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LNS Laboratory for Nuclear Science 1 There is a large discrepancy - PowerPoint PPT Presentation

Dec 31, 2023 •301 likes •780 views

Polarization Observables using Positron Beams Axel Schmidt MIT JPos17, September 12, 2017 LNS Laboratory for Nuclear Science 1 There is a large discrepancy in proton form factor data. 2 Unpolarized d/d 1 . 5 G E /G M 1 0 . 5

  1. Polarization Observables using Positron Beams Axel Schmidt MIT JPos17, September 12, 2017 LNS Laboratory for Nuclear Science 1

  2. There is a large discrepancy in proton form factor data. 2 Unpolarized dσ/d Ω 1 . 5 µG E /G M 1 0 . 5 Polarization asymmetries 0 0 1 2 3 4 5 6 7 8 9 Q 2 [GeV/c] 2 2

  3. Two-photon exchange might be the cause. ? G E ( Q 2 ) , G M ( Q 2 ) − → G E ( Q 2 ) , G M ( Q 2 ) , δ ˜ G E ( Q 2 , ǫ ) , δ ˜ G M ( Q 2 , ǫ ) , ˜ F 3 ( Q 2 , ǫ ) , ˜ F 4 ( Q 2 , ǫ ) , ˜ F 5 ( Q 2 , ǫ ) , ˜ F 6 ( Q 2 , ǫ ) 3

  4. Two-photon exchange might be the cause. ? G E ( Q 2 ) , G M ( Q 2 ) − → G E ( Q 2 ) , G M ( Q 2 ) , δ ˜ G E ( Q 2 , ǫ ) , δ ˜ G M ( Q 2 , ǫ ) , ˜ F 3 ( Q 2 , ǫ ) 4

  5. Two-photon exchange might be the cause. ? G E ( Q 2 ) , G M ( Q 2 ) − → G E ( Q 2 ) , G M ( Q 2 ) , δ ˜ G E ( Q 2 , ǫ ) , δ ˜ G M ( Q 2 , ǫ ) , ˜ F 3 ( Q 2 , ǫ ) σ e + p G M + ǫν − 4 ǫ G E + ν � � � � δ ˜ M 2 ˜ δ ˜ M 2 ˜ + O ( α 4 ) = 1 − 4 G M Re F 3 τ G E Re F 3 σ e − p 5

  6. Recent σ e + p /σ e − p measurements were not a slam dunk. TPE is there. . . . but it’s small. Higher Q 2 ? Afanasev, Blunden, Hasell, and Raue, Prog. Nucl. Part. Phys. (2017) 6

  7. The experimental goal should be to validate theory from multiple angles. A precise experimental determination of TPE will be a challenge. We need to validate theories that allow interpolation/extrapolation. Constraints should come from multiple channels. 7

  8. Constraining TPE using Polarization 1 Polarization transfer with e + Systematically clean Statistics prohibitive 2 Beam-normal single-spin asymmetry Really statistics prohibitive 3 Target-normal single-spin asymmetry Feasible 8

  9. Polarization transfer is a better way to measure the proton form factor ratio. Measurements are performed at one kinematic setting. Radiative corrections are small. Measure a ratio rather than a cross section. 9

  10. What polarization is transfered to the proton? e' e � 2 ǫ ( 1 − ǫ ) G E G M P t = − hP e G 2 M + ǫ τ G 2 � τ τ ( 1 + ǫ ) G E E P t / P l = √ G 2 2 ǫ G M 1 − ǫ 2 P l = hP e M M + ǫ G 2 τ G 2 E 10

  11. What polarization is transfered to the proton? e' e � 2 ǫ ( 1 − ǫ ) G E G M P t = − hP e G 2 M + ǫ τ G 2 � τ τ ( 1 + ǫ ) G E E P t / P l = √ G 2 2 ǫ G M 1 − ǫ 2 P l = hP e M M + ǫ G 2 τ G 2 E 11

  12. Polarization can be measured with a focal plane polarimeter. Focal Plane Polarimeter Drift Chambers Trigger Scintillators Rescatterer Drift Chambers Dipole 12

  13. The FPP converts transverse polarization into an azimuthal distribution. 0.10 0.10 0.08 ) FPP1 FPP2 - + f 0.05 0.05 + )/(f 0.00 0.00 0.06 - - f − 0.05 0.05 + (f < > = 0.153 ε − 0.10 0.10 0.04 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0.10 0.10 0.02 ) - + f 0.05 0.05 + )/(f 0.00 0.00 0.00 - - f − 0.05 0.05 + (f < ε > = 0.638 − 0.10 0.10 − 0.02 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0.10 0.10 0.04 − ) - + f 0.05 0.05 + )/(f 0.00 0.00 - - f − 0.06 − 0.05 0.05 + (f < > = 0.790 ε − 0.10 0.10 − 0.08 0 1 2 3 4 5 6 1 2 3 4 5 6 0 1 2 3 4 5 6 (rad) (rad) ϕ ϕ fpp fpp 13

  14. History of PT measurements 1 . 2 MIT-Bates (1999) Hall A (2001) 1 Mainz (2001) 0 . 8 µ p G Ep 0 . 6 G Mp 0 . 4 0 . 2 0 0 1 2 3 4 5 6 7 8 9 Q 2 [GeV 2 ] 14

  15. History of PT measurements 1 . 2 Hall C (2006) BLAST (2007) 1 0 . 8 µ p G Ep 0 . 6 G Mp 0 . 4 0 . 2 0 0 1 2 3 4 5 6 7 8 9 Q 2 [GeV 2 ] 15

  16. History of PT measurements 1 . 2 Hall A (2006) Hall C (2006) 1 Hall A (2007) Hall A (2010) Hall A (2011) 0 . 8 µ p G Ep 0 . 6 G Mp 0 . 4 0 . 2 0 0 1 2 3 4 5 6 7 8 9 Q 2 [GeV 2 ] 16

  17. History of PT measurements 1 . 2 G E p -I (Hall A) G E p -II (Hall A) 1 G E p -III (Hall C) G E p - 2 γ (Hall C) 0 . 8 µ p G Ep 0 . 6 G Mp 0 . 4 0 . 2 0 0 1 2 3 4 5 6 7 8 9 Q 2 [GeV 2 ] 17

  18. Polarization transfer is sensitive to TPE. � P t 2 ǫ G E = × [ 1 + . . . P l τ ( 1 + ǫ ) G M 18

  19. Polarization transfer is sensitive to TPE. � P t 2 ǫ G E = × [ 1 + . . . P l τ ( 1 + ǫ ) G M � δ ˜ � G M + 1 G E + ν − 2 � ǫν � � � δ ˜ m 2 ˜ δ ˜ ( 1 + ǫ ) m 2 ˜ + Re Re Re F 3 G M + F 3 G M G E G M + O ( α 4 ) + . . . ] 19

  20. Polarization transfer is sensitive to TPE. � P t 2 ǫ G E = × [ 1 + . . . P l τ ( 1 + ǫ ) G M � δ ˜ � G M + 1 G E + ν − 2 � ǫν � � � δ ˜ m 2 ˜ δ ˜ ( 1 + ǫ ) m 2 ˜ + Re Re Re F 3 G M + F 3 G M G E G M + O ( α 4 ) + . . . ] Different dependence from σ ( e + p ) /σ ( e − p ) ! 20

  21. Without TPE, G E G M should be constant with ǫ . � G E τ ( 1 + ǫ ) P t = × [ 1 + . . . ? 2 ǫ G M P l Any ǫ dependence is a signature of TPE. 21

  22. The GEp-2 γ experiment looked for TPE. 40 days, data taken in 2007–08, Hall C Q 2 = 2 . 5 GeV 2 / c 2 Meziane et al., PRL 106, 132501 (2011) A. J. R. Puckett et al., arXiv:1707.08587v1 [nucl-ex] (2017) 22

  23. What do positrons get you? Largest systematics in PT: Proton polarimetry Spin precession in spectrometer fields Alignment of the polarimeter ( P l ↔ P t ) 23

  24. What do positrons get you? Largest systematics in PT: Proton polarimetry Spin precession in spectrometer fields Alignment of the polarimeter ( P l ↔ P t ) By taking the ratio: ( P t ( e + ) / P l ( e + )) / ( P t ( e − ) / P l ( e − )) Proton polarimetry offsets cancel. Point-to-point biases eliminated ǫ -dependence at fixed Q 2 is a signature. Statistics limited measurements! 24

  25. What do positrons get you? Largest systematics in PT: Proton polarimetry Spin precession in spectrometer fields Alignment of the polarimeter ( P l ↔ P t ) By taking the ratio: ( P t ( e + ) / P l ( e + )) / ( P t ( e − ) / P l ( e − )) Proton polarimetry offsets cancel. Point-to-point biases eliminated ǫ -dependence at fixed Q 2 is a signature. Statistics limited measurements! Positrons can’t help you get the form factors (biases have the same sign). 25

  26. Figure-of-merit � d σ F.o.M. ∝ AP e d ΩΩ L T ε A : polarimeter analyzing power − → same P e : beam polarization ≈ 80 % − → ≈ 60 % L : luminosity ≈ 80 µ A − →≈ 100 nA T : run time ??? ε : polarimeter efficiency − → same Factor 38 increase in uncertainty! 26

  27. Imagined set-up Big Cal II SHMS e + / e – beam Big Cal HMS BigCal from GEp-III, GEp-2 γ Protons in SHMS/HMS Non-magnetic lepton detector (BigCal) SHMS for low- ǫ , in parallel with other kinematics in HMS 27

  28. Imagined set-up Big Cal II SHMS e + / e – beam Big Cal HMS BigCal from GEp-III, GEp-2 γ Protons in SHMS/HMS Non-magnetic lepton detector (BigCal) SHMS for low- ǫ , in parallel with other kinematics in HMS 28

  29. Kinematics 5 Bates Mainz Hall A 4 Hall C Q 2 [GeV 2 ] 3 2 1 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ǫ 29

  30. Q 2 = 1 . 15 GeV 2 Hall A (Gayou et al.) 1 . 2 Hall C (MacLachlan et al.) GEp-I, Hall A (Punjabi et al.) 1 . 1 Projected 1 0 . 9 µ p G E /G M 0 . 8 0 . 7 20 days of e + 16+16 4+4 0 . 6 20 days of e − 40 days total 0 . 5 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ǫ 30

  31. Q 2 = 1 . 15 GeV 2 Hall A (Gayou et al.) 1 . 2 Hall C (MacLachlan et al.) GEp-I, Hall A (Punjabi et al.) 1 . 1 Projected 1 0 . 9 µ p G E /G M 0 . 8 0 . 7 45 days of e + 36+36 4+4 0 . 6 45 days of e − 90 days total 0 . 5 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ǫ 31

  32. Q 2 = 1 . 15 GeV 2 Projected: Q 2 = 1 . 15 GeV 2 1 . 4 1 . 2 e + /e − 1 0 . 8 90 days 72 days 18 days 90 days total 0 . 6 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ǫ 32

  33. To summarize: TPE can show up in polarization transfer. e + / e − is a clean way to measure it. Systematics are on the proton side. Non-magnetic lepton detection Getting enough stats is the hard part. 33

  34. Single-spin transverse asymmetries are sensitive to the imaginary part of TPE. Target-normal: � 2 ǫ ( 1 + ǫ ) A n = √ τ � × � M + ǫ G 2 τ G 2 E � G E + ν � 2 ǫν �� � � δ ˜ M 2 ˜ δ ˜ ˜ + O ( α 4 ) − G M Im + G E Im G M + F 3 F 3 M 2 ( 1 + ǫ ) Beam Normal: � B n = 4 mM 2 ǫ ( 1 − ǫ )( 1 + τ ) × M + ǫ Q 2 � G 2 τ G 2 � E � � ν � � ν �� ˜ ˜ ˜ ˜ + O ( α 4 ) − τ G M Im F 3 + F 5 − G E Im F 4 + F 5 M 2 ( 1 + τ ) M 2 ( 1 + τ ) 34

  35. Transverse asymmetries do not violate parity. e' e 35

  36. Transverse asymmetries do not violate parity. e' e e e' 36

  37. Transverse asymmetries do not violate parity. e' e e e' 37

  38. Transverse asymmetries do not violate parity. Target-normal Beam-normal Suppressed by m e / Q ≈ 10 − 4 –10 − 6 ≈ 10 − 3 False asym. in PV Previously measured Previously measured by: 1970’s, looking for SAMPLE T-violation G0 HERMES (including with e + ) Mainz A4 3 He, Hall A HAPPEX/PREX QWeak (prelim) � d σ F.o.M = P d Ω Ω L T 38

  39. Previous beam-normal asymmetry data 0 . 8 SAMPLE 0 . 7 Mainz A4 G0 0 . 6 HAPPEX QWeak 0 . 5 Q 2 [GeV 2 ] 0 . 4 0 . 3 0 . 2 0 . 1 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ǫ 39

  40. Low- ǫ beam-normal asymmetry data 200 SAMPLE 150 G0 G0 ( 2 H ) 100 Mainz A4 Mainz A4 ( 2 H ) 50 A n [ppm] 0 − 50 − 100 − 150 − 200 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 Q 2 [GeV 2 ] 40

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