global fit Result of global fit with NLO QCD with NLO QCD formalismformalism

•• ButBut

•• SoSo

•• And the search began for And the search began for

I.I. Strange quarks in the Strange quarks in the nucleonnucleon

II.II. Other carriers of the spin of Other carriers of the spin of the nucleonthe nucleon

Thanks Thanks Werner!Werner!

Both significant and troubling: Sea quark Both significant and troubling: Sea quark contribution and 75% of proton’s angular contribution and 75% of proton’s angular momentum is not on the quark spin. momentum is not on the quark spin. Why, Why, then, does the naive quark model work so then, does the naive quark model work so well?well?


GMs, (GA) at Q2 = 0.1 GeV2

SAMPLE

HAPPEX GEs + 0.39 GM

s at Q2 = 0.48 GeV2

GEs + 0.08 GM

s at Q2 = 0.1 GeV2

GEs at Q2 = 0.1 GeV2 (4He)

open geometry, integrating

A4

GEs + 0.23 GM

s at Q2 = 0.23 GeV2

GEs + 0.10 GM

s at Q2 = 0.1 GeV2

GMs, GA

e at Q2 = 0.1, 0.23, 0.5 GeV2

Open geometry

Fast counting calorimeter for background rejection

G0

GEs + η GM

s over Q2 = [0.12,1.0] GeV2

GMs, GA

e at Q2 = 0.23, 0.62 GeV2

Open geometry

Fast counting with magnetic spectrometer + TOF for background rejection

K. Kumar CIPANPK. Kumar CIPANP

Overview of ExperimentsKrishna Kumar CIPANP 2006

Overview of ExperimentsKrishna Kumar CIPANP 2006Strange quark Strange quark

magnetization and magnetization and strangeness radius in the strangeness radius in the nucleon seem to be quite nucleon seem to be quite small (compared to small (compared to what? --- theoretical what? --- theoretical expectations motivated expectations motivated by DIS)by DIS)


Ten years progress...Ten years progress...

****

****

**small and coming soonsmall and coming soon

****

**long known to be relatively smalllong known to be relatively small


Thanks Xiangdong (CIPANP)Thanks Xiangdong (CIPANP)


The field of nucleon spin/flavor structure rests on the uneasy The field of nucleon spin/flavor structure rests on the uneasy foundation of foundation of SU(3) symmetry for hyperon axial chargesSU(3) symmetry for hyperon axial charges!!

How sensitive are and to SU(3) violation -- ie. mis-How sensitive are and to SU(3) violation -- ie. mis-estimates of Y?estimates of Y?

So: assume DIS data and stays fixed, how do and So: assume DIS data and stays fixed, how do and vary with Y?vary with Y?

Standard quark model estimates of SU(3) violation 5% --- 7% Standard quark model estimates of SU(3) violation 5% --- 7% correctionscorrections Donoghue, Holstein, Klimpt, Donoghue, Holstein, Klimpt,

‘87‘87Schlumpf hep-ph 9409272Schlumpf hep-ph 9409272

•• But these estimates come from hyperon But these estimates come from hyperon beta-decay, which agree well with exact beta-decay, which agree well with exact SU(3).SU(3).

•• Theory suggests typically ~30% SU(3) Theory suggests typically ~30% SU(3) violation.violation.


A challenge to the A challenge to the Lattice CommunityLattice CommunityCompute Compute

with enough accuracy to detect SU(3) symmetry with enough accuracy to detect SU(3) symmetry violation:violation:

•• It’s a renormalization group invariant, local, non-It’s a renormalization group invariant, local, non-singlet operator, just analogous to gsinglet operator, just analogous to gAA..

•• Must compute in unquenched QCD with realistic quark Must compute in unquenched QCD with realistic quark masses.masses.

•• Would be extremely useful, equivalent to original Would be extremely useful, equivalent to original motivation for elastic neutrino scattering experiment motivation for elastic neutrino scattering experiment LSND!LSND!


Manohar 1990Manohar 1990


•• A flawed scheme dependent analysis (based on axial anomaly) A flawed scheme dependent analysis (based on axial anomaly) led to the expectation that might be huge. led to the expectation that might be huge.

••

•• is also well definedis also well defined

•• But has no definition outside of this equation. No reason But has no definition outside of this equation. No reason it should be ~1. A&R assume it is the “quark model” spin it should be ~1. A&R assume it is the “quark model” spin operator, leading to a huge value of operator, leading to a huge value of

•• But if is so large the quark model must be wrong... But if is so large the quark model must be wrong...

•• And the separation turns out to be scheme dependent and And the separation turns out to be scheme dependent and does not occur in standard, schemedoes not occur in standard, scheme G. Bodwin G. Bodwin

19901990•• Finally, the separation was motivated by the identification of Finally, the separation was motivated by the identification of

the gluon spin with the anomaly (via the Kogut-Susskind the gluon spin with the anomaly (via the Kogut-Susskind current, which is incorrect in any case...current, which is incorrect in any case...


•• Positive?Positive?---- Why?Why?---- The down quark spin is anticorrelated with the The down quark spin is anticorrelated with the nucleon’s spin...nucleon’s spin...---- And at least one (gauge invariant) component is And at least one (gauge invariant) component is negative: the gluon fields associated with the baryon spin negative: the gluon fields associated with the baryon spin splittings.splittings.---- Beware!Beware!•• Large?Large?---- Without the Altarelli-Ross Without the Altarelli-Ross proposal there is no proposal there is no a priori a priori reason for to be large.reason for to be large.

---- Large poses a severe Large poses a severe consistency problem for consistency problem for traditional quark models of hadrons.traditional quark models of hadrons.

•• Model estimates?Model estimates?---- Typically Typically -- -- And don’t forget scale dependenceAnd don’t forget scale dependence

W. VogelsangW. Vogelsang


•• FrustrationFrustration•• UnresolvedUnresolved••

ConnectionConnections?s?•• FrustrationFrustration

•• It takes an off-the-forward direction It takes an off-the-forward direction matrix element to measure orbital matrix element to measure orbital angular momentum.angular momentum.

•• Partonic picture, completely analogous to spin and other DIS Partonic picture, completely analogous to spin and other DIS structure functions...structure functions... Bashinsky & RLJ, Hagler & Bashinsky & RLJ, Hagler &

SchaferSchafer Harindranath & KunduHarindranath & Kundu

Transverse coordinates and derivatives signal Transverse coordinates and derivatives signal requirement of off-forward direction.requirement of off-forward direction.

Typical partonic density, integrated over lightcone, Typical partonic density, integrated over lightcone, function of xfunction of x

PP P'P'

x1Px1P x2P'x2P'


•• Laboratory pictureLaboratory picture

•• Both are measurable in DVCS. Though the gluon Both are measurable in DVCS. Though the gluon angular momentum is very difficult to access.angular momentum is very difficult to access.

Xiangdong Ji, Hoodbhoy & JiXiangdong Ji, Hoodbhoy & Ji

Hermes --- See Ellinghaus @ CIPANP Hermes --- See Ellinghaus @ CIPANP 20062006

•• No gauge invariant separation of gluon contributionNo gauge invariant separation of gluon contribution•• Cannot combine with DIS because they are measuring different Cannot combine with DIS because they are measuring different

quantities (except for quark spin, which is the same on the LC quantities (except for quark spin, which is the same on the LC and in the Lab)and in the Lab)

•• No recent theoretical progressNo recent theoretical progress


Rest frame quark Dirac wavefunctionRest frame quark Dirac wavefunction

Things that depend on the lower components of the Dirac Things that depend on the lower components of the Dirac wavefunction, or quark excitation beyond ground state orbital -- wavefunction, or quark excitation beyond ground state orbital -- “relativistic” effects...“relativistic” effects...

•• Difference between quark helicity and transversity distributionsDifference between quark helicity and transversity distributions•• Deviation of nucleon axial charge from NRQM 5/3Deviation of nucleon axial charge from NRQM 5/3•• Difference between nucleon’s axial charge and its tensor chargeDifference between nucleon’s axial charge and its tensor charge•• Quark orbital angular momentumQuark orbital angular momentum•• Correlation between transverse momentum and transverse spinCorrelation between transverse momentum and transverse spin

Lacking any model independent connection between these things!Lacking any model independent connection between these things!

Six theorists with Six theorists with opinions on the spin of opinions on the spin of

the protonthe proton

Six theorists with Six theorists with opinions on the spin of opinions on the spin of

the protonthe proton

spin: some answers many questions the issues raised by the “spin crisis” of the 1990’s have...

Documents