Coulomb Sum Rule. Huan Yao Advisor: Zein-Eddine Meziani Work support DOE Grant: DE-FG02-94ER40844

Transcription

1 Coulomb Sum Rule Huan Yao Advisor: Zein-Eddine Meziani Work support DOE Grant: DE-FG02-94ER40844 Oct 12, / 30

2 Outline 1 Physics 2 Experiment 3 Data Analysis General Analysis BPM VDC Optics NaI Gas Cherenkov Acceptance 4 To do list 5 Acknowledgements 2 / 30

3 Physics Motivation The test of Coulomb Sum Rule is likely to shed light on the question of whether or not the properties of nucleons are modified in the nuclear medium. Coulomb Sum Rule states that the integration of the charge response of a nucleus over the full range of energy excitation should be equal to the total charge of the nucleus. As a result, quenching of the response at high momentum transfer may indicate the possibility of modification of nucleons properties in the nuclear medium. 3 / 30

4 Physics Motivation The test of Coulomb Sum Rule is likely to shed light on the question of whether or not the properties of nucleons are modified in the nuclear medium. Coulomb Sum Rule states that the integration of the charge response of a nucleus over the full range of energy excitation should be equal to the total charge of the nucleus. As a result, quenching of the response at high momentum transfer may indicate the possibility of modification of nucleons properties in the nuclear medium. 3 / 30

5 Physics Motivation The test of Coulomb Sum Rule is likely to shed light on the question of whether or not the properties of nucleons are modified in the nuclear medium. Coulomb Sum Rule states that the integration of the charge response of a nucleus over the full range of energy excitation should be equal to the total charge of the nucleus. As a result, quenching of the response at high momentum transfer may indicate the possibility of modification of nucleons properties in the nuclear medium. 3 / 30

6 Quasi-elastic Scattering Figure: Quasi-electron scattering where d 3 [ ] σ Q 4 dωdω = σ M q 4 R L( q, ω) + Q2 R T ( q, ω) 2 q 2 ε ε( q, ω, θ) = [1 + 2 q 2 θ Q 2 tan2 2 ] 1 4 / 30

7 Separation of R L and R T R L = q 4 Q 4 σ M 1 (ε f ε b ) (ε fσ f ε b σ b ) R T = q 2 2ε f ε b Q 2 σ M (ε f ε b ) (σ b σ f ) f :forward angle, b :backward angle 5 / 30

8 Coulomb Sum Rule S L ( q) = 1 Z 0+ R L ( q, ω) dω G E 2 q, S L 1 Figure: Data Collection 6 / 30

9 Experimental Setup Inclusive electron quasi-elastic scattering in Jefferson Lab. E: GeV P 0 : GeV θ 0 : 15, 60, 90, 120 LH 2,LH 2 +Pb, 4 He, 12 C, 56 Fe,Optics VDC,S1,S2,Gas Cerenkov,NaI+Pion Rejector (Left),PreShower+Shower (Right) 7 / 30

10 Experimental Setup Inclusive electron quasi-elastic scattering in Jefferson Lab. E: GeV P 0 : GeV θ 0 : 15, 60, 90, 120 LH 2,LH 2 +Pb, 4 He, 12 C, 56 Fe,Optics VDC,S1,S2,Gas Cerenkov,NaI+Pion Rejector (Left),PreShower+Shower (Right) 7 / 30

11 Experimental Setup Inclusive electron quasi-elastic scattering in Jefferson Lab. E: GeV P 0 : GeV θ 0 : 15, 60, 90, 120 LH 2,LH 2 +Pb, 4 He, 12 C, 56 Fe,Optics VDC,S1,S2,Gas Cerenkov,NaI+Pion Rejector (Left),PreShower+Shower (Right) 7 / 30

12 Experimental Setup Inclusive electron quasi-elastic scattering in Jefferson Lab. E: GeV P 0 : GeV θ 0 : 15, 60, 90, 120 LH 2,LH 2 +Pb, 4 He, 12 C, 56 Fe,Optics VDC,S1,S2,Gas Cerenkov,NaI+Pion Rejector (Left),PreShower+Shower (Right) 7 / 30

13 Outline 1 Physics 2 Experiment 3 Data Analysis General Analysis BPM VDC Optics NaI Gas Cherenkov Acceptance 4 To do list 5 Acknowledgements 8 / 30

14 σ raw = dσ de dω = Raw Cross Section N f N i N t E Ω N f = N fraw eff livetime N fraw : Number of Events after all necessary cuts. efficiency: Gas Cerenkov, Scintillator, NaI, Shower/PreShower, VDC livetime T 3(4)/T 3(4) raw N i = I t e BCM Calibration N t = Lρ N A Lρ: thickness of target (g/cm 2 ) N A : Avogadro s Number E = P 0 dp Ω = sinθ φ Here θ is in HRS coordinate. 9 / 30

15 σ raw = dσ de dω = Raw Cross Section N f N i N t E Ω N f = N fraw eff livetime N fraw : Number of Events after all necessary cuts. efficiency: Gas Cerenkov, Scintillator, NaI, Shower/PreShower, VDC livetime T 3(4)/T 3(4) raw N i = I t e BCM Calibration N t = Lρ N A Lρ: thickness of target (g/cm 2 ) N A : Avogadro s Number E = P 0 dp Ω = sinθ φ Here θ is in HRS coordinate. 9 / 30

16 σ raw = dσ de dω = Raw Cross Section N f N i N t E Ω N f = N fraw eff livetime N fraw : Number of Events after all necessary cuts. efficiency: Gas Cerenkov, Scintillator, NaI, Shower/PreShower, VDC livetime T 3(4)/T 3(4) raw N i = I t e BCM Calibration N t = Lρ N A Lρ: thickness of target (g/cm 2 ) N A : Avogadro s Number E = P 0 dp Ω = sinθ φ Here θ is in HRS coordinate. 9 / 30

17 σ raw = dσ de dω = Raw Cross Section N f N i N t E Ω N f = N fraw eff livetime N fraw : Number of Events after all necessary cuts. efficiency: Gas Cerenkov, Scintillator, NaI, Shower/PreShower, VDC livetime T 3(4)/T 3(4) raw N i = I t e BCM Calibration N t = Lρ N A Lρ: thickness of target (g/cm 2 ) N A : Avogadro s Number E = P 0 dp Ω = sinθ φ Here θ is in HRS coordinate. 9 / 30

18 σ raw = dσ de dω = Raw Cross Section N f N i N t E Ω N f = N fraw eff livetime N fraw : Number of Events after all necessary cuts. efficiency: Gas Cerenkov, Scintillator, NaI, Shower/PreShower, VDC livetime T 3(4)/T 3(4) raw N i = I t e BCM Calibration N t = Lρ N A Lρ: thickness of target (g/cm 2 ) N A : Avogadro s Number E = P 0 dp Ω = sinθ φ Here θ is in HRS coordinate. 9 / 30

19 σ raw = dσ de dω = Raw Cross Section N f N i N t E Ω N f = N fraw eff livetime N fraw : Number of Events after all necessary cuts. efficiency: Gas Cerenkov, Scintillator, NaI, Shower/PreShower, VDC livetime T 3(4)/T 3(4) raw N i = I t e BCM Calibration N t = Lρ N A Lρ: thickness of target (g/cm 2 ) N A : Avogadro s Number E = P 0 dp Ω = sinθ φ Here θ is in HRS coordinate. 9 / 30

20 Raw R L,R T and S L R L ( q, ω) = q4 1 Q 4 (ε f ε b ) ([ε σ σ M ] f [ε σ σ M ] b ) R T ( q, ω) = q2 2ε f ε b Q 2 (ε f ε b ) ([ σ σ M ] b [ σ f σ M ] f ) [ 1 ε( q,ω,θ) = q2 tan 2 θ Q 2] Here θ is the scattering angle. 2 q 2 = Q 2 + ω 2 ω 2 = (E i E f ) 2 Q 2 = 2E i E f (1 cosθ) σ M = α2 cos 2 (θ/2) 4Ei 2 sin 4 (θ/2) σ is in the previous slide. S L ( q) = 1 Z 0+ R L ( q,ω) dω G E 2 10 / 30

21 Outline 1 Physics 2 Experiment 3 Data Analysis General Analysis BPM VDC Optics NaI Gas Cherenkov Acceptance 4 To do list 5 Acknowledgements 11 / 30

22 BPM System Purpose Calibrate coefficients in the database to reconstruct beam position and direction at target in [z=0] plane for unrastered beam. Figure: Beam Position Monitor System 12 / 30

23 2 2 Mean x Mean y ± ± 9.785e e Mean x Mean y ± 5.916e-05 ± 9.695e e-06 Physics Experiment Data Analysis To do list Acknowledgements BPM Calibration Result L BPMA X vs Harp A X χ / ndf 2.419e-08 / 5 p e-07 ± 3.435e-05 p ± L BPMA Y vs Harp A Y χ / ndf 6.31e-09 / 5 p e-07 ± 1.57e-05 p ± L BPMB X vs Harp B X χ / ndf 3.744e-09 / p e-06 ± 1.158e-05 p ± L BPMB Y vs Harp B Y χ / ndf 5.59e-09 / 5 p e-05 ± 1.416e-05 p ± L BPMA Y vs X Entries L BPMB Y vs X Entries Figure: Beam Position Calibration BPM Technical Note 13 / 30

24 Outline 1 Physics 2 Experiment 3 Data Analysis General Analysis BPM VDC Optics NaI Gas Cherenkov Acceptance 4 To do list 5 Acknowledgements 14 / 30

25 Basic Purpose Optics is used to reconstruct the target quantities from the measured value at VDC in the spectrometer. φ tg = y sieve+d y x beam cos(θ 0 )+z react sin(θ 0 ) L z react cos(θ 0 ) x beam sin(θ 0 ) θ tg = x sieve +D x y beam L z react cos(θ 0 ) x beam sin(θ 0 ) y tg = y sieve Lφ tg x tg = x sieve Lθ tg dp kin = dp p(m,θ scat) p(m,θ 0 ) p 0 φ tg = j,k,l P jklθ j fp y fp k φl fp θ tg = j,k,l T jklθ j fp y fp k φl fp y tg = j,k,l Y jklθ j fp y fp k φl fp δ = j,k,l D jklθ j fp y fp k φl fp 15 / 30

26 Z react Figure: Optics Target Figure: Zreact Comparison 16 / 30

27 Sieve Slit Figure: Sieve Slit Figure: Sieve Slit Comparison 17 / 30

28 dp kin Figure: dp kin Comparison 18 / 30

29 Outline 1 Physics 2 Experiment 3 Data Analysis General Analysis BPM VDC Optics NaI Gas Cherenkov Acceptance 4 To do list 5 Acknowledgements 19 / 30

30 NaI System Purpose NaI Detector is to reconstruct energy from low energy electron with higher resolution. Figure: NaI Detector 20 / 30

31 L.CSRBox2.asum_p {L.cer.asum_c>1100&&L.cer.asum_c<2300&&L.tr.n==1&&abs(L.gold.dp)<0.04&&abs(L.gold.th)<0.03&&abs(L.gold.ph)<0.03&&L.CSRBox2.trx>-0.3&&L.CSRBox2.trx<0.1&&abs(L.CSRBox2.try)<0.2} Physics Experiment Data Analysis To do list Acknowledgements NaI Calibration Before Calibration Run 3813 E=739MeV, P0=121MeV/C Lead target, 120 Degree h1 Entries Mean 2186 RMS Figure: Run 3813 NaI calibration(xinhu) 21 / 30

32 NaI Cut Efficiency E= MeV, P 0 =665 MeV/c, θ 0 =15, Carbon Left NaI CutEff e- CutEff pion Rej Figure: NaI Cut Efficiency (Xinhu) 22 / 30

33 Outline 1 Physics 2 Experiment 3 Data Analysis General Analysis BPM VDC Optics NaI Gas Cherenkov Acceptance 4 To do list 5 Acknowledgements 23 / 30

34 Gas Cherenkov E= MeV, P 0 =665 MeV/c, θ 0 =15, Carbon Left Purpose Gas Cherenkov Detector is to identify particle ID CutEff e- CerCutEff pion CerCutRej Cer ADC Sum Figure: Gas Cherenkov Cut Efficiency (Xinhu) 24 / 30

35 Outline 1 Physics 2 Experiment 3 Data Analysis General Analysis BPM VDC Optics NaI Gas Cherenkov Acceptance 4 To do list 5 Acknowledgements 25 / 30

36 Basic Reason An ideal spectrometer would have a perfect acceptance with 100% efficiency, and events outside the boundaries would be totally rejected. However, the physical aperture of spectrometer has more complicated hypercube of the five coordinates. Simulation Generate electron seeds at target. Transport to the focal plane through HRS magnets. Add multi-scattering and radiative effect if necessary. Reconstruct back to target using standard Hall A optics for HRS. Compare to data. 26 / 30

37 Basic Reason An ideal spectrometer would have a perfect acceptance with 100% efficiency, and events outside the boundaries would be totally rejected. However, the physical aperture of spectrometer has more complicated hypercube of the five coordinates. Simulation Generate electron seeds at target. Transport to the focal plane through HRS magnets. Add multi-scattering and radiative effect if necessary. Reconstruct back to target using standard Hall A optics for HRS. Compare to data. 26 / 30

38 Basic Reason An ideal spectrometer would have a perfect acceptance with 100% efficiency, and events outside the boundaries would be totally rejected. However, the physical aperture of spectrometer has more complicated hypercube of the five coordinates. Simulation Generate electron seeds at target. Transport to the focal plane through HRS magnets. Add multi-scattering and radiative effect if necessary. Reconstruct back to target using standard Hall A optics for HRS. Compare to data. 26 / 30

39 Basic Reason An ideal spectrometer would have a perfect acceptance with 100% efficiency, and events outside the boundaries would be totally rejected. However, the physical aperture of spectrometer has more complicated hypercube of the five coordinates. Simulation Generate electron seeds at target. Transport to the focal plane through HRS magnets. Add multi-scattering and radiative effect if necessary. Reconstruct back to target using standard Hall A optics for HRS. Compare to data. 26 / 30

40 Basic Reason An ideal spectrometer would have a perfect acceptance with 100% efficiency, and events outside the boundaries would be totally rejected. However, the physical aperture of spectrometer has more complicated hypercube of the five coordinates. Simulation Generate electron seeds at target. Transport to the focal plane through HRS magnets. Add multi-scattering and radiative effect if necessary. Reconstruct back to target using standard Hall A optics for HRS. Compare to data. 26 / 30

41 Preliminary Result in focal plane h_data_thfp_ h_data_thfp_3925 Entries h_data_phfp_3925 h_data_phfp_3925 Entries Mean RMS Mean RMS h_data_yfp_ h_data_yfp_3925 Entries Mean RMS h_data_xfp_ h_data_xfp_3925 Entries Mean RMS Figure: Acceptance ( Preliminary Result with cross section effect ). Black Data, Red Simulation 27 / 30

42 Preliminary Result in target plane h_data_thtg_ h_data_thtg_3925 Entries Mean RMS h_data_phtg_ h_data_phtg_3925 Entries Mean RMS h_data_ytg_ h_data_ytg_3925 Entries Mean RMS h_data_dp_ h_data_dp_3925 Entries Mean RMS h_data_zreact_ h_data_zreact_3925 Entries Mean RMS Figure: Acceptance ( Preliminary Result with cross section effect ). Black Data, Red Simulation, Blue Generator for simulation 28 / 30

43 List Data Quality Check. ( Running >2000 jobs ) Radiative Correction. ( Working ) Acceptance. ( Waiting for Data Quality Check ) Separation of R L and R T. ( Done. But need data to test.) Sum Rule. ( Not start yet ) 29 / 30

44 List Data Quality Check. ( Running >2000 jobs ) Radiative Correction. ( Working ) Acceptance. ( Waiting for Data Quality Check ) Separation of R L and R T. ( Done. But need data to test.) Sum Rule. ( Not start yet ) 29 / 30

45 List Data Quality Check. ( Running >2000 jobs ) Radiative Correction. ( Working ) Acceptance. ( Waiting for Data Quality Check ) Separation of R L and R T. ( Done. But need data to test.) Sum Rule. ( Not start yet ) 29 / 30

46 List Data Quality Check. ( Running >2000 jobs ) Radiative Correction. ( Working ) Acceptance. ( Waiting for Data Quality Check ) Separation of R L and R T. ( Done. But need data to test.) Sum Rule. ( Not start yet ) 29 / 30

47 List Data Quality Check. ( Running >2000 jobs ) Radiative Correction. ( Working ) Acceptance. ( Waiting for Data Quality Check ) Separation of R L and R T. ( Done. But need data to test.) Sum Rule. ( Not start yet ) 29 / 30

48 People 30 / 30