Polarized Structure Functions

Transcription

1 Polarized Structure Functions Gerard van der Steenhoven (NIKHEF) JLab, Newport News, 4 March 22 u u d 9 th Int. Conference on the Structure of Baryons

2 Introduction The origin of spin in the baryon octet: 2 = 2 q +G + L z Developing insight: EMC (SLAC, SMC and HERMES): q :3 : The quark model: q = ("#") =: Relativistic MIT bag model: q ' :6 ; :75 Experimental questions: What about flavour dependence? u(x), d(x), s(x) What about gluons? G(x) What about orbital angular momentum? Deeply Virtual Compton Scattering: L z? What about other baryons? n,,.. What about lattice QCD? longitudinal spin: q ' :8 : transverse spin: q ' :56 :9

3 Outline Introduction Longitudinal spin: Inclusive experiments: g n p (x) g n p 2 (x) Semi-inclusive experiments: q f (x) Photo-production of high p T -pairs: G(x) Deeply-virtual Compton scattering: L z (x) Hyperon production: -spin Transverse spin: Single-spin asymmetries in -production: h (x) h = - Future perspectives: HERMES Run-II COMPASS RHIC-spin SLAC TESLA-N, EIC,...

4 Introduction Polarized Deep Inelastic Lepton Scattering: E' + θ E photon -/2 +/2 quark quark Asymmetry w.r.t. to target spin orientation: A = DP T P B N "# ; N "" N "# + N "" The spin-dependent structure function g (x) : A ' g (x) F (x) ' F (x) with the quark polarization: General objective: X q f (x) = q + f (x) ; q; f (x) f e 2 f q f(x) Spin structure of the nucleon

5 The HERMES experiment The HERMES spectrometer at DESY: m 2 FRONT MUON HODO FIELD CLAMPS DRIFT CHAMBERS TRIGGER HODOSCOPE H PRESHOWER (H2) VERTEX CHAMBERS TARGET CELL VC /2 DRIFT CHAMBERS DVC FC /2 PROP. CHAMBERS MC -3 LUMINOSITY MONITOR - HODOSCOPE H BC /2 STEEL PLATE BC 3/4 TRD CALORIMETER -2 RICH IRON MAGNET WIDE ANGLE MUON HODOSCOPE Internal Target ( ;! H, 2;! H, 3;! He, 4 He, 4 N, 2 Ne, 84 Kr) : gas injection storage cell target vacuum chamber wake field suppressors thin walled beam pipe spectrometer e-beam exit window fixed collimator pumps

6 Data collected in Run I Accumulated polarized DIS events per year: Accumulated DIS [ 3 ] Hermes Running (e + + d ) (e + + p ) 997 (e + + p ) 998/99 (e - + d ) 999 (e + + d ) Days of Running T. Lindemann Hermes Collaboration online analysis Data taking in 2: cell size reduced to 2 X 8.9 mm 2 lower cell temperature: 96! 62 K Luminosity increased by factor 2.5!!

7 Unpolarized data taking End-of-Fill running: Last hour of every fill: high-density targets Loss of normal data taking: few % Targets used: H, 2 H, 4 He, 2 Ne Positron beam life time:.5 2 hours Data collected: 3.6 Million DIS events Fri Jul 4 2: 2 HERA Sun Jul 6 2: 2 Current-p [ma] p: 3.6 [ma] -. [h] 92 [GeV/c] e+: 4. [ma] 6.9 [h] 27.6 [GeV/c] Lifetime-e [h] Current-e [ma] 6 Tau(e) 5 Protons Leptons luminosity run 3 2 Time [h] Maximum luminosity: 4 33 N/cm 2 /s Dedicated HERA run at E = 2 GeV: HERMES spectrometer operated well Collected: Million DIS ev. on H, 2 H, 4 N, 84 Kr.

8 Inclusive measurements - New deuterium data on g d (x)=f d (x): g d F d = + A d == D ; ( ; )Ad 2! g d F d.4 HERMES PRELIMINARY ( data, no smearing correction).3.2 exp. systematic uncertainty uncertainty due to R x Observation: HERMES probes down to x 4 ;3

9 Inclusive measurements - 2 Compare to existing data: g d F d HERMES PRELIMINARY ( data, no smearing correction) SMC E43 E55 (averaged by HERMES) <Q 2 > GeV Conclusion: x g d (x): no strong Q2 dependence

10 Polarized Structure Functions Overview of existing xg (x) data: xg proton SMC HERMES HERMES prel. HERMES prel. rev. E55 E43.4 deuteron.2.2 neutron ( 3 He) E54 E x

11 The structure function g 2 (x) Preliminary data from SLAC E43 and E55x: [g 2 (x) is sensitive to qg-correlations and higher twist] g WW 2 (x) exp.:! solid; M. Stratmann (93):! dot-dash; Gamberg-Weigel (97):! short-dash; Song (96):! dotted; Wakamatsu (96):! long-dash; Wandzura - Wilczek interpretation: g WW 2 (x Q 2 )=;g (x Q 2 )+ Z x g (y Q 2 ) dy y g 2 (x Q 2 ) dominated by twist-2 part

12 Semi-Inclusive Asymmetries Asymmetry for semi-inclusive hadron (h) production: A h (x) = R dz P R dz P f e2 f q f(x) D h f (z) f e2 f q f(x) D h f (z) / N h "# ; N h "" N h "# + N h "" Define purity P h f (x): P h f (x) = R e2 f q f(x) Df P R h (z)dz f e2 f q f(x) Df h (z)dz [probability that hadron h is produced when quark f is hit] Measure asymmetries on various targets: ~A(x) =P(x) ~ Q(x) with ~A(x) =(A p,a h+ p, Ah; p, A d,...) and ~Q(x) =(u(x), d(x), u(x),...) ) Polarized quark distributions: u(x), d(x),...

13 Polarized quark distributions - Measured semi-inclusive asymmetries A h (x):.8.6 A,d HERMES prelim. (spring '99 data) E43 h+ A,d HERMES prelim. (spring '99 data) SMC h A,d x Extracted quark spin distributions:.75 HERMES preliminary (995 - Spring 999).5 ( u+ u )/(u+u ).25.5 ( d+ d )/(d+d ) q s /q s Spin - flavour separation x

14 Polarized quark distributions - 2 Expected data quality with data included: HERMES q extraction MC projection x ( u + u ) x ( d + d ) x u MC: 96/97 H D HERMES publ. PLB 464 (999) 23 CTEQ4LQ / (+R) GRSV 2 / (+R) x d.5 x s = x s x M. Beckmann, J. Wendland, HERMES 2

15 High-p T hadron pairs from H pqcd Compton graph and Photon-Gluon Fusion: q ; ;; ;; q g ; ;; ;; ; ; ; g Asymmetry for high-p T pions (R = PGF = Com ) : A en!h h 2 LL =^a QCDC q q +R +^a PGF G G R +R Target spin-asymmetry on long. polarized H: q q A (p T h,pt h2 ).6.4 p T h >.5 GeV/c G/G=-.2 G/G= HERMES Collaboration PRL 84 (2) GSA (< G/G> ~.4) GSB (< G/G> ~.3) GSC (< G/G> ~ -.) G/G=.4 G/G= p h2 T (GeV/c)

16 High-p T hadron pairs on 2 H Require oppositely charged hadron pairs: PGF produces only (+ ) pairs: favored pqcd on H! more + hadrons: disfavored Preliminary results on 2 H: A (p T h-,p T h+) A (p T h+,p T h-) p T h+ (GeV/c) p T h- (GeV/c) A (p T h,p T h2) A (p T π,p T π2) p T h2 (GeV/c) p T π2 (GeV/c)

17 High-p T kaon pairs Strangeness production suppressed in pqcd... High-p T kaon pairs on H and 2 H: A (p T K,p T K2) A (p T K,p T K2) p T K2 (GeV/c) p T K2 (GeV/c) A (p T K,p T K2) p T K2 (GeV/c) More statistics needed (+ MC studies)

18 Deep Virtual Compton Scattering Off-shell photon -quark scattering: Detect e and, and require: E miss = Ji s sumrule [Phys. Rev. Lett. 78 (997) 6]: Z xdx[h(x 2 )+E(x 2 )] = A q ( 2 )+B q ( 2 ) with 2 = ;t and lim [A q ( 2 )+B q ( 2 )] = 2J quark = q +2L q 2! ) DVCS: total quark angular momentum Experimental considerations: Interference N with Bethe-Heitler process: DVCS BH makes DVCS measurable Detect scattered photon, but suppress s Observe azim. asymmetry: A BetheHeitler LU =

19 First observations of DVCS Missing mass spectrum and A sin LU = 2 N P N i= sin i (P l ) i : Counts sin φ A LU e p e + γ X Counts M x 2 (GeV 2 ) M x (GeV) Azimuthal () distributions from HERMES & JLab: A LU A φ (rad) φ (deg) HERMES, PRL 87( )82 CLAS Collab., PRL 87( )822

20 DVCS: helicity dependence Exclusive leptoproduction of photon: d 4 ddtdq 2 dx = xy 2 32 (2) 4 Q 4 j BH + DVCS j 2 (+4x 2 m 2 =Q 2 ) =2 Leading order interference term: ( BH DVCS + DVCS BH ) pol = 4p 2 me 6 e l P l tqx p ; x r+ ; sin Im M ~ sin P Extract sin()-moment, ALU = 2 N N i= sin i jp l j i : sin φ± A LU e p e + γ X λ Beam = + λ Beam = - Average.2 Data show expected helicity dependence! M x (GeV)

21 DVCS: formalism Beam-charge asymmetry with unpolarised leptons: d(e + p) ; d(e ; p) cos Re ( F H + ) x B (F + F 2 ) H e ; 2 2 ; x B 4M 2F 2E Beam-spin asymmetry with polarised positrons: ;! d( e + p) ; ; d( e + p) sin ( ) Im F H + x B (F + F 2 ) H e ; 2 2 ; x B 4M 2F 2E Relate DVCS amplitudes H H e,.. to GPDs: Im H = ; X q e 2 q (H( 2 ) ; H(; 2 )) Im H e X = ; e 2 ( q H( e 2 )+ H(; e 2 )) q Re H = X q Z + e 2 [P H(x 2 )( q x ; + x + )dx ] ; Re e H = X q e 2 q [P Z + ; eh(x 2 )( x ; ; x + )dx ]

22 New DVCS results Dependence of A sin LU on x and ;t: sin φ A LU e p e + γ X M x <.7 GeV HERMES 96/97 PRELIMINARY -t =.25 GeV 2 Q 2 = 2.46 GeV 2 sin φ A LU e p e + γ X M x <.7 GeV HERMES 96/97 PRELIMINARY x Bj =. Q 2 = 2.46 GeV x Bj t (GeV 2 ) Q 2 -dependence and new 2 data for A sin LU : sin φ A LU e p e + γ X M x <.7 GeV HERMES 96/97 PRELIMINARY x Bj =. -t =.25 GeV 2 A LU e + p e + γ X (M x <.7 GeV) HERMES PRELIMINARY 2 P + P2 sin φ Q 2 (GeV 2 ) P = -. ±.3 (stat) P2 = -.2 ±.4 (stat) φ (rad) No Q 2 -dependence: hard scattering regime!

23 DVCS: beam-charge asymmetry First data for A C = N e+ ;N e; N e+ +N e; on H: A C.6.4 e ± p e ± γ X (M x <.7 GeV) HERMES PRELIMINARY P + P2 cos φ A C cos φ.4.3 e ± p e ± γ X HERMES PRELIMINARY P = -.5 ±.3 (stat) P2 =. ±.4 (stat) A C cosφ M <.7 GeV =. ±.4 (stat) ±.3 (sys) x φ (rad) M x (GeV) Calculation by Kivel et al. [hep-ph/236]: dσ e- / (dq 2 dx B dt dφ) (nb/gev 4 ) e - /e + + p e - /e + + p + γ E e = 27 GeV, Q 2 = 2.5 GeV 2, x B =.3, t = -.25 GeV BH + twist 2 + D-term BH + tw 2 + tw 3 + D-term BH only BH + twist 2 - D-term (σ e+ - σ e- ) / (σ e+ + σ e- ) Φ (deg)

24 The spin structure - Two schemes for the spin content: Quark parton model: s =. SU(3) flavour symm.: s =.6, u = d = -.2 Measure the polarization from! p ; : N dn d = 4 ( + :64 ~ P ^p) Determine u! spin transfer D LL : D LL = P ~P ^L P B D(y) = P f e2 f qn f (x)d f (z) f e2 f qn f (x) D f (z) D u (z) D u (z) Electroproduction of hyperons at HERMES: EVENTS D Λ u - -2 HERMES PRELIMINARY D Λ u n Λ (z), no Monte-Carlo correction Kaidalov, Piskunova de Florian, Stratmann, Vogelsang (LO) de Florian, Stratmann, Vogelsang (NLO) Invariant mass (GeV/c 2 ) z*=(e Λ -m Λ )/ν

25 The spin structure - 2 Data for u! spin transfer: <D LL > =.4(9) consistent with u (CQM prediction). Longitudinal spin fransfer D Λ HERMES PRELIMINARY pqcd (Ma) Diquark (Ma) Diquark, u+d (Boros) naive CQM u+d+s SU(3) f ( BJ) Negative polarisation for x F (= 2p L W ) < : z NOMAD Collab. NPB 588 (2) 3 Contributions from:!!! Longidudinal spin transfer D L Λ along W/γ HERMES PRELIMINARY E e =27.5 GeV NOMAD <E ν > =43.8 GeV WA59 <E _ ν > =44.2 GeV E665 E µ =47 GeV x F

26 Transverse polarization Three leading order distribution functions: f = momentum carried by quarks g = - longitudinal quark spin, h = - transverse quark spin, Importance of h (x) measurements: HERMES data: = is so small because of axial anomaly: Redistribution of angular momentum in nucleon: +:5, G +:, L 2 z ;:65 Redistribution is less in transverse case: < < (Quark Parton Model) Lattice QCD calculation (Phys. Rev. D 56 (997) 433): =.8() and =.56(9)

27 Measurements of h (x) The structure function h (x) is chirally odd : Not accessible in inclusive DIS Use semi-inclusive DIS with chirally-odd H?()u (z) Assume u-quark dominance Asymmetry for Collins process: A + T (x y z) =P T D nn u(x) u(x) H?()u D u (z) H?()u depends on c = h + s ; (z) Evidence for transversity from HERMES H data:.5 π π + π - sinφ A UL z..2 x P (GeV) [HERMES, PRL 84 (2) 447 and PRD 64 (2) 97]

28 Single-Spin Asymmetries on 2 H z, x, p? -dependences of A sin UL for +=; and K + :.5..5 HERMES deuteron π + π - PRELIMINARY.5 HERMES deuteron PRELIMINARY sinφ A UL sinφ A UL -.5 K z z.4 HERMES PRELIMINARY deuteron π + π -.2<z< HERMES deuteron K + PRELIMINARY.2<z<.7 sinφ A UL.2 sinφ A UL x B..2.3 x B.4 HERMES deuteron PRELIMINARY.2<z<.7.6 HERMES deuteron PRELIMINARY.2<z<.7 π + π -.4 K +.2 sinφ A UL sinφ A UL p t / GeV p t / GeV

29 Future: HERMES HERMES - Run II: 2 26 Transverse spin 2-23 Longitudinal spin Excl. react. w. Recoil Detector : Unpolarized end-of-fill runs 2-26 Simulated DVCS data with Recoil Detector ( yr run): A ch. e p e p γ A LU.6 e p e p γ φ γ, rad φ γ, rad HERMES - Run III (beyond 26?) silicon & boards photon detector fibers C2 flange space for connectors C2 collimator Lambda Wheels magnet chamber flange to mm alu pumping cross

30 Future: COMPASS The Compass experiment at CERN: Successful commissioning in 2: Most detectors commissioned at 2 8 /s. Tracking: half of the channels 6 LiD target hosted in SMC magnet: P = 45% 2 weeks smooth data taking Prospects for 22: Complete tracking and finish commissioning First measurement of G=G in 3 month run Other objectives: q(x), h (x), D, spectroscopy

31 Future: RHIC RHIC at BNL as seen by LANDSAT: Experimental break-through at RHIC: Colliding polarized protons at p s = 2 GeV P proton = 7% at injection and 25 % at GeV Luminosity:.5 3 cm ;2 s ; Physics: transverse spin asymmetries A N Longitudinal polarization: spin rotators in 22 Measure G=G from jets, cc,... Measure q f from W + production The PHENIX experiment:

32 Outlook End-station A at SLAC: E6: single spin-asymm. for inelastic J= E6: open charm photoproduction! G=G What to expect in coming years? Polarized quark distributions Polarized gluon distribution The big challenges in spin physics: The role of orbital angular momentum: Analysis and interpretation of DVCS! J q? The role of transverse spin: Measure the (x Q 2 )-dependence of h (x) The more distant future (> 2): Electron-Ion Collider at BNL: 25 GeV 2 TESLA-N at DESY: 25 GeV e + on fixed target