1. Proton Form Factors Over a period of time lasting at least 2000 years,
Q2≤1 GeV2 F1 F2
Over a period of time lasting at least 2000 years,
Man has puzzled over and sought
an understanding of the composition of matter…
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

2. Electromagnetic Hadron Form Factors in Space and Time-like regions
Egle Tomasi-Gustafsson Saclay, France
JLab, May 2, 2008
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

3. PLAN Experimental view: space-like (ep-scattering)
time-like (e+e- or pp annihilation)
Model Independent Statements
Symmetry properties of fundamental
interactions
Kinematical constraints
Models and ‘exact’ calculations
Radiative corrections
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

4. Hadron Electromagnetic Form factors
Characterize the internal structure of a particle
( point-like)
Elastic form factors contain information on the hadron ground state.
In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors.
Neutron and proton form factors are different.
Deuteron: 2 structure functions, but 3 form factors.
Playground for theory and experiment.
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

5. Space-like and time-like regions
FFs are analytical functions.
In framework of one photon exchange, FFs are functions of the momentum transfer squared of the virtual photon, t = q2 = -Q2.
t<0
t>0
Scattering
Annihilation _ _
e- + h => e- + h
e+ + e- => h + h
Form factors are real in the space-like region
complex in the time-like region.
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

6. Crossing Symmetry Scattering and annihilation channels: p2 → – p2
- Described by the same amplitude :
- function of two kinematical variables, s and t
- which scan different kinematical regions
k2 → – k2
p2 → – p2
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

7. Proton Form Factors
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

8. Proton Form Factors Ratio
SLAC Rosenbluth
L. Andivahis PRD50,5491 (1994)
Jlab Super Rosenbluth
I.A. Qattan et al.PRL (2005)
POLARIZATION Exp
Jlab E , E99-007
Spokepersons: Ch. Perdrisat, V. Punjabi, M. Jones, E. Brash
M. Jones et al., Phys. Rev. Lett. 84,1398 (2000)
O. Gayou et al., Phys. Rev. Lett. 88, (2002)
V. Punjabi et al., Phys. Rev. C 71, (2005)
Linear deviation from dipole: mGEpGMp
Jlab E04-108/019 , NOW running !
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

9. The Rosenbluth separation (1950)
Elastic ep cross section (1g exchange)
point-like particle:  Mott
Linearity of the reduced cross section!
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

10. The Rosenbluth separation
The dynamics is contained in FFs
 t, Q2
The kinematics : energies, angles
The reaction mechanism?
 Holds for 1g exchange only
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

11. Rosenbluth separation
Contribution of the electric term
=0.8
…to be compared to the absolute value of the error on s and to the size and e dependence of RC
=0.2
=0.5
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

12. The polarization method (1967)
The polarization induces a term in the cross section proportional to GE GM
Polarized beam and target or
polarized beam and recoil proton polarization
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

13. Neutron Form Factors
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

14. Neutron Form Factors
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

15. The reaction d(e,e’n)p - Ax
g* + d  n + p
FSI
Select quasi-elastic
kinematics
Pol electron beam,
pol target or
neutron polarimeter
Large dependence of
asymmetry on GEn!
GEn
DWF
GEp
G.I. Gakh, A. P. Rekalo, E. T.-G. Annals of Physics 319, 150 (2005)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

16. The reaction d(e,e’n)p - Ax
The KHARKOV model:
- Impulse Approximation
- Deuteron structure
- Kinematics: proton spectator
- Polarization observables
G.I. Gakh, A. P. Rekalo, E. T.-G. Annals of Physics 319, 150 (2005)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

17. The reaction d(e,e’n)p – Ax/Az
GEn
g* + d  n + p
Asymmetry ratio
DWF
Does not depend on beam helicity
FSI
A(0,1):T –LT SFs(W,Q2,q*)
Generalization of the polarization method
E.T-G., G.I. Gakh, A. P. Rekalo, M. P. Rekalo, PRC70, (2004)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

18. GEn from the deuteron GEn > GEp starting from 2 GeV2 !
E. T-G. and M. P. Rekalo, Europhys. Lett. 55, 188 (2001)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

19. The nucleon form factors
E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh, EPJA 24, 419 (2005)
Electric
Magnetic
VDM : IJL
F. Iachello..PLB 43, 191 (1973)
proton
Hohler
NPB 114, 505 (1976)
Extended VDM (G.-K. 92):
E.L.Lomon PRC 66, )
Bosted
PRC 51, 409 (1995)
neutron
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

20. STATUS on EM Form factors
Space-like region
"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.
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

21. Nucleon models... Skyrme Models (Soliton)
Vector Dominance Models (G-K, IJL…)
Perturbative QCD
(Relativistic) Constituent Quark Model
Di-quark models
GPD
……..
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

22. The nucleon form factors
E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh, EPJA 24, 419 (2005)
Electric
Magnetic
VDM : IJL
F. Iachello..PLB 43, 191 (1973)
proton
Hohler
NPB 114, 505 (1976)
Extended VDM (G.-K. 92):
E.L.Lomon PRC 66, )
Bosted
PRC 51, 409 (1995)
neutron
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

23. Time-like region
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

24. Time-like observables: | GE| 2 and | GM| 2 .
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).
As in SL region:
- Dependence on q2 contained in FFs
- Even dependence on cos2q (1g exchange)
- No dependence on sign of FFs
- Enhancement of magnetic term
but TL form factors are complex!
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

25. Time-Like Region proton neutron VDM : IJL Extended VDM (G.-K. 92):
F. Iachello..PLB (1973)
Extended VDM (G.-K. 92):
E.L.Lomon PRC (2002)
neutron
‘QCD inspired’
E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 24, 419 (2005)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

26. STATUS on EM Form factors
Time-like region
No individual determination of GE and GM
Assume GE=GM (valid only at threshold) VMD or pQCD inspired parametrizations (for p and n):
3) TL nucleon FFs are twice larger than SL FFs
4) Recent data from Babar (radiative return) :
interesting structures in the Q2 dependence of GM(=GE)
GM≠GE.
A(p) = 56.3 GeV4
A(n) = GeV4
L=0.3 GeV is the QCD scale parameter
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

27. Spin Observables Double spin observables Analyzing power, A
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

28. Models in T.L. Region (polarization)
Ayy Ay
Axx
VDM : IJL
Ext. VDM
‘QCD inspired’
Axz
Azz R
E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 24, 419(2005)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

29. Time-Like Region: GE versus GM
Cross section at 900
GE=0
Asym
GE=GM
GE=GD
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

30. Perspectives in Time-Like region
Frascati
GE = GM ?
Panda
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

31. Physics Polarization Staging Signals Timeline
Facilty for Antiproton and Ion Research
(GSI, Darmstadt, Germany)
Proton linac (injector)
2 synchrotons (30 GeV p)
A number of storage rings
 Parallel beams operation
Physics Polarization Staging Signals Timeline

32. Towards a unified description of Hadron Form factors to clarify:
Towards a unified description of Hadron Form factors to clarify: - zero of GEp - asymptotic properties - reaction mechanism
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

33. Comparison BABAR-LEAR
Analytical Expression for R(q2)
Dispersion Relations (S. Pacetti)
q2 (GeV2)
Space-like
Time-like
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

34. Phragmèn-Lindelöf theorem
Asymptotic properties for analytical functions
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.
D=0.05, 0.1
E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265 (2005)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

35. Phragmèn-Lindelöf theorem
Connection with QCD asymptotics?
GM (TL)
Applies to NN and NN
Interaction
(Pomeranchuk theorem ):
t=0 : not a QCD regime!
GM (SL)
GE (SL)
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

36. Reaction mechanism 1g-2g interference
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

37. Two-photon exchange New mechanism? 1g-2g ~ a=e2/4p=1/137
Different results with different
experimental methods !!
- Both methods based on the
same formalism
- Experiments repeated
New mechanism?
1g-2g ~ a=e2/4p=1/137
1970’s: Gunion, Lev…
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

38. e± + p→ e± + p 4 spin ½ fermions → 16 amplitudes in the general case.
T-invariance of EM interaction,
identity of initial and final states,
helicity conservation,
unitarity
Two EM form factors
Real (in SL region)
Functions of one variable (t)
Describe e+ and e- scattering
Three structure functions
Complexe
Functions of TWO variables (s,t)
Different for e+ and e- scattering
1g exchange
2g exchange
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

39. Model independent considerations for e± N scattering
Determination of EM form factors,
in presence of 2g exchange:
electron and positron beams
- longitudinally polarized ,
- in identical kinematical conditions,
M. P. Rekalo, E. T.-G. , EPJA (2004), Nucl. Phys. A (2003)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

40. Model independent considerations for e± N scattering
If no positron beam…
Either three T-odd polarization observables….
Ay: unpolarized leptons, transversally polarized target (or Py: outgoing nucleon polarization with unpolarized leptons, unpolarized target )
Depolarization tensor (Dab): dependence of the b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
..or five T-even polarization observables….
among ds/dW, Px(le), Pz(le), Dxx, Dyy, Dzz, Dxz
M. P. Rekalo, E. T.-G. , EPJA (2004), Nucl. Phys. A (2003)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

41. { { 1g-2g interference 1g 2g 1{g
M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C60, (1999) 1g 2g
1{g { {
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

42. The 1g-2g interference destroys the linearity of the Rosenbluth plot!
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

43. 1g-2g interference (e-d)
C/A
D/A
M. P. Rekalo, E. T-G and D. Prout, Phys. Rev. C60, (1999)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

44. JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

45. Parametrization of 2g-contribution for e+p
From the data:
deviation from linearity
<< 1%!
E. T.-G., G. Gakh, Phys. Rev. C 72, (2005)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

46. The 2g amplitude is expected to be mostly imaginary.
Two-Photon exchange
The 2g amplitude is expected to be mostly imaginary.
In this case, the 1g-2g interference is more important in time-like region, as the Born amplitude is complex.
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

47. TL unpolarized cross section
e+ +e-  p + p
2g-contribution:
Induces four new terms
Odd function of q:
Does not contribute at q =90°
E. T.-G., G. Gakh, NPA (2007)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

48. (equivalent to non-linearity in Rosenbluth fit)
Symmetry relations
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
E. T.-G., G. Gakh, NPA (2007)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

49. Symmetry relations Differential cross section at complementary angles:
The SUM cancels the 2g contribution:
The DIFFERENCE enhances the 2g contribution:
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

50. Radiative Return (ISR)
e+ +e-  p + p + 
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

51. Angular distribution Mpp=1.877-1.9 Mpp=2.4-3 JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

52. Mpp=
A=0.01±0.02
Mpp=2.4-3
E. T.-G., E.A. Kuraev, S. Bakmaev, S. Pacetti, Phys. Lett. B (2008)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

53. Radiative Corrections to the data
- RC can reach 40% on s
- Declared error ~1%
Same correction for GE and GM
- Have a large e-dependence
- Affect the slope
sel=smeas · RC
slope
Slope negative if :
The slope is negative starting from 2-3 GeV2
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

54. Reduced cross section and RC
Data from L. Andivahis et al., Phys. Rev. D50, 5491 (1994)
Q2=1.75 GeV2
Q2=2.5 GeV2
Q2=3.25 GeV2
Q2=4 GeV2
Q2=5 GeV2
Q2=6 GeV2
Slope from P. M.
Radiative Corrected data
Q2=7 GeV2
Raw data without RC
E. T.-G., G. Gakh, PRC 72, (2005)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

55. Scattered electron energy
final state emission
Initial state emission
Quasi-elastic scattering 3%
Not so small! Y0
Shift to LOWER Q2
All orders of PT needed 
beyond Mo & Tsai approximation!
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

56. Radiative Corrections (SF method)
SLAC data
JLab data
Polarization data
Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C75, (2007)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

57. Instead of Conclusions…
Fundamental measurement: the electric and the magnetic distributions of the proton are different in SL region. What about TL ? Separation of GE and GM via angular dependence of differential cross section
Unified description in TL and SL region : zero of GEp?
Asymptotic properties : QCD and analyticity
Clarify reaction mechanism: 2g - exchange by model independent symmetry requirements
Model independent properties
Lessons from QED
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

58. The work presented here was initiated in a collaboration with
Prof. M. P. REKALO
JLab, May 2,2008
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59. Experimental correlation
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
sel=smeas · RC
RC(e)
only published values!!
Q2 > 2 GeV2
Q2 < 2 GeV2
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

60. Experimental correlation
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
Correlation (<RC•e>)
Q2 < 2 GeV2
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

61. The Pauli and Dirac Form Factors
The electromagnetic current in terms of the Pauli and Dirac FFs:
Normalization
F1p(0)=1, F2p(0)= κp
Related to the Sachs FFs :
GEp(0)=1, GMp(0)=μp=2.79
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

62. electron-muon scattering constitutes an upper limit!
Two Photon Exchange
No exact calculation for ep scattering
( inelastic intermediate states..)
but
electron-muon scattering
constitutes an upper limit!
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

63. Interference of 1 2 exchange
Explicit calculation for structureless proton
The contribution is small, for unpolarized and polarized ep scattering
Does not contain the enhancement factor L
The relevant contribution to K is ~ 1
E.A.Kuraev, V. Bytev, Yu. Bystricky, E.T-G, Phys. Rev. D74, (1076)
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

64. proton electron QED versus QCD Imaginary part of the 2g amplitude
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

65. QED versus QCD Q2=0.05 GeV2 Q2=1.2 GeV2 Q2=2 GeV2 JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

66. Structure Function method
E. A. Kuraev and V.S. Fadin, Sov. J. of Nucl. Phys. 41, 466 (1985)
SF method applied to QED processes: calculation of radiative corrections with precision of 0.1%.
Takes into account the dynamics of the process
Formulated in terms of parton densities (leptons, antileptons, photons)
Many applications to different processes
Lipatov equations (1975)
Electron SF: probability to ‘find’ electron in the
initial electron, with energy fraction x and virtuality up to Q2
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

67. Unpolarized Cross section
Q2=1 GeV2
Q2=3 GeV2
Born +dipole FFs
(=unpolarized experiment+Mo&Tsai)
SF (with dipole FFs)
SF+2 exchange
Q2=5 GeV2
SF: change the slope!
2 exchange very small!
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON

68. Polarization ratio 2 exchange very small! 2 destroys linearity!
Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C 75, (2007)
q =80°
Born SF
SF+2 exchange
q =60°
q =20°
2 exchange very small!
2 destroys linearity!
JLab, May 2,2008
Egle TOMASI-GUSTAFSSON