Small Angle GDH & polarized 3 He target

Transcription

1 Small Angle GDH & polarized 3 He target Nguyen Ton University of Virginia 04/14/2016 1

2 Outline Physics: Electron scattering GDH theory: sum rules. Experiment E97110 at Jefferson Lab: Setup Analysis status: asymmetries, elastic carbon cross sections Future plan Polarized 3 He target: Spin exchange optical pumping Polarimetries: NMR, EPR and Pulse- NMR 2

3 Small angle GDH (Gerasimov-Drell-Hearn) Theory: Electron scattering Sum rules: v GDH for real photon. v GDH for virtual photon. 3

4 distance [m] e Nucleus nuclear binding force n P strong force d u u Proton spin 1/2 Spin crisis 4

5 Probing a nucleon e detect e d u u Advantages of electron scattering? QED is well- known and perturbative calculable. Clean probe. 5

6 Kinematic variables 4- momentum: q 2 =- Q 2. Virtual photon energy: ν = E E d u u Final state invariant mass W 6 = M 6 + 2Mν Q 6 In Bjorken limit Q 6, ν x = Q6 2Mν in deep inelastic region 6

7 Electron scattering 7

8 Cross section Cross section = (point- like) x ( spin- independent + spin- dependent) F 1,F 2 : unpolarized structure function. F 1 = > 6 (x) distribution. Quark s momentum g 1,g 2 : polarized structure function. g 1 = > 6 (x) Quark s polarization distribution. v Electron scattering cross section with exchange of virtual photon: Cross section = f(σ G, σ H, σ GG, σ HG ) σ G = σ I/6 + σ >/6 2 σ GG = σ I/6 σ >/6 2 8 F 1 g 1, g 2

9 Sum rule All energies Internal properties: Form factors, Structure functions Global properties: Mass, anomalous magnetic moment, Coupling constant (Compton scattering amplitude) 9

10 Gerasimov- Drell- Hearn (GDH) sum rule (Q 2 = 0, real photon) U I MNO = P σ >/6 σ V WXY dv I/6 ν = 2απ6 κ 6 M 6 Experimentally measured Static property of target Theory prediction σ >/6, σ I/6 : photon absorption cross section, with photon helicity is anti- parallel or parallel to target spin. κ: anomalous magnetic moment M: target s mass GDH at Q 2 =0 10 Q 2

11 Generalized GDH sum rule (virtual photon, Q 2 >0) From real to virtual photon: change photon production cross section with electro- production cross section Or rewrite it in term of Compton scattering amplitudes (By Ji and Osborne): S1(Q 2 ), S2(Q 2 ) which are calculable at all Q 2. Hadronic d.o.f 16απ 6 Q 6 > P g > dx ] Generalized GDH = 2απ 6 S > GDH at Q 2 =0 11 Q 2

12 Bjorken sum rule Experimentally measured Difference in spin structure functions Theory Well- measured Axial charge from neutron decay Compare GDH at Q 2 =0 12 Q 2

13 Bjorken sum rule Experimental measured Difference in spin structure functions Theory Well- known Axial coupling constant from neutron decay v For finite Q 2, Bjorken sum rule is: Z 1 0 (g p 1 (x, Q2 ) g n 1 (x, Q 2 ))dx = 1 6 g a(1 + s(ln(q 2 )) +...)+... Hadronic d.o.f Generalized GDH Partonic d.o.f GDH at Q 2 =0 13 Q 2

14 Low Q 2 Chiral perturbation theory: effective theory at low energy Virtual forward Compton spin- dependent scattering amplitudes S1,2(Q 2 ) High Q 2 Use Operator Product Expansion: (perturbative)*(non- perturbative). ga ~ ga * (1+QCD radiative corrections) Z 1 0 (g p 1 g n 1 )dx = g a 6 (pqcd) χpt effective theory Generalized GDH pqcd Q 2 (GeV 2 )

15 Current data for GDH at low Q 2 region Sum rule on neutron Experiment: E94010 (1998) Hall A. E97110 (2003) Hall A. Figure from V. Sulkosky Show a smooth transition from partonic to hadronic, we expect a sharp change in slope at Q 2 <0.1 GeV 2 à important to do experiment at lower Q 2 15

16 Gerasimov- Drell- Hearn (GDH) sum rule (Q 2 = 0, real photon) U I MNO = P σ >/6 σ V WXY dv I/6 ν = 2απ6 κ 6 M 6 Experimental measured Static property of target Theory prediction σ >/6, σ I/6 : photon absorption cross section, with photon helicity is anti- parallel or parallel to target spin. κ: anomalous magnetic moment M: target s mass GDH at Q 2 =0 16 Q 2

17 Current data for GDH at low Q 2 region Sum rule on neutron Experiment: E94010 (1998) Hall A. E97110 (2003) Hall A. Figure from V. Sulkosky Show a smooth transition from partonic to hadronic, we expect a sharp change in slope at Q 2 <0.1 GeV 2 à important to do experiment at lower Q 2 17

18 Experiment E97110 Precise measurement of generalized GDH integral at 0.02<Q 2 <0.3 GeV 2. Inclusive experiment: 3 He(e, e )X Measured polarized cross section differences. Continuous beam with P e ~85%. Seven different beam energies from 1.1 GeV to 4.4 GeV and two angles (6 o and 9 o ). A B C Polarized 3 He: P t ~40%. Spokespersons:J.P Chen, A. Deur, F. Garibaldi. 18

19 Experiment setup 1 st period: mis- wired septum 2 nd period: good septum <Q 2 <0.3 GeV 2

20 6 GeV target cell Laser Laser Pumping chamber e beam Target chamber 20

21 Kinematic plot for experiment 10 1 Q 2 GeV First Period Second Period 2 Body Breakup 2 Constant Q W [MeV] 21

22 Analysis working people Supervisors: Jian- ping Chen, Alexandre Deur. Ph. D thesis: Vincent Sulkosky, Jaideep Singh, Jing Yuan (2 nd period). Others: Nilanga Liyanage, Timothy Holmstrom, Hai- jiang Lu. Present students: Chao Peng (work on 2 nd period), Nguyen Ton (work on 1 st period) 22

23 Analysis flow chart detector eff, deadtime acceptance/optic, target density N2, glass, unpolarized bkgd dilution Sum rule Data Radiative corrections g1, g2 N + ; N - Araw PID done by H. Lu PID acceptance cuts Charge livetime 23 Pb,Pt N2, glass, unpolarized bkgd dilution

24 Scaler asymmetry Charge asymmetry: A a = ab ca d a b ea d Livetime asymmetry: A HG = N e gtt N e N gtt N c N e gtt c c N e + N gtt N c Raw/scaler asymmetry: A ugv = N e N c N c + N c Where Q +, Q - are accumulated beam charge for helicity plus and helicity minus. N +, N - are number of total trigger for each helicity. N acc+, N acc- are number of accepted trigger for each helicity. 24 I = N g t offset g Calibration constant

25 Charge asymmetry for 1 st period Run# 25

26 Livetime and raw asymmetry Livetime asymmetry ( case) Livetime asymmetry ( case) Raw asymmetry ( case) Raw asymmetry ( case) 26

27 Septum+ HRS (high resolution spectrometer) optics x δ y Y target target θ Focal plane variables Forward Only 1 st order θ target Target plane variables VDC Focal plane HRS optics Q1 Q2 Dipole Target Septum magnet 27

28 Optics study Normal analysis procedure (2 nd period), we have both forward and reverse matrices. Optimize transport matrix to get best match between target reconstructed variables and target quantities from survey. Our case (1 st period), only have focal plane quantities (which come from detector). There is no standard way to deal with this. Standard procedure Mreverse Focal plane Target Mforward 28

29 Optics study Mis- wired septum Mreverse Focal plane Target Mforward Work on focal plane variables & rely on simulation Use forward matrix to transport from target to focal plane (simulation). Use target variables (phi and theta) to get geometry solid angle and then get experimental cross section. How good is our optics? How to test it? 29 Single carbon foil + elastic

30 Procedure to get cross section for focal plane method θ focal θ or From analysis cut At target (a) y focal (b) or θ or Count events inside θ focal Count events after focal plane cut, - > get cross section 30k Transport 20k (c) or 30 (d) y focal

31 Elastic carbon cross section result with focal plane method for 2 nd period (with good septum) Center foil δp=0% δp=- 2% (ub) σ ~gg (ub) % data & sim 7% 6% Conclusion: Focal plane method works well δp: position of elastic peak at focal plane 31

32 Apply focal plane method to 1 st period 32

33 Elastic carbon cross section result for 1 st period (with defective septum) Center foil δp= 0 % δp= - 2 % (ub) σ ~gg (ub) % difference 3 6 Focal plane method works well for 1 st period (with defective septum) with single foil at center position. 33

34 Future plan Finish single carbon foil for other beam energies, and foil positions. Move to extended target: N 2, 3 He. Inelastic cross sections and asymmetries. 34

35 Polarized 3 He target for 6 GeV experiments 35

36 Polarized 3 He Target ü 3 He as an effective polarized neutron target. q Neutron decay time ~ 15 mins (no free neutron target). q Deuteron (1p+1n - > uncertainty comes from extracting n and there is >50% contribution from p). 3 He wavefunction = P 3 He P P ~ n P P P n n S- wave 90% S - wave 1.5% D- wave 8% 36

37 How to polarized 3 He q We can polarized 3 He directly by metastability exchange optical pumping. Usually for low density gas. q For our case, high density (use for electron scattering), we use spin exchange optical pumping. An indirect method: use electron from alkali atom. Alkali electron e 3 He nucleus Optical pumping Spin- exchange alkali- 3 He 37

38 Optical pumping o o Apply magnetic field, energy split between 5S1/2 & 5P1/2. Use circularly polarized laser with 795nm. 5P 1/2 5S 1/2 M=-1/2 M=+1/2 38

39 Optical pumping o o Apply magnetic field, energy split between 5S1/2 & 5P1/2. Use circularly polarized laser with 5P 1/2 Collision mixing 795nm. o 5S1/2 absorbs σ e - > excited state. D1 795 nm o Decay back to ms =+1/2 or ms=- o 1/2 equally. Finally, electrons end up in 5S 1/2 m s =1/2 state M=-1/2 M=+1/2 39

40 Spin- exchange Alkali- 3 He interact through: hyperfine interaction. Rb 3 He Rb 3 He 3 He is polarized 40

41 6 GeV target cell Laser Laser Pumping chamber e beam Target chamber Glass cell 41

42 Polarimetry (polarization measurement) q q NMR: nuclear magnetic resonance (relative/absolute). EPR: electron paramagnetic resonance (absolute). 42

43 General principle 3 He Change to transverse plane (NMR). B 0 = 25 G z Keep along Z- axis but flip (EPR) 43

44 NMR (nuclear magnetic resonance) N 3 He H 1 S At the right frequency, resonance will happen. Natural frequency of spin is the Larmor frequency: ω = γ ƒ B 0 Where γ is the gyromagnetic magnetic ratio of 3 He 44

45 NMR cont. q q q AFP(adiabatic fast passage): slow & fast. Measure the transverse component of magnetization which induces signal in pair of pick- up coils. Relative measurement, need to calibrate with EPR or with known thermal equilibrium polarization of water. RF field Sweep the B0 field mv 45 Gauss

46 EPR (electron paramagnetic resonance) q Principle: Use Alkali EPR resonance frequency and the shift in frequency due to small contribution from 3 He field. B 0 khz second From frequency difference, 3 He polarization is extracted. 46

47 6 GeV improvements from target q q Spectrally- narrowed diode laser (FWHM = 0.2 nm), improves absorption efficiency. Hybrid mixture (K- Rb) increases spin- exchange efficiency. Rb K Polarization 42% - > 60% (in- beam) 70% without beam Rb K 3 He K 3 He 47

48 Overview of 3 He target upgrade plan Target will take 30 ua beam current with convection cell. 3% systematic uncertainty for polarimetry. Using convection cell: decrease polarization gradient. Pulse NMR calibrated with EPR/NMR. Convection cell 48

49 Pulse NMR q PNMR: metal windows target chamber, can t send RF field through metal. (end of target chamber). q Principle: q Send a pulse at Larmor frequency (81kHz). q 3 He spin precesses and tips away from main field. q Detect free- induction- decay signal (FID). Measure the transverse component of magnetic moment. B 0 RF field B 0 Detect FID signal 49

50 PNMR setup Send RF signal Receive signal 50

51 PNMR vs NMR in target chamber PNMR vs NMR pnmr mv 90 χ 2 / ndf / 16 Prob slope ± bkgd ± NMR mv Hot spin down measurement (2hours). No convection. Pulse NMR measure at target chamber. Pulse NMR works for spin up, hot spin down with and without convection. 51

52 People at working on 3 He target (at JLab) q Supervisor: Jian- ping Chen q Student: Kai Jin Jie Liu Nguyen Ton 52

53 Next steps Get uncertainty at low polarization region and high polarization region. Get uncertainty of calibration constant from pnmr vs NMR measurement. Aim to reach 1%. Then move to do measurement at transfer tube instead of target chamber. Characterize new cell, optimize conditions to get high polarization. 53

54 Conclusion v Small angle GDH (1 st period): Done scaler. Optics is on going. Plans: Finish optics, elastic 3 He, inelastic N 2, 3 He. v Polarized target: Finish pulse NMR test and get uncertainty. Characterize new cell, optimize conditions to get high polarization. 54

55 People at Jlab: Jian- ping Chen, Alexandre Deur. People at Uva: Xiaochao Zheng, Vincent Sulkosky, Jie Liu 55

56 e(e,k ) Probing a nucleon e(e,k) q(v,q) d u u Quark, antiquark, gluon Nucleon Constituent quark 56 Valence quark Q2

57 1D plot for target and focal plane quantities for 2 nd period θ fp (rad) y (m) fp y (m) tg W (GeV)

58 Result for downstream foil Downstream foil, δp=0% Standard method Focal plane method (ub) σ ~gg (ub) % data & sim Reason: Falling edge of acceptance. Focal plane method works well in this area too. But due to cut was not the same between 2 methods, it created the difference between 2 methods. 58

59 Kinematic variables 4- momentum: q 2 =- Q 2 à how hard Virtual photon energy: ν = E E x = Q6 2Mν In Bjorken limit Q 6, ν : finite x p p (1 x) p d u u Final state invariant mass W 6 = M G 6 + 2M G ν Q 6 59

60 Relation between electro- production cross section and structure functions d 2 d de 0 = [ T + L hp x p 2 (1 ) LT hp z p 1 2 TT ] T = 4 2 MK F 1 L = 4 2 K [F 2 (1 + 2 ) F 1 M ] LT = 4 2 MK (g 1 + g 2 ) TT = 4 2 MK (g 1 2 g 2 ) 60

61 AFP loss and lifetime for protovec- 1 AFP loss Pumping chamber(%) Target chamber(%) Coolwithout convection Hot without convection Hot with convection Lifetime Pumping chamber(hr) Target chamber(hr) Cool without convection Hot without convection Hot with convection