Spin Structure of the Proton and Deuteron

Transcription

1 Spin Structure of the Proton and Deuteron K. Griffioen College of William & Mary Spin Structure at Long Distances Jefferson Lab 12 March 2009

2 Inelastic Scattering Q 2 increases 12 March 2009 SS@LD (JLab) 2

3 F 2p (x,q 2 ) and g 1p (x,q 2 ) 12 March 2009 SS@LD (JLab) 3

4 g 1p (x,q 2 ) 12 March 2009 SS@LD (JLab) 4

5 g 1p (x,q 2 ) 12 March 2009 SS@LD (JLab) 5

6 Infinite Q 2 The Q 2 Map Parton Model, PDF(x) Large Q 2 pqcd, PDF(x,log(Q 2 )) Medium Q 2 Low Q 2 Tiny Q 2 Higher twist, target mass correct. Resonances (complexity) Chiral perturbation theory Zero Q 2 Real photons Complexity, as measured by γ 0, δ LT, d 2 and Γ 1, disappears rapidly at high and low Q 2 12 March 2009 SS@LD (JLab) 6

7 Regions of Q 2 CLAS EG1 Data scaling: lnq 2 higher twist: (1/Q 2 ) n no nice expansion χpt: (Q 2 ) n 12 March 2009 SS@LD (JLab) 7

8 Long-standing program in Hall-B at JLab to measure longitudinal double spin asymmetries A on 15 NH 3 and 15 ND 3 EG1: 0.05<Q 2 <3.5 GeV 2 data (2001); anal (2008) EG4: 0.01<Q 2 <1 GeV 2 data (2006); anal (2009) EG12: 0.5<Q 2 <7 GeV 2 data (2012?); anal (2014) Spin Structure with CLAS 12 March 2009 SS@LD (JLab) 8

9 CLAS EG1 g 1 p (Q 2 <0.7) At low Q 2 the Δ resonance drives g 1 negative Extensive x-range at fixed Q 2 allows integration over x Red curve is the EG1 model used for radiative corrections 12 March 2009 SS@LD (JLab) 9

10 CLAS EG1 g 1 p (Q 2 >0.7) & g 1 /F 1 At higher Q 2, g 1 becomes positive everywhere g 1 /F 1 falls far below the DIS extrapolation at low Q 2 Red curve is the EG1 model (dashed: DIS extrapolation) 12 March 2009 SS@LD (JLab) 10

11 A 1 Data from EG1 W > 2; Q 2 > 1 ~g 1 /F 1 Close and Melnitchouk, PRC 68, (2003) Isgur, PRD 59, (2003) pa HF perturbed QM World Data parm Q 2 = 10 GeV 2 Symmetric Q Wave function Helicity 3/2 suppression Spin 3/2 suppression CLAS-EG1b Q 2 = GeV 2 SMC SLAC - E143 SLAC - E155 HERMES pqcd SU(6) ) HF perturbed QM d1.4 c te re c o1.2 (D-sta te 1 d A World Data parm Q 2 = 10 GeV 2 World Data Parm + d WF Q 2 = 4.2 GeV 2 Symmetric Q Wave function suppression Helicity 3/2 suppression Spin 3/2 suppression CLAS-EG1b Q 2 = GeV 2 SMC SLAC - E143 SLAC - E155 HERMES pqcd SU(6) Proton Deuteron x bj x bj 12 March 2009 SS@LD (JLab) 11

12 Quark polarization in the valence limit CLAS EG1 Data Simulated Data for EG12 Extracted from A 1 p, A 1 d and d/u 12 March 2009 SS@LD (JLab) 12

13 PDFs and CLAS Error envelopes for PDFs from LSS05 global analysis (green) CLAS EG1 data significantly improve errors on Δu, Δd, Δx and ΔG (blue) CLAS EG12 (12 GeV upgrade) will especially improve ΔG (red) 12 March 2009 (JLab) 13

14 Higher Twist from g 1 in CLAS EG1 F 1 from NMC fit to F 2 and 1998 SLAC fit to R g 1 (leading twist) from NLO fit at high Q 2 h from fit to all data, especially CLAS in the pre-asymptotic region d 2 : twist-3, f 2 : twist-4 12 March 2009 SS@LD (JLab) 14

15 Bjorken Sum & Higher Twist Bjorken Sum Rule: CLAS: Deur Fit Γ 1 p-n to powers of 1/Q 2 and extract f 2 p-n 12 March 2009 SS@LD (JLab) 15

16 Nachtmann Moments CLAS, Osipenko PLB609(05) March 2009 (JLab) 16

17 Color Polarizability Osipenko, CLAS, proton, PLB609(05)249 f 2 = 0.039(39) χ E = 0.026(27) χ B = (13) E94-010, Hall A, neutron f 2 = 0.034(43) χ E = 0.033(29) χ B = (16) Deur, CLAS, Bjorken (p-n) f 2 = (74) χ E = (50) χ B = 0.024(28) More accurate determinations are needed. 12 March 2009 SS@LD (JLab) 17

18 WW g = 2 1 Wandzura-Wilczek g + 1 Q 2 =1.28 GeV 2 x g 1 y dy g = 2 g WW + 2 RSS g 2 p Burkhardt-Cottingham Sum Rule 1 Γ = 2 0 g 2 (x,q 2 )dx = 0 g2 Hall C: Slifer et al. arxiv: March 2009 SS@LD (JLab) 18

19 Duality Hall C PRL85(00)1182 Global duality to 10% Local duality to 10% W=1.232, 1.535, GeV Duality - structure functions averaged over resonances behave according to DIS systematics Global - all resonances Local - one resonance 12 March 2009 SS@LD (JLab) 19

20 Polarized Duality Hall C RSS, Wesselmann, Slifer Q 2 =1.379 GeV 2 Target Mass Corrections applied to PDFs No duality for Δ PRL98(07) GRSV: Phys. Rev. D 53, (1996) 4775 BSB : Eur. Phys. J. C 41, (2005) 327 AAC : Phys. Rev. D 62, (2000) March 2009 SS@LD (JLab) 20

21 Duality at CLAS (EG1) Proton Deuteron Δ (1232) S 11 (1535) Δ (1232) S 11 (1535) Global F 15 (1680) F 15 (1680) Global 12 March 2009 SS@LD (JLab) 21

22 CLAS Moments Γ 1 p,d low Q 2 fit GDH + χpt PRELIMINARY PRELIMINARY 12 March 2009 SS@LD (JLab) 22

23 Forward Spin Polarizability PRELIMINARY real photon point CLAS EG1 Data 12 March 2009 (JLab) 23

24 γ 0 p-n and γ 0 p+n A Deur CLAS + Hall A For isovector (p-n) case Δ contribution cancels 12 March 2009 SS@LD (JLab) 24

25 Latest CLAS Data Recent results from CLAS EG1b Uses data from all 4 beam energies 12 March 2009 SS@LD (JLab) 25

26 EG1b Fitting A 1 + ηa 2 12 March 2009 SS@LD (JLab) 26

27 EG1b A 1 vs. x Blue line: DIS model of A 1 at Q 2 =10 GeV 2 Δ dip is still significant at Q 2 ~ 2 GeV 2 12 March 2009 SS@LD (JLab) 27

28 EG1b A 2 Black points: extraction from EG1b Black line: eg1b model for A 2 Blue points: RSS data 12 March 2009 SS@LD (JLab) 28

29 EG1b g 1p for Various Q 2 s 12 March 2009 SS@LD (JLab) 29

30 EG1b g 1 d Q 2 =0.07 g 2 extracted from A 1 & A 2 g 1 D vs. x (left) vs. Q 2 (right) for W<2 GeV PRELIMINARY Q 2 =4 Bjorken x 12 March 2009 SS@LD (JLab) 30

31 EG1b A 1 d A3/2 transition is dominant PRELIMINARY _(1232)P33 N( )D13/S13 A1/2 transition is dominant 12 March 2009 SS@LD (JLab) 31

32 EG1b A 1 d g 2 extracted from A 1 & A 2 A 1 vs. x (left) vs. Q 2 (right) for W<2 GeV PRELIMINARY W(GeV) 12 March 2009 SS@LD (JLab) 32

33 EG1b g 1p /F 1p vs. Q 2 Scaling starts at: x Q March 2009 SS@LD (JLab) 33

34 EG1b g 2 g 2 extracted from A 1 & A 2 vs. x (left) vs. Q 2 (right) for W<2 GeV 12 March 2009 SS@LD (JLab) 34

35 EG1b Γ 2 & d 2 12 March 2009 SS@LD (JLab) 35

36 EG1b Γ p 1,3,5 12 March 2009 SS@LD (JLab) 36

37 EG4 Γ 1 p Expected 12 March 2009 SS@LD (JLab) 37

38 EG1b γ 0 p Error est. on g 2 (100%) PRELIMINARY PRELIMINARY 12 March 2009 SS@LD (JLab) 38

39 EG1b γ 0 d Error est. on g 2 (100%) PRELIMINARY PRELIMINARY 12 March 2009 SS@LD (JLab) 39

40 Higher Twist d 2 CLAS EG1 (proton) Osipenko, PRD71(05) Model-dependent determination Hall A (neutron) E Amarian, PRL92(04) March 2009 SS@LD (JLab) 40

41 R = σ L /σ T (DIS) Hall C: E Tvaskis, PRL98(07) March 2009 SS@LD (JLab) 41

42 Hydrogen Hyperfine Splitting = 6.48(89) = -0.57(57) Δ pol = 1.34(24) ppm from CLAS 12 March 2009 SS@LD (JLab) 42

43 EG1b B 1 and B 2 g 2 extracted from A 1 & A 2 vs. x (left) vs. Q 2 (right) for W<2 GeV 12 March 2009 SS@LD (JLab) 43

44 Moments Elastic and resonant scattering are higher twists One must be careful when to include elastic WW (leading twist) [does not] Γ (n) 1,2 = <x n g 1,2 (x)> [does not] Γ (0) 2 = 0 (Burkardt-Cottingham) [does] Γ (0)WW 2 = 0 (thus elastic cancels higher twist) Γ (2)WW 2 = -(2/3)Γ (2) 1 d 2 = 3Γ (2) 2 + 2Γ (2) 1 (higher twist) [does (not)] d 2 = 0 if Γ (2) 2 = Γ (2)WW 2 (no higher twist) B 1,2 [do not] 12 March 2009 SS@LD (JLab) 44

45 Commensurate Scaling Brodsky, Lu, PRD51(95)3652; Deur, PLB650(07) March 2009 (JLab) 45

46 A wealth of data exists for g 1, g 2 What s still missing: high x: A 1 p,d (CLAS12) Conclusions g 2 p on the proton (transverse target); SANE (Hall C) covers Q 2 >1 GeV 2; nobody s measuring Q 2 <1 GeV 2 precision and full kinematic coverage for 1< Q 2 <10 (CLAS12) low Q 2 evolution of g 1 p,d (EG4) What s gained: understanding three regions Q 2 near 0 (χpt) Q 2 from GeV 2 (TMC, higher twists, resonances, the transition) Q 2 near infinity (pqcd) 12 March 2009 SS@LD (JLab) 46