1. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 1 Space-Like and Time-Like Form Factors Compared analysis Egle Tomasi-Gustafsson SPhN-Saclay and IPN-Orsay 2009 Varenna, June 16, 2009

2. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 2 PLAN Introduction: Form factors in one photon exchange approximation …. Model Independent Statements q 2 >0 e-e- e+e+ p p Experimental Situation –Space-Like –Time-like Future Panda/FAIR and JLab 12 GeV: –Determination of proton form factors –Transition to QCD: Asymptotics –Reaction mechanism (1 or 2  exchange) Conclusions

3. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 3 Hadron Electromagnetic Form factors –Characterize the internal structure of a particle (  point-like) –In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors. –Elastic form factors bring information on the nucleon ground state –Neutron and proton form factors are different –Playground for theory and experiment –at low q 2 probe the size of the nucleus, –at high q 2 test QCD scaling

4. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 4 The proton vertex is parametrized in terms of FFs: Pauli and Dirac F 1,F 2 Electromagnetic Interaction q 2 <0 e-e- e-e- pp or in terms of Sachs FFs: GE=F 1 -  F 2, GM=F 1 +F 2,  =-q 2 /4M 2 The electron vertex is known,   The interaction is carried by a virtual photon of mass q 2 What about high order radiative corrections ?

5. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 5Analyticity _ _ q 2 <0 e-e- e-e- pp q 2 >0 e-e- e+e+ p p q2q2 q 2 =4m p 2 FFs are complex FFs are real Unphysical region GE=GM Space-like Time-like GE(0)=1 GM(0)=  p Asymptotics - QCD - analyticity p+p ↔ e + +e - e+p  e+p p+p ↔ e + +e - + 

6. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 6 The Rosenbluth separation  Holds for 1  exchange only Linearity of the reduced cross section PRL 94, 142301 (2005)  tan 2  e dependence  Q 2 fixed

7. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 7 Crossing Symmetry Scattering and annihilation channels: - Described by the same amplitude : - function of two kinematical variables, s and t p 2 → – p 2 k 2 → – k 2 - which scan different kinematical regions

8. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 8 Time-like observables: | G E | 2 and | G M | 2. As in SL region: - Dependence on q 2 contained in FFs - Even dependence on cos 2  (1  exchange) - No dependence on sign of FFs - Enhancement of magnetic term but TL form factors are complex! A. Zichichi, S. M. Berman, N. Cabibbo, R. Gatto, Il Nuovo Cimento XXIV, 170 (1962) B. Bilenkii, C. Giunti, V. Wataghin, Z. Phys. C 59, 475 (1993). G. Gakh, E.T-G., Nucl. Phys. A761,120 (2005).

9. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 9 Experimental Status (space-like) q 2 <0 e-e- e-e- pp

10. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 10 The nucleon form factors VDM : IJL F. Iachello..PLB 43, 191 (1973) Extended VDM (G.-K. 92): E.L.Lomon PRC 66, 045501 2002) Hohler NPB 114, 505 (1976) Bosted PRC 51, 409 (1995) ElectricMagnetic neutron proton E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh, EPJA 24, 419 (2005) To update…new data!

11. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 11 The simultaneous measurement of Pt and Pl reduces the systematic errors ! Polarization Method (exp) A.I. Akhiezer, M.P. Rekalo

12. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 12 Statistics and Preliminary Results from G Ep (III) New equipment worked beautifully: BigCal and FPP 8.54 GeV 2 point: 1.63 billion triggers collected Analyzing power at 5.4 GeV/c close to Dubna value 6.8 GeV 2 point: 160 million triggers 5.2 GeV 2 point: a test of the spin transport at 180 o μ p G Ep /G Mp =1.056-0.1427Q 2 C. Perdrisat, V. Punjabi

13. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 13 STATUS on EM Form factors Space-like region 1)"standard" dipole function for the nucleon magnetic FFs GMp and GMn 2) linear deviation from the dipole function for the electric proton FF GEp 3) contradiction between polarized and unpolarized measurements 4) non vanishing electric neutron FF, GEn.

14. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 14 Two-photon exchange Different results with different experimental methods !! - Both methods based on the same formalism - Experiments repeated New mechanism ? 1  -2  ~  =e 2 /4  =1/137 1970’s: Gunion, Lev…

15. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 15 Experimental Status (time-like) q 2 >0 e-e- e+e+ p p

16. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 16 Time-Like Region E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 24, 419 (2005) VDM : IJL F. Iachello..PLB43 191 (1973) Extended VDM (G.-K. 92): E.L.Lomon PRC66 045501(2002) ‘QCD inspired’ proton neutron

17. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 17 STATUS on EM Form factors Time-like region 1)No individual determination of |GE| and |GM| 2)Assume GE=GM (valid only at threshold) 3)TL nucleon FFs are twice larger than SL FF   QCD =0.3 GeV A(p) = 56.3 GeV 4 A(n) = 77.15 GeV 4 VMD or pQCD inspired parametrizations (for p and n):

18. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 18 Models in T.L. Region (polarization) VDM : IJL Ext. VDM ‘QCD inspired’ R AyAxx Ayy Axz Azz E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 24, 419(2005)

19. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 19 Space-like and Time-like E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)  =0.5  =0.2  =0.8 F E =  G 2 E  red F E =    tot F M =    tot   GeV 2 ----- 8 GeV 2

20. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 20 Space-like and Time-like  =0.2  =0.5  =0.8 E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007) 10% F E =  G 2 E  red

21. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 21 Radiative Return (ISR) e + +e -  p + p +  B. Aubert ( BABAR Collaboration) Phys Rev. D73, 012005 (2006)

22. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 22 Results (ISR) G E = G M ? B. Aubert [Babar Collaboration, PRD 73, 012005 (2006)

23. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 23 Form Factors with p+p e + + e - 1) Knowledge of proton form factors up to large q 2 2) Transition to QCD: Asymptotics 3) Reaction mechanism (1 or 2 photon exchange)

24. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 24 D. Marchand, IPN Orsay 24 3 body reactions: “easy” to eliminate  kinematical constraints  PID  2 charged body reactions (π + π -, μ + μ -, K + K - ) Most important background is π + π - : Are we able to discriminate e + e - from π + π - ? YES ! High statistics GEANT4 simulations  Worse case : few 0 / 00 pollution / cos  CM bin (0.1)  < 1% on the total cross section up to 16 GeV 2 Physical Background

25. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 25 Individual determination of GE and GM up to large Q 2 Expected Results(I) R=GE/GM BaBAR PS170 PANDA sim L = 2x10 32 cm -2.s -1, 10 7 s (~100 days)

26. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 26 Proton: F2 /F1 and pQCD Brodsky and Farrar (75): Q 2 F 2 /F 1 constant Belitsky, Ji and Yuan (03): Q 2 F 2 /F 1 → ln 2 (Q 2 /  2 ) → C. Perdrisat

27. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 27 -Asymptotic region -Test of analytical properties Expected Results (II)

28. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 28 Phragmèn-Lindelöf theorem Asymptotic properties for analytical functions E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265 (2005)  =0.05, 0.1 If f(z)  a as z  along a straight line, and f(z)  b as z  along another straight line, and f(z) is regular and bounded in the angle between, then a=b and f(z)  a uniformly in the angle.

29. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 29 Phragmèn-Lindelöf theorem E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Applies to NN and NN Interaction (Pomeranchuk theorem) t=0 : not a QCD regime! Connection with QCD asymptotics?

30. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 30 Conclusions Hadron form factors: a bridge between perturbative and non perturbative QCD Progress in experiment and theory Next future (> 2014) –12 GeV beams at JLab: increase Q 2 to 15 GeV 2. Two experiment in preparation - Fair@GSI, antiprotons up to 15 GeV/c Precise determination of |GE| and |GM| Cross section measurement up to q 2 to ~20 GeV 2. Towards a unified description of form factors, for a better comprehension of the hadron structure

31. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 31 G Ep /G Mp with 12 GeV at JLab 31 Two new experiments approved to run after the 12 GeV upgrade (to be completed end of 2013). Whether they should run depends again on Dubna calibration to 7.5 GeV/c (12.5 GeV 2 ).

32. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 32 Two-Photon exchange 1  -2  interference is of the order of  =e 2 /4p=1/137 (in usual calculations of radiative corrections, one photon is ‘hard’ and one is ‘soft’) The 2  amplitude is expected to be mostly imaginary. The 1  -2  interference is more important in time- like region, as the Born amplitude is complex In the 70’s it was shown [ J. Gunion and L. Stodolsky, V. Franco, F.M. Lev, V.N. Boitsov, L. Kondratyuk and V.B. Kopeliovich, R. Blankenbecker…] that, at large momentum transfer, due to the sharp decrease of the FFs, if the momentum is shared between the two photons, the 2  - contribution can become very large.

33. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 33 Two Photon exchange

34. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 34 Fitting the angular distributions.. E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Cross section at 90 0 Angular asymmetry The form of the differential cross section: is equivalent to:

35. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 35 Mpp=1.877-1.9 A=0.01±0.02 Mpp=2.4-3 E. T.-G., E.A. Kuraev, S. Bakmaev, S. Pacetti, Phys. Lett. B (2008)

36. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 36 Simulations Approximations: Neglect contributions to GE,GM Consider only real part Main effect: odd cos  - distribution q 2 =5.4,8.2,13.8 GeV 2

37. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 37 2  0.02 2  0.05 2  0.2 11 q 2 =5.4 GeV 2 N=a 0 +a 2 cos  sin 2  +a 1 cos 2 , a 2 ~2 

38. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 38 Two photon exchange The calculation of the box amplitude requires the description of intermediate nucleon excitation and of their FFs at any Q 2 Different calculations give quantitatively different results Theory not enough constrained! Model independent statements

39. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 39 1{g1{g 1  -2  interference { 22 11 { M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C60, 042202 (1999)

40. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 40 Unpolarized cross section Induces four new terms Odd function of  Does not contribute at  =90° Two Photon Exchange:

41. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 41 Properties of the TPE amplitudes with respect to the transformation: cos  = - cos  i.e.,    -  (equivalent to non-linearity in Rosenbluth fit) Based on these properties one can remove or single out TPE contribution Symmetry relations E. T.-G., G. Gakh, NPA (2007)

42. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 42 Differential cross section at complementary angles: Symmetry relations The DIFFERENCE enhances the 2  contribution: The SUM cancels the 2  contribution:

43. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 43 Is there any experimental evidence of two photon exchange? (real part) NO

44. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 44

45. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 45 From the data: deviation from linearity << 1%! Parametrization of 2  -contribution for e+p E. T.-G., G. Gakh, Phys. Rev. C 72, 015209 (2005)

46. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 46 Linear fit to e+ 4 He scattering

47. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 47 2γ -Gamma Models and Data 47 The inclusion of hard 2γ exchange: Chen et al (2003) with GPDs, Blunden et al (2003) in hadronic model 12/7/2015 Expt. Jlab 04-019 measured Ratio PL/PT for Q 2 =2.49 GeV 2 at 3 values of ε PRELIMINARY C. Perdrisat,L. Pentchev NO ε-dependence at 0.01 level NO evidence of 2  contribution Bystriskyi et al., LSF PR C75, 015207 (2007)

48. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 48 Asymptotics