How does the proton spin?

Transcription

1 How does the proton spin? Steven Bass Proton spin problem: Where does the spin of the nucleon (proton and neutron) come from? E.g. The key difference between 3 He and 4 He in low temperature physics comes from the spin of the extra neutron in 4 He 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 ~ 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 Oberwölz, September

2 Science: March 23, 2007 Rev Mod Phys: October 2005 Book: WSPC, Nov

3 From Quarks to Hadrons What happens to spin in the quark-gluon dof to proton transition? 3

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 proton s spin (!) Where is the missing spin? What does this result tell us about spin and constituent quarks? 4

5 Deep Inelastic Scattering Inclusive electron proton scattering Cross-sections behave like incoherent elastic scattering on nearly-free quarks (fermions) inside 5

6 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 6

7 Deep Inelastic Spin Sum Rule Dispersion relation for polarized photon-nucleon scattering + operator product expansion Sum Rule Here nature helps us (Bjorken): g (3) A = 1.26 (same matrix element measured in neutron beta decay) g A (8) = / (extracted from hyperon beta decays) Perturbative QCD corrections calculated to high precision (Larin et al) Guess (Ellis-Jaffe hypothesis): Strangeness contribution ~ 0 g (8) A = g (0) ~ A 0.6 TEST THIS IN EXPERIMENT 7

8 The Spin Structure of the Proton Polarized Deep Inelastic Scattering First moment g A (0) ~ / (small x extrapolation biggest source of EP error) WHERE IS THE MISSING SPIN? Strangeness polarization ~ / Spawned vast new EP program and theoretical ideas 8

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] 9

10 Sum rules Sum rules for g A (0) singlet axial charge ( e.g. Ellis-Jaffe #2) what dynamics separates its value from g A (8)? and ½ = Quark spin + Glue spin + Orbital 10

11 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 11

12 QCD and g A (0) How does the polarized DIS measurement fit with the constituent quark picture? What have we really measured? 12

13 Polarized glue Attempts to understand the polarized DIS values of g A (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 13

14 Summary so far: What is Delta s? 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 k t piece associated with quark antiquark sea» Large k t 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! 14

15 Gluon polarization appears small! 15

16 What about polarized strangeness? Tag on final state pion or kaon Spin-Flavour separation No evidence of negative strangeness polarization 16

17 New from COMPASS Valence quark polarization measured using a deuteron target 17

18 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 18

19 Physics interpretation Constituent quark = (topological) condensate + partons 19

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? 20

21 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 21

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 22

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 23

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 3 He) 24

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27 Elastic neutrino proton scattering Independent weak interaction measurement of g A (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 = Direct measurement of Delta s (independent of potential subtraction constants) 27

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 Q 5 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! 28

29 Photon gluon fusion with k t cuts Photon gluon fusion is an important sea generating mechanism Conjectured to be responsible for the small value of g A (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? 29

30 Forward Compton amplitude Subtraction at infinity (?) Hadron tensor for polarized deep inelastic Scaling structure functions 30

31 Dispersion relation for polarized DIS Crossing symmetry Define Dispersion relation with possible finite subtraction at infinity or in terms of g 1 Subtraction constant must be non-polynomial in Q^2 31

32 Moments and the OPE Analytic for Taylor series expansion Compare result with light-cone OPE Equating powers of 1/x, the subtraction constant affects just the first moment 32