1. 1 An investigation of the Spin structure of the proton in D.I.S. of polarised muons on polarised protons by The European Muon Collaboration (EMC) 1989 8/02/07

2. 2 Introduction Before mid 1960’s proton was thought of as being elementary. (Q model +SLAC) Since 1970’s many experiments studied internal structure of nucleon via DIS (via e/ν). Elucidated the q-g structure of nucleons, which showed internally p are very complex->rather simple objects (Nuclear Physics). Showed p = valq’s + sq’s + gluons (q of diff. 3xcolours/colors & 6xflavours )moving in a highly relativistic non-static way. => q’s have half-integral spin (fermions).

3. 3 Of the upmost importance was to disentangle what fraction of q’s & g’s contributed to p’s overall ‘macroscopic’ property (charge, mass, spin (S)). However, little info existed on how S was distributed among its constituent partons. Compare Q=vq’s only & mass=dynamics of g+q’s inside. Difference in σ‘s for DIS between polarised μ‘s parallel (↑↑) and antiparallel (↑↓) to spin of target p (in single γ * exchange): where: G 1 and G 2 are the Spin Dependent Structure Functions (SDSF) & in Bjorken scaling limit Q 2, ν→∞ => G 1 →g 1 (x) and G 2 → g 2 (x). (x= Q 2 / 2Mv) These SDSF’s are what one measures by measuring between 2 different relative orientations of the incident μ beam and p target spins for which unpolarised SISF’s F 1 and F 2 cancel out. => Need polarised beam and target, to probe the spins of constituents of p. Note:Here one measures g 1 since g 2 is small+vanishes (suppressed by γ 2 ~ 1/Q 2 => can neglect it) for target long. To measure need a beam long on target transverse.

4. 4 A little history - SLAC 1st such polarised on polarised DIS was at SLAC (late 1970’s & early 1980s’) by E80 & E130 collaborations (Yale-SLAC). 23GeV e long ->on-> p long using butanol (C 6 O 4 H 8 ) target. (C&O nuclei S=0=> only H used) Discovered vq’s of p (uud) account for only a small fraction of total p spin. Disagreed with naïve simple non-relativistic Quark-Parton Model(QPM), which predicted 100%. QPM- proton = uud + sea strange only and A 1 p = 5/9 (see later). But in good agreement with Ellis-Jaffe & Bjorken sum rule (2 plausible models of p + n spin structure & incorporated pQCD). So in mid 1980’s (84+85) the EMC at CERN subsequently picked up the baton & used polarised positive μ long ’s on polarised p long ’s. Advantage: higher beam E (m μ > m e ) => extends kinematic region (can probe lower x). Disadvantage: lower luminosity than e beam=> higher statistical uncertainty than SLAC.

5. 5 The EMC’s experiment As previously mentioned, idea is to measure SDSF g 1 p (x). g 1 p (x)-Σ over all q flavours(f), probability density, weighted by the (charge) 2, of finding a q of a given f having a certain % of p total momentum and with its spin projected along or opposite to the p’s spin. Experimentally measure the spin dependent asymmetry: i.e. A is sensitive to whether the spin of lepton probe is parallel or antiparallel to p spin vector. one should find a different number of leptons scattered depending on if ↑↑ or ↑↓ If A=0 => q doesn’t contribute to total spin of p. This is the measurement they make. Note: This was Inclusive DIS (only leptons detected).

6. 6 A 1 –Virtual γ asymmetry. Whether γ is ↑↑ or ↑↓ to p spin vector. Having measured A, then use: In γ*–p rest frame, σ for absorption of a γ* by p when projection of total J γ-p is along incident lepton direction μ γ γ p p D-Depolarisation factor of γ* (how purely polarised long is it, always some transverse).Depends on kinematic info of γ* & R: =3/2=1/2 Finally, use: Using known values for F 2 and R. q q Key point: Helicity conservation. Initially: q+ γ *. Finally: q. So (neglecting L) J= ΣS =S γ + S q (initial state) J= S q =1/2 (final state). => initial S q = -1/2 (must be since no 3/2 S q ) => A γ * can only be absorbed by a q with opposite helicity to it. So when one measures: σ 1/2 -> q has spin parallel to spin of proton. σ 3/2 -> q has spin anti-parallel to spin of proton. -> extracting information on spin orientations of q’s inside p relative to its parent p. (How many q spins ↑↑ and ↑↓ sum to give the p spin).

7. 7 Experimental procedure Using μ beam from the SPS at CERN.( p’s on a 9 4 Be target-> π’s & K’s -> μ+ν ). 2 cells positioned longitudinally along beam => same beam flux passed through each. Data taken in 11 separate runs with various E beam :100, 120 & 200GeV. μ + beam passes through 2 cylindrical cells of solid NH 3 (highest H content available) each of length=36cm & V=1litre. 14 7 N=Spin-1 1 1 H=Spin-1/2 Free p’s (H nuclei) in each cell polarised in opp. directions ↑↑ and ↑↓ (so measure σ 1/2 / 3/2 ) to incident beam direction by method of Dynamic Nuclear Polarisation (DNP). A measured by differences in count rates of events whose vertices were reconstructed in the two target cells. Beam intensity≤4x10 per SPS pulse (2s). & repeated every 14s. Beam polarisation~80%. μ + long Note: Reversal of target spin direction(both cells)->reduce Error sys time-dependent variations of detector effic’s. Once per run here, with results before& after averaged.

8. 8 Results (1) A 1 p distribution: Free p asymmetry A 1 p vs x with previous experiments. At high x, good agreement between SLAC & CERN (EMC) data (taking into account error bars). Calitz-Kaur (based on QPM) agrees well with x>0.2 but fails below this. (However, changed m u & m d in this model & get much better agreement at low x!).

9. 9 Results (2) Now using these values of A 1 can now find the SDSF of the proton, namely: g 1 p (x). and find that: EMC data alone: EMC & SLAC data: i.e. only 12% of the p spin is carried by valence q + sea q’s! The smooth curve is ∫ using parameterisation of A 1 -used to estimate in regions not covered by the data, namely: x 0.7. Also note errors are cumulative.

10. 10 Systematic uncertainties / Conclusion The value here is in disagreement( ) and violates Ellis-Jaffe sum rule. Was dubbed ‘The Proton Spin Crisis’. QPM predicted 100% of total spin from q’s but not 12%. Where did all the spin go? Experiment questioned, other QCD related theories proposed, evidence against QCD!?. But really situation looks more like: ½=1/2ΔΣq + Δg + = S+L = J Various sources: 1)(Main) one-uncertainty in beam& target polarisations& value for F 2. 2)R (σ L /σ T ) 3)F (dilution factor->fraction of events scattering off free (polarised)p’s in target 3/17 4)Radiative corrections (theory=1 γ * exchange, experiment = all LO+HO) 5)EW effects-negligible at Q 2 range in this experiment. 6)K-app acceptance ratios: from 2cells before & after polarisation. Should be =. 3=H, 17=3xH 1 +N 14, but not exactly true since: σ n ≠ σ p and σ bound nuc ≠ σ free nuc ) small ~unknown & next challenge g’s+q’s orbital angular momentum

11. 11 :Experiments The result gave birth to a new series of experiments to measure g 1 of neutron. Began almost concurrently in 1990 at CERN, DESY and SLAC. A whole list: 1992-1996 SMC CERN, 1992-1999 E142,E154,E155, E155x SLAC, ? FNAL E704, 1995- HERMES DESY, 2002- COMPASS CERN, JLAB Japan, PHENIX RHIC-I, II, BNL. Name change! Latest value: (2006). Gluon contribution? Photon Gluon Fusion (PGF) Indirect method Detect high-p T hadron pairs Measure asymmetry between these h ± Various beam E’s, various other targets (n, D), measure g 2 (x) aswell.

12. 12 Acknowledgments Thanks to Bino Maiheu.

13. 13 Dynamic Nuclear Polarisation (DNP) Used for a range of hydrogenous materials. Transfer spin polarisation of e ±  nuclei. Require system of unpaired e ± spins(if paired not free to invert spins)& introduce into the material (NH 3 here).-unknown here?, in SMC-water doped with paramagnetic molecules. At low temperatures & in strong B-field( 3 He- 4 He dilution refrigerator+2.5T superconducting solenoid with axis = to μ + beam => to obtain longitudinal protons),e spins from paramagnetic (net magnetic dipole moments) centres become highly polarised. Transfer this polarisation by microwave irradiation at a frequency f ≈e spin resonance. Paramagnetic= random dipole moments (μ) align with external B-field. Cold-to reduce random collisions between atoms so disrupting the alignment. S μzμz -ve lowest E B-field External μzμz μzμz Highest E Process called ‘spin-flipping’ (ΔE=Highest-lowest)