1. Egle TOMASI-GUSTAFSSON
Conclusions
Discussion
Homework
Egle Tomasi-Gustafsson
IRFU, SPhN-Saclay,
and
IN2P3- IPN Orsay France
Orsay, October 8, 2013
Orsay, 8-X-2013
Egle TOMASI-GUSTAFSSON

2. Egle TOMASI-GUSTAFSSON
Questions
Which are my OBSERVABLES?
What am I measuring?
What do I extract from the data?
Orsay, 8-X-2013
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3. Egle TOMASI-GUSTAFSSON
The Rosenbluth separation (1950)
Elastic ep cross section (1-γ exchange)
point-like particle:  Mott
Linearity of the reduced cross section!
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4. The polarization method (1967)
The Rosenbluth separation (1950)
The polarization induces a term in the cross section proportional to GE GM
Polarized beam and target or
polarized beam and recoil proton polarization
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5. The proton magnetic form factor
The polarization
results induce
1.5-3% global effect
The difference is not at the level of the measured observables, but on the slope (derivative)!
E. Brash et al. Phys. Rev. C65, (2002)
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6. Rosenbluth separation
Contribution of the electric term
=0.8
…to be compared to the absolute value of
 and to the size and dependence of RC
=0.2
=0.5
Orsay, 8-X-2013
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7. Egle Tomasi-Gustafsson Gatchina, July 10, 2012
Two-Photon exchange
1g-2g interference is of the order of a=e2/4p=1/137 (in usual calculations of radiative corrections, one photon is ‘hard’ and one is ‘soft’)
“Invent a mechanism” to enhance this contribution
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 and J. Gunion] that, at large momentum transfer, due to the sharp decrease of the FFs, if the momentum is shared between the two photons, the 2g- contribution can become very large.
The 2g amplitude is expected to be mostly imaginary.
Egle Tomasi-Gustafsson Gatchina, July 10, 2012

8. Egle TOMASI-GUSTAFSSON
1-2 interference
M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C (1999) 1 2
1{g { {
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9. The 1-2 interference destroys the linearity of the Rosenbluth plot!
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10. Egle TOMASI-GUSTAFSSON
1-2 interference (ed)
C/A
D/A
M. P. Rekalo, E. T-G and D. Prout, Phys. Rev. C60, (1999)
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11. Egle TOMASI-GUSTAFSSON
Parametrization of 2-contribution for e+p
From the data:
deviation from linearity
<< 1%!
E. T.-G., G. Gakh, Phys. Rev. C (2005)
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12. Linear fit to e+4He elastic scattering
G.I Gakh, and E. T.-G., Nucl.Phys. A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina, July 10, 2012

13. Egle Tomasi-Gustafsson Gatchina, July 10, 2012
WHY these points are aligned?
Egle Tomasi-Gustafsson Gatchina, July 10, 2012

14. Egle TOMASI-GUSTAFSSON
Two-Photon exchange
The 2 amplitude is expected to be mostly imaginary.
In this case, the 1-2 interference is more important in time-like region, as the Born amplitude is complex.
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15. Unpolarized cross section
2contribution:
Induces four new terms
Odd function of 
Does not contribute at =90°
Orsay, 8-X-2013
Egle TOMASI-GUSTAFSSON

16. Egle TOMASI-GUSTAFSSON
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
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17. Egle TOMASI-GUSTAFSSON
Symmetry relations
Differential cross section at complementary angles:
The SUM cancels the 2 contribution:
The DIFFERENCE enhances the 2 contribution:
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18. Egle TOMASI-GUSTAFSSON
Angular distribution
Mpp=
Mpp=2.4-3
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19. Egle TOMASI-GUSTAFSSON
Mpp=
A=0.01±0.02
Mpp=2.4-3
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20. Radiative Corrections to the data
- RC can reach 40% on 
- Declared error ~1%
Same correction for GE and GM
- Have a large -dependence
- Affect the slope
el=meas · RC
slope
Slope negative if :
The slope is negative starting from 2-3 GeV2
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21. 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 Phys. Rev. C (2005)
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22. Radiative Corrections (ep)
Andivahis et al., PRD50, 5491 (1994)
Q2=1.75 GeV2
Q2=3.75 GeV2
May change
the slope of sR
(and even the sign !!!)
Q2=5 GeV2
RC to the cross section:
- large (may reach 40%)
e and Q2 dependent
- calculated at first order
C.F. Perdrisat,, Progr. Part. Nucl. Phys. 59,694 (2007)
Egle Tomasi-Gustafsson Gatchina, July 10, 2012

23. Experimental correlation
el=meas · RC
RC()
only published values!!
Correlation (<RC•)
Q2 > 2 GeV2
Q2 < 2 GeV2
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24. Egle TOMASI-GUSTAFSSON
Results
Q2=1 GeV2
Q2=3 GeV2
SF Born
RC Born
………
Polarization
Q2=5 GeV2
Both calculations assume dipole FFs
The slope changes
(due to different RC)
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25. Correction (SF method)
SLAC data
JLab data
Polarization data
Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C 75, (2007)
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26. Egle TOMASI-GUSTAFSSON
Polarization ratio
 =80°
Born
SF …..
 =60°
 =20°
2 exchange very small!
Orsay, 8-X-2013
Egle TOMASI-GUSTAFSSON

27. Egle TOMASI-GUSTAFSSON
Homework
Exercise
-Table with SLAC kinematics, data etc…
-Extract published radiative corrections
-Plug-in ‘your’ radiative corrections
(in MC: ratio of histos..)
- Plot RC(epsilon)
-Autopsia of RC (epsilon)
-Outcome: report GDR-PH-QCD and more
ECT*, 17-VII-2007
Egle TOMASI-GUSTAFSSON

28. Egle TOMASI-GUSTAFSSON
Homework
Exercise
Even electron
Even proton
interference
Total
ECT*, 17-VII-2007
Egle TOMASI-GUSTAFSSON

29. 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. D (1076)
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30. Perspectives and 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
Clarify reaction mechanism: 2exchange by model independent symmetry requirements
Unified description in TL and SL region : zero of GEp?
Asymptotic properties : QCD and analyticity
Model independent properties
Lessons from QED
Orsay, 8-X-2013
Egle TOMASI-GUSTAFSSON