E97-110: Small Angle GDH
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1 E97-110: Small Angle GDH Experimental Status Report Jaideep Singh University of Virginia on the behalf of the Spokespeople: JP Chen, A Deur, F Garibaldi Thesis Students: J Singh, Dr Vincent Sulkosky, PhD, and J Yuan and the rest of YOU, the Hall A Collaboration Hall A Collaboration Meeting CC Auditorium, June 22, 2007 E97-110: Small Angle GDH p1/51
2 GDH sum rule ( Q 2 = 0 ) Firstderivedinthemid-1960 sbygerasimovanddrell&hearn,thesumrule for spin-i particles is based on the following modest yet robust arguments: ν th σ A (ν) σ P (ν) dν ν = 2π 2 α em (2m I ) [ µ/e h I Z M ] 2 E97-110: Small Angle GDH p2/51
3 GDH sum rule ( Q 2 = 0 ) Firstderivedinthemid-1960 sbygerasimovanddrell&hearn,thesumrule for spin-i particles is based on the following modest yet robust arguments: Cause precedes Effect analyticity dispersionrelations ν th σ A (ν) σ P (ν) dν ν = 2π 2 α em (2m I ) [ µ/e h I Z M ] 2 E97-110: Small Angle GDH p3/51
4 GDH sum rule ( Q 2 = 0 ) Firstderivedinthemid-1960 sbygerasimovanddrell&hearn,thesumrule for spin-i particles is based on the following modest yet robust arguments: Cause precedes Effect analyticity dispersionrelations Conservation of Probability unitarity OpticalTheorem ν th σ A (ν) σ P (ν) dν ν = 2π 2 α em (2m I ) [ µ/e h I Z M ] 2 E97-110: Small Angle GDH p4/51
5 GDH sum rule ( Q 2 = 0 ) Firstderivedinthemid-1960 sbygerasimovanddrell&hearn,thesumrule for spin-i particles is based on the following modest yet robust arguments: Cause precedes Effect analyticity dispersionrelations Conservation of Probability unitarity OpticalTheorem ν th σ A (ν) σ P (ν) dν ν = 2π 2 α em (2m I ) [ µ/e h I Z M ] 2 σ A : m I σ P : m I E97-110: Small Angle GDH p5/51
6 GDH sum rule ( Q 2 = 0 ) Firstderivedinthemid-1960 sbygerasimovanddrell&hearn,thesumrule for spin-i particles is based on the following modest yet robust arguments: Cause precedes Effect analyticity dispersionrelations Conservation of Probability unitarity OpticalTheorem Lorentz& gauge invariance Special Relativity Conservation of Charge Low Energy Theorem ν th σ A (ν) σ P (ν) dν ν = 2π 2 α em (2m I ) [ µ/e h I Z M ] 2 σ A : m I σ P : m I E97-110: Small Angle GDH p6/51
7 GDH sum rule ( Q 2 = 0 ) Firstderivedinthemid-1960 sbygerasimovanddrell&hearn,thesumrule for spin-i particles is based on the following modest yet robust arguments: Cause precedes Effect analyticity dispersionrelations Conservation of Probability unitarity OpticalTheorem Lorentz& gauge invariance Special Relativity Conservation of Charge Low Energy Theorem ν th σ A (ν) σ P (ν) dν ν = 2π 2 α em (2m I ) [ µ/e h I Z M ] 2 σ A : m I total particle mm point-like mm is the charge-to-mass ratio σ P : m I E97-110: Small Angle GDH p7/51
8 GDH sum rule ( Q 2 = 0 ) Firstderivedinthemid-1960 sbygerasimovanddrell&hearn,thesumrule for spin-i particles is based on the following modest yet robust arguments: Cause precedes Effect analyticity dispersionrelations Conservation of Probability unitarity OpticalTheorem Lorentz& gauge invariance Special Relativity Conservation of Charge Low Energy Theorem ν th σ A (ν) σ P (ν) dν ν = 2π 2 α em (2m I ) [ µ/e h I Z M ] 2 σ A : m I total particle mm point-like mm is the charge-to-mass ratio σ P : m I I GDH = µbfortheneutron I GDH = µbfor 3 He E97-110: Small Angle GDH p8/51
9 Generalization for Q 2 >0 (I =1/2) ν th K (ν, Q 2 ) K (ν, 0) [ 2σ TT + (0 or 1) ( ) Q ν 2σ LT ] dν ν = 2π 2 α em M ( Q 2) E97-110: Small Angle GDH p9/51
10 Generalization for Q 2 >0 (I =1/2) LHS: Experimentally measureable via polarized inclusive electron scattering from a polarized target ν th K (ν, Q 2 ) K (ν, 0) [ 2σ TT + (0 or 1) ( ) Q ν 2σ LT ] dν ν = 2π 2 α em M ( Q 2) E97-110: Small Angle GDH p10/51
11 Generalization for Q 2 >0 (I =1/2) LHS: Experimentally measureable via polarized inclusive electron scattering from a polarized target ν th K (ν, Q 2 ) K (ν, 0) [ 2σ TT + (0 or 1) ( ) Q ν 2σ LT ] dν ν = 2π 2 α em M ( Q 2) 2σ TT : σ LT : E97-110: Small Angle GDH p11/51
12 Generalization for Q 2 >0 (I =1/2) LHS: Experimentally measureable via polarized inclusive electron scattering from a polarized target ν th K (ν, Q 2 ) K (ν, 0) [ 2σ TT + (0 or 1) ( ) Q ν 2σ LT ] dν ν RHS: Calculable quantity using theoretical tools = 2π 2 α em M ( Q 2) 2σ TT : σ LT : E97-110: Small Angle GDH p12/51
13 Generalization for Q 2 >0 (I =1/2) LHS: Experimentally measureable via polarized inclusive electron scattering from a polarized target ν th K (ν, Q 2 ) K (ν, 0) [ 2σ TT + (0 or 1) ( ) Q ν 2σ LT ] dν ν RHS: Calculable quantity using theoretical tools = 2π 2 α em M ( Q 2) 2σ TT : Low Q 2 expansionoftheelasticsubtracted virtual forward Compton amplitude: 2σ LT : M ( Q 2) = ( κ M ) 2 + Q 2 dm dq 2 + Q 2 =0 E97-110: Small Angle GDH p13/51
14 Generalization for Q 2 >0 (I =1/2) LHS: Experimentally measureable via polarized inclusive electron scattering from a polarized target ν th K (ν, Q 2 ) K (ν, 0) [ 2σ TT + (0 or 1) ( ) Q ν 2σ LT ] dν ν RHS: Calculable quantity using theoretical tools = 2π 2 α em M ( Q 2) 2σ TT : Low Q 2 expansionoftheelasticsubtracted virtual forward Compton amplitude: 2σ LT : M ( Q 2) = ( κ M ) 2 + Q 2 dm dq 2 + Q 2 =0 slope from Chiral Perturbation Theory E97-110: Small Angle GDH p14/51
15 Generalization for Q 2 >0 (I =1/2) LHS: Experimentally measureable via polarized inclusive electron scattering from a polarized target = : Science! ν th K (ν, Q 2 ) K (ν, 0) [ 2σ TT + (0 or 1) ( ) Q ν 2σ LT ] dν ν RHS: Calculable quantity using theoretical tools = 2π 2 α em M ( Q 2) 2σ TT : Low Q 2 expansionoftheelasticsubtracted virtual forward Compton amplitude: 2σ LT : M ( Q 2) = ( κ M ) 2 + Q 2 dm dq 2 + Q 2 =0 slope from Chiral Perturbation Theory E97-110: Small Angle GDH p15/51
16 The spin structure of 3 He and the Neutron at low Q 2 I A n, Extended GDH Integral (normalized to sum rule) Q, squared four-momentum transfer (GeV/ c) E94010 (PRL ) E97110,expected (Part 1) E97110, expected (Part 2) MAID 2003 (NPA ) MAID turnover MAID slope at Q 2 = 0 JKO (PLB ) BHM (PLB ) BHM + (PRD ) Data was collected in summer E97-110: Small Angle GDH p16/51
17 The spin structure of 3 He and the Neutron at low Q 2 I A n, Extended GDH Integral (normalized to sum rule) Q, squared four-momentum transfer (GeV/ c) E94010 (PRL ) E97110,expected (Part 1) E97110, expected (Part 2) MAID 2003 (NPA ) MAID turnover MAID slope at Q 2 = 0 JKO (PLB ) BHM (PLB ) BHM + (PRD ) The old data appears to overshootthe Q 2 = 0sum! E97-110: Small Angle GDH p17/51
18 The spin structure of 3 He and the Neutron at low Q 2 I A n, Extended GDH Integral (normalized to sum rule) Q, squared four-momentum transfer (GeV/ c) E94010 (PRL ) E97110,expected (Part 1) E97110, expected (Part 2) MAID 2003 (NPA ) MAID turnover MAID slope at Q 2 = 0 JKO (PLB ) BHM (PLB ) BHM + (PRD ) MAID model has turnover and a negative slope E97-110: Small Angle GDH p18/51
19 The spin structure of 3 He and the Neutron at low Q 2 I A n, Extended GDH Integral (normalized to sum rule) Q, squared four-momentum transfer (GeV/ c) E94010 (PRL ) E97110,expected (Part 1) E97110, expected (Part 2) MAID 2003 (NPA ) MAID turnover MAID slope at Q 2 = 0 JKO (PLB ) BHM (PLB ) BHM + (PRD ) Howdothese χpt slopes compare to our data? E97-110: Small Angle GDH p19/51
20 Q2 (GeV 2) Kinematic Coverage 9 deg 4404 GeV 3775 GeV 3319 GeV 6 deg 4209 GeV GeV 2845 GeV 2135 GeV 1147 GeV 001 E (1232) W (GeV) E97-110: Small Angle GDH p20/51
21 Asymmetries 1/8 A phys = ( N + ) Q + L + ( ) N + Q + L + + ( ( ) N Q L ) N Q L 1 P b P t d N2 d glass good e count charge livetime beam pol target pol N 2 dilution glass dilution E97-110: Small Angle GDH p21/51
22 Asymmetries 2/8 A phys = ( N + ) Q + L + ( ) N + Q + L + + ( ( ) N Q L ) N Q L 1 P b P t d N2 d glass good e count charge livetime beam pol target pol N 2 dilution glass dilution standard trigger and PID cuts relatively loose acceptance cuts E97-110: Small Angle GDH p22/51
23 Asymmetries 3/8 A phys = ( N + ) Q + L + ( ) N + Q + L + + ( ( ) N Q L ) N Q L 1 P b P t d N2 d glass good e count charge livetime beam pol target pol N 2 dilution glass dilution only 10% of the runs have a charge asymmetry of > 200 ppm E97-110: Small Angle GDH p23/51
24 Asymmetries 4/8 A phys = ( N + ) Q + L + ( ) N + Q + L + + ( ( ) N Q L ) N Q L 1 P b P t d N2 d glass good e count charge livetime beam pol target pol N 2 dilution glass dilution only 15% of the runs have a deadtime > 10% E97-110: Small Angle GDH p24/51
25 Asymmetries 5/8 A phys = ( N + ) Q + L + ( ) N + Q + L + + ( ( ) N Q L ) N Q L 1 P b P t d N2 d glass good e count charge livetime beam pol target pol N 2 dilution glass dilution Moller corrected w/hall C bleedthrough: 6 degrees 68% 9 degrees 75% overall 71% Still need to check bleedthrough correction with Compton where available! E97-110: Small Angle GDH p25/51
26 Asymmetries 6/8 A phys = ( N + ) Q + L + ( ) N + Q + L + + ( ( ) N Q L ) N Q L 1 P b P t d N2 d glass good e count charge livetime beam pol target pol N 2 dilution glass dilution Water NMR and EPR calibrations differ by 15% relative There may be a subtle effect due to the fringe fields of the septum magnet We are trying to track down the source of this difference E97-110: Small Angle GDH p26/51
27 Asymmetries 7/8 A phys = ( N + ) Q + L + ( ) N + Q + L + + ( ( ) N Q L ) N Q L 1 P b P t d N2 d glass good e count charge livetime beam pol target pol N 2 dilution glass dilution can be as low as 85% at low beam energy and high ν analysis by: Xiaohui Zhan (MIT) E97-110: Small Angle GDH p27/51
28 Asymmetries 8/8 A phys = ( N + ) Q + L + ( ) N + Q + L + + ( ( ) N Q L ) N Q L 1 P b P t d N2 d glass good e count charge livetime beam pol target pol N 2 dilution glass dilution can be as low as 50% at low beam energy and high ν analysis by: Xiaohui Zhan (MIT) E97-110: Small Angle GDH p28/51
29 Unpolarized Cross Sections 1/5 σ 0 = [ good e count charge livetime target density detector eff acceptance N 0 (Q 0 e)l 0 ρǫ det ] 1 ( Z Ω E f ) E97-110: Small Angle GDH p29/51
30 Unpolarized Cross Sections 2/5 σ 0 = [ N 0 (Q 0 e)l 0 ρǫ det ] 1 ( Z Ω E f ) good e count charge livetime target density detector eff acceptance standard trigger and PID cuts relatively tight acceptance cuts N 2 reference cell subtraction empty reference cell subtraction kinematic matching V Sulkosky and R Feuerbach E97-110: Small Angle GDH p30/51
31 Unpolarized Cross Sections 3/5 σ 0 = [ N 0 (Q 0 e)l 0 ρǫ det ] 1 ( Z Ω E f ) good e count charge livetime target density detector eff acceptance cell avg (amg) fill pb (rel) Proteus % Penelope % Priapus % reanalysis of PB data by: Vladimir Nelyubin (UVa) E97-110: Small Angle GDH p31/51
32 Unpolarized Cross Sections 4/5 σ 0 = [ good e count charge livetime target density detector eff acceptance N 0 (Q 0 e)l 0 ρǫ det ] 1 ( Z Ω E f ) PID efficiencies done by Hai-jiang Lu (USTC) VDC multitrack identification in progress by Jing Yuan (Rutgers) E97-110: Small Angle GDH p32/51
33 Unpolarized Cross Sections 5/5 σ 0 = [ good e count charge livetime target density detector eff acceptance N 0 (Q 0 e)l 0 ρǫ det ] 1 ( Z Ω E f ) A lot of progress has been made by Vince Sulkosky, but we still have some issues to work out E97-110: Small Angle GDH p33/51
34 Kinematic Matching Goal: To insure that the A phys and σ 0 are extracted for the same ν and average scattering angle θ sc Apply loose cuts to get more statistics for A phys E97-110: Small Angle GDH p34/51
35 Kinematic Matching Goal: To insure that the A phys and σ 0 are extracted for the same ν and average scattering angle θ sc Apply loose cuts to get more statistics for A phys Calculate A phys per ν bin E97-110: Small Angle GDH p34/51
36 Kinematic Matching Goal: To insure that the A phys and σ 0 are extracted for the same ν and average scattering angle θ sc Apply loose cuts to get more statistics for A phys Calculate A phys per ν bin For each ν bin, using the A phys sample, calculate θ sc E97-110: Small Angle GDH p34/51
37 Kinematic Matching Goal: To insure that the A phys and σ 0 are extracted for the same ν and average scattering angle θ sc Apply loose cuts to get more statistics for A phys Calculate A phys per ν bin For each ν bin, using the A phys sample, calculate θ sc Apply tighter cuts to select a super-clean subset of A phys sample for the σ 0 analysis E97-110: Small Angle GDH p34/51
38 Kinematic Matching Goal: To insure that the A phys and σ 0 are extracted for the same ν and average scattering angle θ sc Apply loose cuts to get more statistics for A phys Calculate A phys per ν bin For each ν bin, using the A phys sample, calculate θ sc Apply tighter cuts to select a super-clean subset of A phys sample for the σ 0 analysis Calculate σ 0 for each ν & φ tg bin E97-110: Small Angle GDH p34/51
39 Kinematic Matching Goal: To insure that the A phys and σ 0 are extracted for the same ν and average scattering angle θ sc Apply loose cuts to get more statistics for A phys Calculate A phys per ν bin For each ν bin, using the A phys sample, calculate θ sc Apply tighter cuts to select a super-clean subset of A phys sample for the σ 0 analysis Calculate σ 0 for each ν & φ tg bin For each ν-φ tg bin, using the σ 0 sample, calculate θ sc E97-110: Small Angle GDH p34/51
40 Kinematic Matching Goal: To insure that the A phys and σ 0 are extracted for the same ν and average scattering angle θ sc Apply loose cuts to get more statistics for A phys Calculate A phys per ν bin For each ν bin, using the A phys sample, calculate θ sc Apply tighter cuts to select a super-clean subset of A phys sample for the σ 0 analysis Calculate σ 0 for each ν & φ tg bin For each ν-φ tg bin, using the σ 0 sample, calculate θ sc For each ν bin, interpolate σ 0 along φ tg to match θ sc with the corresponding θ sc for the A phys sample E97-110: Small Angle GDH p34/51
41 Some linear algebra, pt 1 & refer to the target spin para & perp to the beam line σ is the cross section difference between the target spin pointing up vs down the other stuff is just kinematic factors like the beam energy, the energy loss, and the scattering angle ( σ, = 2 A, σ 0 ) ( σ + cos(α) + sin(α) = 2Γ σ sin(α) + cos(α) ) pvirt ( σ TT σ LT ) E97-110: Small Angle GDH p35/51
42 RC Formalism 1 Radiative Corrections to Elastic and Inelastic ep and µp Scattering LW Mo and YS Tsai, RMP 41, (1969) 2 Radiative Corrections to Electron Scatterings Yung-Su Tsai, SLAC-PUB-848, January Electron scattering at 4 o with energies of GeV S Stein et al, PRD 12, (1975) 4 Measurement of kinematic and nuclear dependence of R = σ L /σ T in deep inelastic electron scattering S Dasu, et al, PRD 49, (1994) 5 POLRAD 20 FORTRAN code for the Radiative Corrections Calculation to Deep Inelastic Scattering of Polarized Particles I Akushevich, A Ilyichev, N Shumeiko, A Soroko, and T Tolkachev arxiv:hep-ph/ v1 26 Jun 1997 E97-110: Small Angle GDH p36/51
43 Raw data vs Elastic tail 20, 2135 MeV (nb/mev/sr) o at σ el π ν (MeV) E97-110: Small Angle GDH p37/51
44 After elastic RC vs Elastic tail 20, 2135 MeV (nb/mev/sr) o at σ el π ν (MeV) E97-110: Small Angle GDH p38/51
45 After elastic RC vs After inelastic RC 20, 2135 MeV (nb/mev/sr) o at σ el π ν (MeV) E97-110: Small Angle GDH p39/51
46 After all RC vs Raw data 20, 2135 MeV (nb/mev/sr) o at σ el π ν (MeV) E97-110: Small Angle GDH p40/51
47 Features in σ from E QE E = 086 GeV 1 QE E = 17 GeV 0 nb/mev sr 0 Delta (Q^2 ~ 004 GeV^2) nb/mev sr 1 2? Delta (Q^2 ~ 02 GeV^2) 10? σ σ W (MeV) (from K Slifer) 1 broad peak (defines absolute sign of σ) 2 zero-crossing near π-threshold σ σ W (MeV) 3 less broad QuasiElastic peak with opposite sign 4 threshold behaviour with same sign E97-110: Small Angle GDH p41/51
48 After all RC vs Raw data 20, 2135 MeV (nb/mev/sr) o at σ el π ν (MeV) E97-110: Small Angle GDH p42/51
49 Some linear algebra, pt 2 Γ is the virtual photon flux α is the lab angle between the target spin and q pvirt is the virtuality matrix ( σ σ ) = 2Γ ( + cos(α) + sin(α) sin(α) + cos(α) ) pvirt ( σ TT σ LT ) E97-110: Small Angle GDH p43/51
50 Integrand of I 3 A χpt calculations for the slope are given with respect to this form of the generalized integral: I 3 A (Q2 ) = dv 2(1 x)σ TT ν th ν I m about to show you the integrand at constant energy versus W! NOTE: These results are preliminary! E97-110: Small Angle GDH p44/51
51 33 GeV at 9 deg 5 0 (µ b/mev) (1-x)σ TT /ν E = 33 GeV π (1232) W (GeV) elastic threshold E97-110: Small Angle GDH p45/51
52 22 GeV at 9 deg 5 0 (µ b/mev) (1-x)σ TT /ν E = 22 GeV π (1232) W (GeV) elastic threshold E97-110: Small Angle GDH p46/51
53 28 GeV at 6 deg 5 0 (µ b/mev) (1-x)σ TT /ν E = 28 GeV π (1232) W (GeV) elastic threshold E97-110: Small Angle GDH p47/51
54 21 GeV at 6 deg 5 0 (µ b/mev) (1-x)σ TT /ν E = 21 GeV π (1232) W (GeV) elastic threshold E97-110: Small Angle GDH p48/51
55 11 GeV at 9 deg 5 0 (µ b/mev) (1-x)σ TT /ν E = 11 GeV π (1232) W (GeV) elastic threshold E97-110: Small Angle GDH p49/51
56 What do we need for the neutron integral? Goal: Form the generalized integral I A (Q 2 ) for the neutron Model and subtract quasielastic contribution E97-110: Small Angle GDH p50/51
57 What do we need for the neutron integral? Goal: Form the generalized integral I A (Q 2 ) for the neutron Model and subtract quasielastic contribution Interpolate quantities from constant energy to constant Q 2 E97-110: Small Angle GDH p50/51
58 What do we need for the neutron integral? Goal: Form the generalized integral I A (Q 2 ) for the neutron Model and subtract quasielastic contribution Interpolate quantities from constant energy to constant Q 2 Extract integrated neutron quantities from integrated 3 He quantities E97-110: Small Angle GDH p50/51
59 What do we need for the neutron integral? Goal: Form the generalized integral I A (Q 2 ) for the neutron Model and subtract quasielastic contribution Interpolate quantities from constant energy to constant Q 2 Extract integrated neutron quantities from integrated 3 He quantities Estimate the DIS W > 2 GeV contribution to the integral E97-110: Small Angle GDH p50/51
60 Error Budget, so far (last slide!) Rad corr? J Singh (finite acc/target effects) Acceptance 75% V Sulkosky/J Singh (elastic x-check) Target pol 75% J Singh Beam Pol 35% J Singh (x-check with Compton) VDC multitracks 25% J Yuan (in progress) Target density 20% done Charge 10% done PID cuts/effs < 10% done dilution factors < 10% done total syst stat near > 12% getting there tiny E97-110: Small Angle GDH p51/51
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