QCD and the Spin Structure of the Nucleon

Transcription

1 Graduiertenkolleg: Physik an Hadronbeschleunigern QCD and the Spin Structure of the Nucleon Gerhard K. Mallot CERN/PH 16 January 2013

2 Plan Introduction Tools: DIS SIDIS pp, Experiments Helicity structure Transverse structure & transverse momentum Outlook G. K. Mallot GK, Freiburg,

3 Introduction probing partons inclusive lepton nucleon scattering large momentum and energy transfer Q 2 and ν finite ratio Q 2 / ν large c.m. energy of the hadronic final state W > 2 GeV

4 The beginnings Electron scattering at SLAC in the late 1960ies Structure function is Q 2 independent (scaling) point-like partons in the nucleon quarks Friedman, Kendall, Taylor 1990

5 Deep inelastic scattering Bjorken-x: fraction of longitudinal momentum carried by the struck quark in infinite- momentum frame (Breit)

6 Distance scales probed longitudial transverse for for the longitudinal scale is 1 fm the transverse scale is 0.2 fm

7 Spin in the static quark model SQM: up and down quarks carry the nucleon spin! EMC: Quarks spins contribute little (1987/88) ΔΣ = 0.12

8 Parton distribution functions Three twist-2 PDFs q(x) f 1 q (x) Dq(x) g 1q (x) D T q(x) h 1q (x) unpolarised PDF quark with momentum xp in a nucleon well known unpolarized DIS helicity PDF quark with spin parallel to the nucleon spin in a longitudinally polarised nucleon known polarized DIS transversity PDF quark with spin parallel to the nucleon spin in a transversely polarised nucleon chiral odd, fairly known G. K. Mallot GK, Freiburg,

9 Tools to study the spin structure Factorization of hard interaction and fragmentation (additional input on fragmentation from e + e - ) DIS SIDIS pp

10 Polarised DIS x-sect. asymmetries (flavours ignored) J z: only quarks with opposite helicity can absorb the polarized photon via spin-flip Measure asymmetry 3/2 1/2 need polarised photons & nucleons

11 Laboratories SLAC 49 GeV e CERN DESY 27 GeV e ± RHIC 160/280 GeV µ + JLab GeV pp 6 GeV e G. K. Mallot GK, Freiburg,

12 Experiments SLAC CERN DESY JLab RHIC E80 E130 E142/3 E154/5 EMC SMC COMPASS HERMES CLAS/HALL-A Phenix/Star A worldwide effort since decades

13 longitudinally polarised muon beam logitudinally or transversely polarised proton (NH 3 ) or deuteron ( 6 LiD) target 2-stage magnetic spectrometer particle ID (RHIC, ECAL, HCAL) luminosity: cm 2 s -1 beam intensity: /s in spill beam momentum: 160 GeV/c beam polarisation: 80% target polarisation: 90% (p), 50% (d) LHC SPS

14 COMPASS Beam: 160 GeV µ +, pol. 80% from π decay Two-stage spectrometer 60 m long Hodoscopes SM1 Polarised Target 160 GeV µ beam E/HCAL1 RICH1 SM2 Straws, Gems Muon Wall 1 Muon Wall 2 MWPC E/HCAL2 MWPC, Gems, Scifi, W45 (not shown) Scifi, Silicon Micromegas, SDC, Scifi

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16 COMPASS Target system 3 He 4 He dilution refrigerator (T~50mK) solenoid 2.5T dipole magnet 0.5T acceptance ± 180 mrad 6 LiD/NH 3 50/90% pol. 40/16% dil. f. μ

17 RHIC pp (Long Island) 250G ev+250 GeV

18 RHIC polarised pp Collider absolute polarimeter (H jet) PHOBOS pc polarimeters BRAHMS & PP2PP PHENIX snakes snakes STAR spin rotators pol. H spin rotators source LINAC BOOSTER 200 MeV polarimeter AGS 5% snake pc polarimeter 20 % snake Siberian Snake

19 Siberian Snakes (helical dipoles) from Th. Roser AGS partial snakes, 1.5T (RT) & 3T(SC) 2.6 m 2.6 m RHIC full Siberian Snakes: 4 x 4 T (SC), each 2.4 m 9.6 m w/o snakes: 1000 depolarising resonances

20 Example: Phenix Also STAR

21 Helicity structure G. K. Mallot GK, Freiburg,

22 Factorisation & x-sect. asymmetries Inclusive scattering Semi-inclusive scattering long. double spin asymmetry transverse single asymmetry G. K. Mallot GK, Freiburg,

23 Proton asymmetries incl. & semi-incl. asymmetries, similar data for deuteron incl. π + K + π K G. K. Mallot GK, Freiburg,

24 Structure function g 1 (x,q 2 ) xg 1 ½ F 2 A 1 very precise data only COMPASS for x < 0.01 (Q 2 > 1) p deuteron data: ΔΣ= 0.33±0.03±0.05 Δs+Δs = 0.08±0.01±0.02 d (ΔΣ = a 0, Q 2 ) G. K. Mallot GK, Freiburg,

25 Sum rules for g 1 first moment 1 of g 1 with Neutron decay a 3 = g a Hyperon decay (3F-D)/3 Σ From 1, a 3 and a 8 we obtain Σ without assuming s = 0

26 Sum rules PLB 690 (2010) 466 from neutron β decay

27 The role of quark flavours LO analysis of 5p+5d asymmetries, DSS FF Line: NLO DSSV not including these data 5-flavour fit, assuming Δs = Δs Data (LO analysis): PLB693 (2010) 227 PRD80 (2009)

28 Angular momentum of the nucleon quarks gluons orbital small ~0.3 Small, still poorly known unknown G. K. Mallot GK, Freiburg,

29 Why is D so small? What about gluons? Considered Options (as of 1988): Skyrmions: model, all orbital angl. mom. ( BEK) maybe Bjorken sum rule broken? Measurement wrong? (LA) no! Large ΔG ~ at EMC Q 2 could mask measure quark spin via axial anomaly (ET, AR) gluon! no! requires fine tuning of cancelation of ΔG and orbital angular (orb. ang. mom. is generated at gluon emision)

30 Scaling violations (gluons) with increasing Q 2 more details are resolved quarks/gluons split and produce more partons the new partons have smaller x-bjorken PDFs and SFs became functions of Q 2 : P(x) P(x,Q 2 ) the Q 2 evolution is calculable in perturbative QCD, if the PDFs P(x,Q 2 0) are known at some Q 2 0 (DGLAP equations) x dependence is non-perturbative and not described in pqcd The gluon distribution can be determined from these scaling violations

31 F 2 (x,q 2 ) g 1 (x,q 2 ) p

32 DGLAP Gobal NLO QCD analysis choose scheme (MS, AB, jet) and Q 0 2 optionally fix ns moments from hyperon decays (a 3, a 8 ) fit PDFs for quark non-singlet and singlet and gluon to data extra problems in polarized case no positivity condition, no momentum sum rule Recent analyses include semi-inclusive and RHIC data DSSV 2009 arxiv: ; PRD80:034030,2009 Hirai, Kumano arxiv: ; NPB813: ,2009

33 RHIC polarized pp

34 QCD analyses Vogelsang: DIS 2012

35 Gluon polarization from PGF (LO) 0 D * D π s K π π s Data not yet in global fits G. K. Mallot GK, Freiburg,

36 Transverse spin structure G. K. Mallot GK, Freiburg,

37 TMD parton distributions 8 intrinsic-transverse-momentum dependent PDFs at LO Azimuthal asymmetries with different angular modulations in the hadron and spin azimuthal angles, Φ h and Φ s aka Sivers Boer Mulders Transversity G. K. Mallot GK, Freiburg,

38 SSA: transversity (Collins) and Sivers transversity chiral odd, can be measured in SIDIS (not in incl. DIS) leads to an azimuthal asymmetry if the chiral-odd Collins fragmentation function is non-zero Sivers function leads to an azimuthal asymmetry naive T-odd final/initial state interaction should change sign for SIDIS/DY related to orbital angular momentum

39 Transversity PDF Couple to chiral odd Collins FF Azimuthal cross-section asymmetry: G. K. Mallot GK, Freiburg,

40 Collins Asymmetries large asymmetry for proton ~10% zero deuteron result important opposite sign of u and d proton h - h + G. K. Mallot GK, Freiburg,

41 Global Fit Fit to COMPASS d, HERMES, BELLE (Collins FF, e + e - ) in good agreement with new proton data G. K. Mallot GK, Freiburg,

42 Sivers function Sivers Asymmetry: proposed (1990, Sivers) thought to vanish (1993, Collins) resurrected (2002, Brodsky, Hwang, Schmitt) different sign in DY and SIDIS G. K. Mallot GK, Freiburg,

43 Proton Sivers Asymmetry compatible with zero for the deuteron non-zero asymmetry for pos. hadrons h + h G. K. Mallot GK, Freiburg,

44 What s next? Focus on transverse structure of the nucleon Transverse size and orbital angular momentum (GPDs) Restricted universality of T-odd TMDs (Sivers, Boer-Mulders), sign change from SIDIS to DY, additional TMDs (pretzelocity, worm-gear) COMPASS-II wwwcompass.cern.ch/compass/proposal/compass-ii_proposal/compass-ii_proposal.pdf Other (new) facilities/experiments RHIC, JLAB 11 GeV, JPARC, erhic/elic, NICA (JINR)

45 GPD s H (E) for nucleon helicity (non)conservation PDFs and elastic FF as limiting cases ~ H, H f 1, g 1 for 0; Correlating transverse spatial and longitudinal momentum DoF tools: DVCS, HEMP (vector & pseudoscalar) Total orbital momentum: DVCS X.-D. Ji, PRL 78 (1997) 610

46 DVCS DVCS can be separated from BH and constrain the GPD H e.g. using crosssections for different μ beam charge & spin (e μ & P μ ) Deep VCS Bethe-Heitler Note: μ ± have opposite polarisation at COMPASS Charge & Spin difference and sum: Im and Re related to

47 DVCS DVCS is the cleanest process to determine GPDs need a world-wide effort global analysis over large kinematic range mandatory COMPASS-II: from HERA to JLAB 12 GeV kinematics fixed target collider B

48 transverse proton size The distance r 2 between struck quark and spectator c.m. given by t-slope of DVCS cross-section 0 (as function of x Bj, LO) Does not require full GPD determination Reminder Subtract BH, integrate over azim. φ 0 H1 exp. found fm at x Bj 10-3 Parametrisation

49 projected t-slope & transv. size COMPASS-II projection, 2 years of data taking, pilot run 2012 x B region unique to COMPASS transition from HERA HERMES/JLab

50 RPD design and electronics 3.6 m long scintillator slabs ~ 300ps timing resolution Gandalf Project: 1 GHz digitalisation of the PMT signal to cope for high rate Freiburg

51 DVCS run 18 th of October G. K. Mallot GK, Freiburg,

52 Drell Yan Process No fragmentation function involved Convolution of two PDFs Best: pol. antiproton proton (long-term) Simpler: negative pion on pol. proton (short-term) Pion valence anti-u annihilates with proton u

53 Restricted universality in SIDIS and pol. DY T-odd TMD `gauge link changes sign for T-odd TMD, restricted universality of T-odd TMDs J.C. Collins, PLB536 (2002) 43 Sivers Boer-Mulders

54 Projected measurement Sivers Boer-Mulders Sivers Boer-Mulders BM Pretze. BM transv BM Pretze. BM transv x F =x -x p x F =x -x p x F =x -x p x F =x -x p

55 Summary A lot has been learned in the last decades on pol. quark PDFs of the nucleon. Gluon polarisation is small and the shape still not known New concepts and research fields: TMD, GPDs Freiburg participates in the global effort as COMPASS member

56 (Nucleon) Spin is fun

57

58 Backup

59 DIS cross section cross section: lepton spin nucleon leptonic tensor : kinematics (QED) factorisation hadronic tensor : nucleon structure (QCD)

60 Quark Parton Model in the QPM: partons for massless spin-½ unpolarised SF, momentum distributions polarised SF, spin distributions no Q 2 dependence (scaling) Calan Gross relation g 2 twist-3 quark gluon correlations

61 Cross-Section Asymmetries unpolarised: longitudinally polarised nucleon: β=0,π transversely polarised nucleon: β=±π/2 Measure asymmetries:

62 Q 2 evolution and gluon polarization Q 2 dependence of g 1 data related to gluon polarization (DGLAP) Limited kinematic range (c.f. unpol. HERA) p d CLAS G. K. Mallot GK, Freiburg,

63 JHEP06 (2008) 066 Orbital angular momentum A model-dependent case-study

64 `Tomography ξ=0 t = Δ T 2, no long. transfer Transverse size as function of longitudinal momentum fraction adapted from JLAB 12 GeV CDR

65 Contributions of DVCS and BH at E =160 GeV 27 Deep VCS Bethe-Heitler μ * μ d T DVCS 2 + T BH 2 + Interference Term p θ Monte-Carlo Simulation for COMPASS set-up with only ECAL1+2 Missing DVCS acceptance without ECAL0 BH dominates study of Interference DVCS dominates excellent Re T DVCS study of d DVCS /dt reference yield or Im T DVCS Transverse Imaging N. d Hose, SPSC June 2010

66 Deeply Virtual Compton Scattering 28 dσ (μp μp ) = dσ BH + dσ DVCS unpol + P μ dσ DVCS pol + e μ a BH Re A DVCS + e μ P μ a BH Im A DVCS Phase 1: DVCS experiment to study the transverse imaging with +, - beam + unpolarized 2.5m long LH2 (proton) target S CS,U d ( + ) + d ( - ) d BH d Using S CS,U and integration over and BH subtraction DVCS Int unpol K. s 1 sin d DVCS /dt ~ exp(-b t ) μ μ * p θ N. d Hose, SPSC June 2010

67 Beam Charge and Spin Difference (using D CS,U ) 31 Comparison to different models μ μ * p θ =0.8 = years of data 160 GeV muon beam 2.5m LH 2 target global = 10% Systematic error bands assuming a 3% charge-dependent effect between + and - (control with inclusive evts, BH )

68 Polarized e + N at EIC Range of a Future EIC at BNL