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How does the proton spin ?

Steven Bass

Oberwlz, September 9 2008

Proton spin problem:Where does the spin of the nucleon (proton and neutron) come from ?

E.g. The key difference between 3He and 4He in low temperature physics comes from the spin of the extra neutron in 4He where does this spin come from at the quark level ?

Relativistic quark models ~ 60% of protons spin carried by intrinsic spin of quark and anti-quark constituentsPolarized Deep Inelastic Scattering quark spin content ~ 30%

Where is the missing spin ? (polarized gluons, L_z, ?)Gluon topology and the transition from current to constituent quarks elegant solution (SDB) Testable signatures in experiment

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Science: March 23, 2007

Rev Mod Phys: October 2005

Book: WSPC, Nov. 2007

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From Quarks to Hadrons

What happens to spin in the quark-gluon dof to proton transition ?

4

Proton Spin What do we expect for the proton spin content ?

Static quark model 100 %

Relativistic effects Constituent quark models ~ 60 %

[e.g. Bag Lower component of Dirac spinor is in p-wave: Shift of J from intrinsic spin orbital angular momentum ]

What has been measured ?

Quarks seem to contribute just 30 % of the protons spin (!)

Where is the missing spin ?

What does this result tell us about spin and constituent quarks ?

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Deep Inelastic Scattering Inclusive electron proton scattering

Cross-sections behave like incoherent elastic scattering on nearly-free quarks (fermions) inside

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Partonic spin structure of the proton Spin independent

and spin dependent structure functions

Have the parton interpretation

Where the distributions measure the probability to find an (anti-)quark with given polarization and momentum fraction x of the protons momentum

In QCD the first moment of the spin distributions are measured through axial current matrix elements

7

Deep Inelastic Spin Sum Rule

Dispersion relation for polarized photon-nucleon scattering + operator product expansion Sum Rule

Here nature helps us (Bjorken):

gA(3) = 1.26 (same matrix element measured in neutron beta decay)

gA(8) = 0.58 +/- 0.03 (extracted from hyperon beta decays)

Perturbative QCD corrections calculated to high precision (Larin et al)

Guess (Ellis-Jaffe hypothesis): Strangeness contribution ~ 0

gA(8) = gA(0) ~ 0.6

TEST THIS IN EXPERIMENT

8

The Spin Structure of the Proton

Polarized Deep Inelastic Scattering

First moment gA(0) ~ 0.33 +/- 0.06

(small x extrapolation biggest source of EP error)

WHERE IS THE MISSING SPIN ?

Strangeness polarization

~ -0.08 +/- 0.02

Spawned vast new EP program and theoretical ideas

9

Is there a catch ? Sum Rule is derived starting from the dispersion relation

Assumes no contribution from the circle at infinity

Otherwise we get a (finite) correction to the first moment sum rule !

[SDB, Zakopane lectures 03 and RMP]

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Sum rules

Sum rules for

gA(0) singlet axial charge ( e.g. Ellis-Jaffe #2)

what dynamics separates its value from gA(8) ?

and

= Quark spin + Glue spin + Orbital

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Convergence of the first moment integrals

COMPASS and HERMES data:

isosinglet integral converges at x ~ 0.05

~50% of isovector integral comes from

x < 0.1

Spin problem associated with collapseof the singlet structure function at small x

12

QCD and gA(0)

How does the polarized DIS measurement fit with the constituent quark picture ?

What have we really measured ?

13

Polarized glue Attempts to understand the polarized DIS values of gA(0) and Delta s

Gluon polarization

Sea and valence quark polarization

measure through hard processes in (semi-inclusive) DIS, jets, polarized pp collisions at RHIC (should have good map of the spin-flavour structure at end of this decade)

QCD inspired models predict values of gluon polarization up to about 0.6 [SDB, Brodsky, Schmidt] - about 30% of what is needed to explain the missing spin

Measurements at COMPASS and RHIC and HERMES

14

What is Delta s ?

Summary so far:

Spin content is small something to do with Delta s

What is the QCD quark-gluon interpretation of this symbol ?

Naive parton model Delta s (= includes everything)

Low kt piece associated with quark antiquark sea

Large kt piece which makes a local probe of gluon polarization in the proton

Possible term associated with the circle at infinity and Bjorken x=0 (no energy and no momentum)

polarized condensate inside a proton

Different experiments can filter out different components !

15

Gluon polarization appears small !

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What about polarized strangeness ? Tag on final state pion or kaon Spin-Flavour separation

No evidence of negative strangeness polarization

17

New from COMPASS

Valence quark polarization measured using a deuteron target

18

Whats left ?

Suppose that ongoing experiments confirm small glue and strange sea polarization,

where are we ?

Consider non-perturbative aspects of the axial anomaly

19

Physics interpretation

Constituent quark =

(topological) condensate

+ partons

20

Subtraction and the Axial Anomaly A closer look at the axial anomaly

Partially conserved (but gauge dependent) current

In A+=0 gauge [Parton Model] the forward matrix elements of K+ are invariant under residual gauge dof

corresponds to the polarized gluon contribution

? What about other gauges ?

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What about other gauges ?

The forward matrix elements are invariant under small gauge transformations (read: pQCD) but not large g.t.s which change topological winding number [Jaffe + Manohar]

Topological winding number is non-local (b.c. at infinity)

Take Fourier transformation to momentum space and get a delta(x) term corresponds after some math to the circle at infinity contribution in the dispersion relation seen earlier [SDB]

Physics interpretation: Polarized topological condensate inside a proton

Perhaps the EJ sum-rule is not so bad for constituent quarks but in the transition from current quarks (measured in pDIS) to constituent quarks some fraction of the singlet axial charge goes into this topological condensate

Constituent quark = (topological) condensate + partons

Can we test this ? Yes, hard but worthwhile

22

The proton in QCD

Quarks, antiquarks and gluon partons

Beyond pQCD, QCD vacuum is Bloch superposition of vacuum states with different topological winding numbers, and different chiralities

23

Example of x=0 polarization Vacuum tunneling processes (instantons, )

the chirality of moving quarks gets flipped but the total is conserved

Is absorbed into the vacuum and

Spin asymmetry of moving partons gets washed out with spin shifted to x=0

x=0 carries some of the spin !

subtraction constant in dispersion relation for g_1

24

Understanding the proton spin

The glue which holds the proton together is important !

Role of gluon topology in dynamical symmetry breaking and the

transition from current to constituent quarks

Spin transferred from (valence) quarks to the QCD theta-vacuum

SIDIS data + RHIC Spin Glue and sea polarization appears small

Is the proton spin problem valence like or in the sea ?

Possible elegant solution:

In the transition from current to constituent quarks:

Is there a polarized condensate inside the proton ?

(c.f. A-phase of low temperature 3He)

25

26

27

Elastic neutrino proton scatteringIndependent weak interaction measurement of gA(0)

Measure matrix element of non-singlet current

Axial charge

Measures strangeness up to heavy quark corrections

NLO heavy quark calculation [SDB,Crewther,Steffens,Thomas]

Small = -0.02

Direct measurement of Delta s (independent of potential subtraction constants)

28

Example: Crewther t Hooft Dichotomy The Crewther `t Hooft dichotomy in quark instanton interactions

The chiralities of a flavour singlet combination of quarks carrying finite momentum gets flipped in scattering from an (anti-)instanton.

Should this chirality be measured by the g.i. or partially conserved current ?

Has Physics Consequences !!!

Count change in zero modes

In both scenarios the chirality measured by Q5 of moving quarks gets flipped, thus washing out the spin asymmetry

If the X chirality is conserved [Crewther] this effect is compensated by shift of spin into the vacuum at x=0 formation of polarized condensate !

29

Photon gluon fusion with kt cuts Photon gluon fusion is an important sea generating mechanism

Conjectured to be responsible for the small value of gA(0) through polarized glue

Lets look at the development of the polarized sea as a function of transverse momentum of the produced quark antiquark pair (units of alpha_s / 2 pi) [SDB, 2003]

Strange quark production Light quark production

Does HERMES have the luminosity and angular coverage to see the high p_t piec