1. Two-photon Exchange John Arrington Argonne National Lab International Workshop on Positrons at Jefferson Lab, Mar 25-27, 2009

2. 2 Unpolarized Elastic e-N Scattering Early form factor measurements used Rosenbluth separation  R = d  /d  [  (1+  )/  Mott ] =  G M 2 +  G E 2 in Born approx. (  = Q 2 /4M 2 ) GM2GM2 GE2GE2  =180 o  =0 o Reduced sensitivity to… G M if Q 2 << 1 G E if Q 2 >> 1 G E if G E 2 <<G M 2 (e.g. neutron) Form factor extraction is very sensitive to angle-dependent corrections in these cases

3. 3 New techniques: Polarization and A(e,e’N) Mid ’90s brought measurements using improved techniques –High luminosity, highly polarized electron beams –Polarized targets ( 1 H, 2 H, 3 He) or recoil polarimeters –Large, efficient neutron detectors for 2 H, 3 He(e,e’n) –Improved models for nuclear corrections Polarized 3 He target BLAST at MIT-Bates Focal plane polarimeter – Jefferson Lab LT:   G M 2 +  G E 2 PT:  G E /G M

4. 4 Polarization vs. Rosenbluth: G E /G M  p GEp/GMp from Rosenbluth measurements I. A. Qattan, et al, PRL 94, 142301 (2005) JLab Hall A: M. Jones, et al.; O. Gayou, et al. New data: Recoil polarization and p(e,p) “Super-Rosenbluth” Slope from recoil polarization

5. 5 Two-photon exchange corrections Clear discrepancy between LT, PT extractions Two-photon exchange effects can explain discrepancy in G E Requires ~3-6%  -dependence, weekly dependent on Q 2, roughly linear in  Guichon and Vanderhaeghen, PRL 91, 142303 (2003) JA, PRC 69, 022201 (2004) If this were the whole story, we would be done: L-T would give G M, PT gives G E Still need to be careful when choosing form factors as, e.g. input to fits or data analysis There are still issues to be addressed What about the constraints (~1%) from positron-electron comparisons? TPE effects on G M ? TPE effects on polarization transfer? TPE effects on other measurements?

6. 6 Tests of Two-Photon Exchange (’50s and ’60s) Secondary beams had low luminosity; data taken at high Q 2 OR large , never both. If correction is at large  (small  ), it would not have been clearly seen JA, PRC 69, 032201 (2004)

7. 7 Aside: Rosenbluth separation for e + p PT resultsLT (electron) LT (positron) (G E /G M ) 2 <1 Small (3-5%)  -dependent TPE correction can yield large (>100%) corrections to G E, since G E contributes so little to cross section Focus has been on how TPE impacts G Ep at high Q 2 Biggest issue, but not the only important one

8. 8 Low-Q 2 behavior: Unpolarized, Polarizated 0.01-0.06 GeV 2 0.1-0.6 1.0-6.0 0.1,0.2,0.3,0.6,1.0 GeV 2 TPE effect does not approach zero as Q 2  0 P. Blunden, W. Melnitchouk, and J. Tjon, PRC 72, 034612 (2005)

9. 9 G Mp from inclusive measurements – data extend to 30 GeV 2 Impact on G Mp Proton form factor measurements from Rosenbluth separations –TPE correction to G E is large, so are (most) LT uncertainties –Correction to G M much smaller, but large compared to uncertainties G Mp from inclusive measurements – data extend to 30 GeV 2 With TPE corrections (Blunden, et al.), G Mp shifts by up to 2-3 sigma  p GEp/GMp from Rosenbluth measurements New data: Recoil polarization  p GEp/GMp from Rosenbluth measurements New data: Recoil polarization and p(e,p) “Super-Rosenbluth”

10. 10 “Indirect” impact: Parity Measurements Neglect TPE in calculating A PV  small effect (top) –Especially for small angles (large  ) where most data is taken –Missing  -Z box, which is typically the largest correction, but is still small Neglect TPE in extracting EM FFs  much larger effect (bottom) –Corrections largest at large  –Note: form factor uncertainties typically taken as <1%, but TPE corrections can be significantly larger (and correlated) JA and Ingo Sick, PRC 76, 035201 (2007)

11. 11 Effect on Rosenbluth (L-T) Extractions LT PT LT + BMT PT Hadronic calculation resolves the discrepancy up to 2-3 GeV 2 Note: TPE effects of ~same size for cross section and polarizations Effect on G E amplified in high-Q 2 Rosenbluth measurements Most polarization (and cross section) measurements at large , smaller TPE P. Blunden, W. Melnitchouk, and J. Tjon, PRC 72, 034612 (2005) Note: Limited direct evidence for TPE, other RC issues to be addressed Extraction of proton form factors not too sensitive to details, but does assume entire effect is TPE (e.g. no correction at  = 1) J. Arrington, W. Melnitchouk, and J. Tjon, PRC76, 035205 (2007)

12. 12 TPE Beyond the Elastic Cross Section TPE Calculations sufficient for extracting proton form factor –Additional uncertainty at high Q 2 Precise experimental tests of TPE calculations possible for the proton –Important for validating calculations used for other reactions –Hadronic, partonic calculations yield different sign for recoil polarization Important direct and indirect consequences on other experiments High-precision quasi-elastic expts.  - N scattering measurements Proton charge radius, hyperfine splitting Strangeness from parity violation Neutron, Nuclear form factors Transition form factors Bethe-Heitler, Coulomb Distortion,… D.Dutta, et al., PRC 68, 064603 (2003) JA, PRC 69, 022201(R) (2004) H.Budd, A.Bodek, and JA hep-ex/0308005 P.Blunden and I.Sick, PRC 72, 057601 (2005) S.Brodsky, et al., PRL 94, 022001 (2005) A.Afanasev and C.Carlson, PRL 94, 212301 (2005) JA and I.Sick, nucl-th/0612079 P.Blunden, W.Melnitchouk, and J.Tjon, PRC72, 034612 (2005) A.Afanasev, et al., PRD 72, 013008 (2005) S. Kondratyuk and P. Blunden, NPA778 (2006) V. Pasculutsa, C. Carlson, M. Vanderhaeghen, PRL96, 012301 (2006)

13. 13 TPE measurements in e-p scattering Precise e-p elastic cross sections (JLab,Mainz) -  dependence of cross section Polarization transfer: P l /P t (Jlab) -  dependence of polarization ratio Positron-electron comparisons (VEPP, JLab, DESY) - Clean extraction of two-photon terms - Map out Q 2 and  dependence of  TPE Can test TPE explanation Map out TPE up to Q 2 ~ 2 GeV Map out TPE for Q 2 > 1-2 GeV 2 Longer term (test calculations for e-p, other reactions) Short term (verify TPE, determine proton form factors) Born-forbidden observables in p(e,e’p) – imaginary part of TPE amplitude - Beam single-spin asymmetries (SAMPLE, A4, G0, HAPPEX) - Normal polarization transfer, normal target spin asymmetries Measurements to constrain TPE in other reactions - Elastic form factors for neutron or light nuclei - Other exclusive processes (e.g. N   form factors) - Experimentally, very little can be done without positron beams - Need well tested, well constrained calculations

14. 14 Benefits of improved LT separations Compare precise LT and PT to constrain linear part of TPE corrections –Limiting factor in constraining TPE from PT-LT difference is precision of LT data At high Q 2, almost all  -dependence comes from TPE

15. 15 Nonlinearity Tests Born approx   R linear in ε, TPE can have nonlinearity SLAC NE11, JLab E01-001: quadratic terms consistent with zero Global fit, averaged over all Q 2 yields P 2 = 0.019 ± 0.027 E05-007: Project  P 2 ≈ ± 0.020 for both linearity scans, with global  P 2 ≈ ± 0.011 Set meaningful limits over a wide Q 2 range NE11: L. Andivahis, et al, PRD 50, 5491 (1994) E01-001: I. A. Qattan, et al, PRL 94, 142301 (2005) Global linearity limits: V.Tvaskis, et al., PRC 73, 025206 (2006)

16. 16 E04-019:  dependence in polarization transfer Preliminary results suggest little or no  -dependence Experiment ran in early 2008 Preliminary results suggest little or no  -dependence

17. 17 Two-Photon Exchange Measurements Comparisons of e + -p, e - -p scattering [VEPP-III, Hall B, DESY-Olympus proposal] World’s data Novosibirsk Previous comparisons limited to low Q 2 or small scattering angle (large  ) Examination of angular dependence yields evidence (3  level) for TPE in existing data J. Arrington, PRC 69, 032201(R) (2004)

18. 18

19. 19 Test run at Novosibirsk

20. 20 Two-Photon Exchange Measurements Comparisons of e + -p, e - -p scattering [VEPP-III, Hall B, DESY-Olympus]  dependence of polarization transfer and unpolarized  e-p [Hall C] World’s data Novosibirsk JLab – Hall B Previous comparisons limited to low Q 2 or small scattering angle (large  ) Examination of angular dependence yields evidence (3  level) for TPE in existing data J. Arrington, PRC 69, 032201(R) (2004)

21. 21 Two-Photon Exchange Measurements Comparisons of e + -p, e - -p scattering [VEPP-III, Hall B, DESY-Olympus]  dependence of polarization transfer and unpolarized  e-p [Hall C] –More quantitative measure of the discrepancy –Test against models of TPE at both low and high Q 2 TPE effects in Born-forbidden observables [Hall A, Hall C, Mainz] –Target single spin asymmetry, A y in e-n scattering –Induced polarization, p y, in e-p scattering –Vector analyzing power, A N, in e-p scattering (beam normal spin asymmetry) World’s data Novosibirsk JLab – Hall B Previous comparisons limited to low Q 2 or small scattering angle (large  ) Examination of angular dependence yields evidence (3  level) for TPE in existing data J. Arrington, PRC 69, 032201(R) (2004)

22. 22 Why do we need more? The proposed e+/e- experiments are very limited (but very important) –Verify TPE as source of discrepancy –First quantitative measure of TPE effect on cross section –Begin to test , Q 2 dependence of calculations No plans to study polarization observables Nothing proposed to look at other reactions –Very limited tests might be possible with CLAS or Olympus To thoroughly test calculations, need other measurements: –Polarization, Born-forbidden observables –Range of positron/electron comparisons (polarization, other reactions…) A “real” positron beam, e.g. 1  A, would be a huge improvement –Great coverage for elastic, many other reaction channels –Higher current or polarization  TPE in polarization observables

23. 23

24. 24 Fin…

25. 25 Radiative Corrections: Beyond the Born Approximation Additional two-photon contributions expected to be small (~  EM ) Theoretical estimates generally indicated ~1% corrections Linearity of Rosenbluth plot taken as evidence of small TPE Comparison of positron to electron scattering was the “definitive” test

26. 26 JLab E01-001: Test of Radiative Corrections RC terms largely  -independent except for electron brem. Form factor ratios for Q 2 of 2.5-2.64 GeV 2, before and after RC - Andivahis, Qattan, and Walker (solid = after RC)

27. 27 E05-017: Extended “Super-Rosenbluth” 102 Kinematics points Q 2 0.40-5.76 GeV 2 13 points at Q 2 =0.983 10 points at Q 2 =2.284 Ran summer 2007 in Hall C at Jefferson Lab Extremely high precision LT separations over large kinematic range –Improved measurement of TPE effects over large Q 2 range –Very precise linearity tests at Q 2 = 0.983, 2.284 GeV 2 –Nearly all  dependence is TPE for Q 2 > 5 GeV 2

28. 28 Positron-electron comparison in CLAS@JLab

29. 29 Positron-electron comparison in CLAS@JLab 1%

30. 30 CLAS TPE Test Run Focus was on background issues Clearly identified e - p and e + p elastic events ratio of yield e - p/e + p lepton scattering lab angle Leptons in sector 5 only: 1/6 of data Red for negative torus polarity, Black for positive. Only crude CLAS calibrations Q 2 <0.5 GeV 2 0.4<  <0.95 ratio ~1

31. 31 OLYMPUS: BLAST@DORIS

32. 32 The BLAST Detector Left-right symmetric Large acceptance: 0.1 < Q 2 /(GeV/c) 2 < 0.8 20 o <  < 80 o, -15 o <  < 15 o COILS B max = 3.8 kG DRIFT CHAMBERS Tracking, PID (charge)  p/p=3%,  = 0.5 o CERENKOV COUNTERS e/  separation SCINTILLATORS Trigger, ToF, PID (  /p) NEUTRON COUNTERS Neutron tracking (ToF) DRIFT CHAMBERS CERENKOV COUNTERS SCINTILLATORS NEUTRON COUNTERS TARGET BEAM COILS All the advantages of VEPP-3 expt. –Pure beam, well defined energy Q 2,  coverage close to CLAS Coincidence measurement –Could do (e,e’n), other reactions