Two photon exchange: What to measure next Jan C. Bernauer ACFI workshop ”The Electroweak Box” – September 2017 1
Phenomenology 2 Rosenbluth Polarization Litt ’70 Gayou ’01 Bartel ’73 Punjabi ’05 Andivahis ’94 Jones ’06 Walker ’94 Puckett ’10 1 . 5 Christy ’04 Paolone ’10 Qattan ’05 Puckett ’12 µG E /G M 1 0 . 5 VEPP-3 JLAB OLYMPUS 0 0 1 2 3 4 5 6 7 Q 2 [(GeV/ c ) 2 ] 2
Phenomenology 2 Rosenbluth Polarization Fits Bernauer ’13 Litt ’70 Gayou ’01 Fit Rosenbluth Bartel ’73 Punjabi ’05 Fit all + phen. TPE Andivahis ’94 Jones ’06 Walker ’94 Puckett ’10 1 . 5 Christy ’04 Paolone ’10 Qattan ’05 Puckett ’12 µG E /G M 1 0 . 5 VEPP-3 JLAB OLYMPUS 0 0 1 2 3 4 5 6 7 Q 2 [(GeV/ c ) 2 ] 3
Direct measurement: Three modern experiments CLAS e − to γ to e + / − Kinematic Reach of Two-Photon Experiments -beam 5 5 Phys. Rev. C 95, CLAS VEPP-3 Run I OLYMPUS VEPP-3 Run II 065201 (2017) 4 4 PRL 114, 062003 Q 2 [ ( GeV /c ) 2 ] VEPP-3 3 3 1.6/1 GeV beam no field 2 2 Phys. Rev. Lett. 114, 062005 (2015) 1 1 OL MPUS 0 0 DORIS @ DESY 0 0 0 . 2 0 . 2 0 . 4 0 . 4 0 . 6 0 . 6 0 . 8 0 . 8 1 1 2 GeV beam ǫ Phys. Rev. Lett. 118, 092501 (2017) 4
OLYMPUS results (B. Henderson et al., Phys. Rev. Lett. 118, 092501 (2017)) Main spectrometer 1 . 05 12 ◦ telescopes Correlated uncertainty 1 . 04 Blunden N only Blunden N + ∆ Bernauer 1 . 03 Tomalak 1 . 02 R 2 γ 1 . 01 1 0 . 99 0 . 98 0 . 97 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 ǫ 2.0 1.5 1.0 0.5 0.0 [ (GeV /c ) 2 ] Q 2 5
OLYMPUS results re-binned Main spectrometer 1 . 05 12 ◦ telescopes Correlated uncertainty 1 . 04 Blunden N only Blunden N + ∆ Bernauer 1 . 03 Tomalak 1 . 02 R 2 γ 1 . 01 1 0 . 99 0 . 98 0 . 97 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 ǫ 2.0 1.5 1.0 0.5 0.0 [ (GeV /c ) 2 ] Q 2 6
Difference of data to prediction: Blunden’s hadronic calculation 0 . 03 0 . 02 0 . 01 0 − R pred . 2 γ − 0 . 01 R meas . 2 γ − 0 . 02 − 0 . 03 − 0 . 04 OLYMPUS VEPP-3 CEBAF − 0 . 05 0 0 . 5 1 1 . 5 2 Q 2 [ ( GeV /c ) 2 ] 7
Difference of data to prediction: Bernauer et al. phenomenological prediction 0 . 03 0 . 02 0 . 01 0 − R pred . 2 γ − 0 . 01 R meas . 2 γ − 0 . 02 − 0 . 03 − 0 . 04 OLYMPUS VEPP-3 CEBAF − 0 . 05 0 0 . 5 1 1 . 5 2 Q 2 [ ( GeV /c ) 2 ] 8
χ 2 of the world data set VEPP-3 CLAS OLYMPUS World χ 2 χ 2 χ 2 χ 2 N. N. n d.f. n d.f. n d.f. n d.f. No hard TPE 7.97 0.84 0.43 σ 0.65 0.75 σ 1.53 Blunden 4.01 0.70 1.23 σ 0.73 2.14 σ 1.088 Bernauer 1.95 0.58 -0.40 σ 0.49 0.45 σ 0.679 CLAS and OLYMPUS have too large errors Vepp-3 rules out no hard TPE Blunden et al get slope right, but large normalization shifts. Probability for worse shift in same direction: < 0.4% Phenomenological fit clearly preferred by all three experiments 9
My view on this For the measured values, good agreement with phenomenological extraction. 10
My view on this For the measured values, good agreement with phenomenological extraction. But not in good agreement with theory. 11
My view on this For the measured values, good agreement with phenomenological extraction. But not in good agreement with theory. Not clear how to calculate at higher Q 2 → Can not extract G E and G M from Rosenbluth exps! − Not clear if TPE is full effect → Can not trust polarization based exps on G E / G M ? − 12
My view on this For the measured values, good agreement with phenomenological extraction. But not in good agreement with theory. Not clear how to calculate at higher Q 2 → Can not extract G E and G M from Rosenbluth exps! − Not clear if TPE is full effect → Can not trust polarization based exps on G E / G M ? − Need new measurements at relevant kinematics 13
Phenomenology 2 Rosenbluth Polarization Fits Bernauer ’13 Litt ’70 Gayou ’01 Fit Rosenbluth Bartel ’73 Punjabi ’05 Fit all + phen. TPE Andivahis ’94 Jones ’06 Walker ’94 Puckett ’10 1 . 5 Christy ’04 Paolone ’10 Qattan ’05 Puckett ’12 µG E /G M 1 0 . 5 VEPP-3 JLAB OLYMPUS 0 0 1 2 3 4 5 6 7 Q 2 [(GeV/ c ) 2 ] 14
Effect size We assume a correction to the cross section: d σ → d σ ( 1 + δ TPE ) How does δ TPE depend on ǫ, Q 2 ? 15
Effect size We assume a correction to the cross section: d σ → d σ ( 1 + δ TPE ) How does δ TPE depend on ǫ, Q 2 ? From linearity of Rosenbluth: δ TPE = ( 1 − ǫ ) f ( Q 2 ) Effect on G E / G M seems to be linear in Q 2 16
Effect size We assume a correction to the cross section: d σ → d σ ( 1 + δ TPE ) How does δ TPE depend on ǫ, Q 2 ? From linearity of Rosenbluth: δ TPE = ( 1 − ǫ ) f ( Q 2 ) Effect on G E / G M seems to be linear in Q 2 However: � � 1 + ( 1 − ǫ ) × f ( Q 2 ) = ǫ G 2 E + τ G 2 d σ red → d σ red M 17
Effect size We assume a correction to the cross section: d σ → d σ ( 1 + δ TPE ) How does δ TPE depend on ǫ, Q 2 ? From linearity of Rosenbluth: δ TPE = ( 1 − ǫ ) f ( Q 2 ) Effect on G E / G M seems to be linear in Q 2 However: � � 1 + ( 1 − ǫ ) × f ( Q 2 ) = ǫ G 2 E + τ G 2 d σ red → d σ red M ⇒ G E ∼ 1 − ατ f ( Q 2 ) = G M We can only expect weak dependence on Q 2 = ⇒ Logarithmic dependence in Mainz fit, many calculations 18
Constructing a figure of merit Use Mainz fit as benchmark of effect size to reconcile FF measurements. Signal is larger for smaller ǫ , larger Q 2 , but then σ is smaller → larger uncertainty 19
Constructing a figure of merit Use Mainz fit as benchmark of effect size to reconcile FF measurements. Signal is larger for smaller ǫ , larger Q 2 , but then σ is smaller → larger uncertainty FOM is the deviation of R 2 γ from unity, measured in units of uncertainty: � � � R 2 γ − 1 � FOM = � ∆ 2 stat + ∆ 2 syst � 2 Statistical error: ∆ stat = σ × L × t × A Systematical error: ∆ syst = 1 % 20
Possible locations for experiments at high Q 2 Positron beams are scarce 21
Possible locations for experiments at high Q 2 Positron beams are scarce In the relevant energy range, almost non-existent 22
Possible locations for experiments at high Q 2 Positron beams are scarce In the relevant energy range, almost non-existent Jefferson Lab Has detectors, but no beam (yet) 23
Possible locations for experiments at high Q 2 Positron beams are scarce In the relevant energy range, almost non-existent Jefferson Lab Has detectors, but no beam (yet) DESY Has no detectors, but beam However: small time window: PETRA 3 will run with electrons only! 24
DESY DESY might have a test beam facility with positron/electron beams. Current: 60 nA (single bunch, maybe can do more?) Short window of opportunity: PETRA 3 might stop positron running. Target: Borrow from Mainz? Detector: Borrow something developed for Panda? Calorimeter? Assume 10 msr 25
DESY @ 15 days per species FOM for DESY @ 15 day/species beamtime 12 10 10 8 Beam energy [GeV] 8 Q 2 [(GeV /c ) 2 ] 6 FOM 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ǫ 26
DESY @ 30 days per species FOM for DESY @ 30 day/species beamtime 12 10 10 Q 2 [(GeV /c ) 2 ] 8 Beam energy [GeV] 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 6 FOM 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 4 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 2 2 0 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ǫ 27
DESY projected errors (15 days per species) 1 . 14 E beam = 2 . 85 GeV 1 . 12 1 . 1 1 . 08 R 2 γ 1 . 06 1 . 04 1 . 02 1 0 . 98 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ǫ 28
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