** Towards an understanding of the nucleon’s spin structure:** from hard to soft scales 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 constituents Polarized Deep Inelastic Scattering quark “spin content” ~15 - 35% Where is the missing “spin” ? (polarized gluons, L_z, … ?) Transition from current to constituent quarks elegant “solution” (SDB) Testable signatures in ongoing and future experiments Steven Bass, Innsbruck BNL, June 05 2006

**Reviews of Modern Physics, Oct. 2005**

**From Quarks to Hadrons** • What happens to spin in the quark-gluon dof to proton transition … ?

**QCD: 99.99% of the mass of the visible Universe **

**What about Spin ?** • Fundamental property of nature • Pauli principle stability of the Universe • Proton: eigenstate of the Poincare algebra spin ½ • How to understand in terms of the quarks and gluons inside ?

**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 ?

**Deep Inelastic Scattering** • Inclusive electron proton scattering • Cross-sections behave like incoherent elastic scattering on nearly-free quarks (fermions) inside

**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

**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

**Polarized Deep Inelastic Scattering** First moment gA(0)~ 0.15 – 0.35 (small x extrapolation biggest source of EP error) WHERE IS THE „MISSING SPIN“ ? „Strangeness polarization“ ~ -0.10 +/- 0.04 Spawned vast new EP program and theoretical ideas … The Spin Structure of the Proton

**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]

**Sum rules** • Sum rules for gA(0) singlet axial charge (… e.g. Ellis-Jaffe #2) or ½ = Quark spin + Glue spin + Orbital

**Possible path to understanding …** • Subtraction at infinity is non-perturbative (if finite) Come back to this shortly • Let us first look in detail at the isovector part of g_1 No gluonic contributions (cancel between proton and neutron) • How good are quark model predictions ? • If good, how far can we use our understanding of constituent quarks (dynamical symmetry breaking in QCD) to try to understand the flavour-singlet part of g_1 ?

**The Bjorken Sum Rule** • Things work very well in the isovector channel (proton – neutron) • The Bjorken Sum Rule for the isovector part of g1 and where it comes from in Bjorken x • Experiment: • Works to 10% accuracy • Quark models get gA(3) right ! Curious EP result: c. 50% of the Bjorken SR comes from x < 0.12

**Regge theory and perturbative evolution** • The isovector part of g_1 rises at small x as ~ x-0.5 c.f. soft Regge prediction ~ x+0.4 • Rise needed to accomodate area under the Bjorken sum-rule • Soft Regge input at soft scales + perturbative QCD evolution • OR • A separate hard exchange (a_1 + hard pomeron cut ?) • Look for in polarized photoproduction (EIC) or • the spin dependent part of the total cross-section at RHIC (LL) ?

**Isosinglet spin structure function**

**QCD and gA(0)** • How does the polarized DIS measurement fit with the constituent quark picture ? • What have we really measured ?

**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 50% of what is needed to explain the „missing spin“ • Forthcoming measurements at COMPASS and RHIC: if gluon polarization turns out to be much larger, what dynamics could produce such an effect ?

**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 !

**Gluon polarization appears small !** First data ……………….

**What about polarized strangeness ?** • Tag on final state pion or kaon Spin-Flavour separation • No evidence of the negative strangeness polarization seen in inclusive data

**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 ?

**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 …

**Physics interpretation** Constituent quark = „(topological) condensate“ + partons

**Quarks, antiquarks and gluon partons** Beyond pQCD, QCD vacuum is Bloch superposition of vacuum states with different topological winding numbers, and different chiralities The proton in QCD

**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

**Elastic neutrino proton scattering** Independent 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)

**Understanding the proton spin ** • The glue which holds the proton together is important ! • Dynamical symmetry breaking and the transition from current to constituent quarks (possible evidence of topological properties of gluon gauge fields) • EP: Parton contributions being mapped out in ongoing and planned experiments : COMPASS, HERMES, Jlab, RHIC spin (next 7+ years) gluon, valence and sea quark polarizations Ideas to do the neutrino-proton measurement (JPARC …2011) • 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)

**Isovector structure functions** Plot the spin dependent and spin independent isovector s.f.s together • Ratio R(3) = 2x g1(p-n)/F2(p-n) measures ratio of spin to non-spin isovector distributions. • Interesting: Essentially constant in the measured region for x < 0.2 at the value predicted by simple quark models. • Why should quark model expectations work for x < 0.1 ? • NOWHERE ELSE TO PUT THE AREA UNDER THE BJORKEN SUM RULE !!