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How does the proton spin ?

Steven Bass

Oberwölz, 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 proton’s 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 … ?

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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 proton‘s 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 proton´s momentum

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

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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

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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 …

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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

½ = 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 „collapse“of the singlet structure function at small x

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QCD and gA(0)

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

• What have we really measured ?

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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

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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 !

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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

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New from COMPASS

• Valence quark polarization measured using a deuteron target

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What‘s left ?

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

… where are we ?

• Consider non-perturbative aspects of the axial anomaly …

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Physics interpretation

Constituent quark =

„(topological) condensate“

+ partons

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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 …

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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

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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

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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)

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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)

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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“ !

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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

– Let´s 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 piece ?

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Subtraction at infinity (?)• Forward Compton amplitude

• Hadron tensor for polarized deep inelastic

• Scaling structure functions

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Dispersion relation for polarized DIS• Crossing symmetry

• Define

• Dispersion relation with possible finite subtraction at infinity

• … or in terms of g1

• Subtraction constant must be non-polynomial in Q^2

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• Analytic for � Taylor series expansion

• Compare result with light-cone OPE

• Equating powers of 1/x, the subtraction constant affects just the first moment

Moments and the OPE