Two photon saga

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Two photon saga
Egle Tomasi-GustafssonSaclay, France
July 17, 2007
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WHY these three points are aligned?
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Rosenbluth separation
Contribution of the electric term
?0.8
to be compared to the absolute value of s and
to the size and e dependence of RC
?0.2

• ?0.5

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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, 051001 (2002)
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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

selsmeas ? RC
slope
Slope negative if
The slope is negative starting from 2-3 GeV2
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Reduced cross section and RC
Data from L. Andivahis et al., Phys. Rev. D50,
5491 (1994)
Q21.75 GeV2
Q22.5 GeV2
Q23.25 GeV2
Q24 GeV2
Q25 GeV2
Q26 GeV2
Slope from P. M.
Radiative Corrected data
Q27 GeV2
Raw data without RC
E. T.-G., G. Gakh Phys. Rev. C (2005)
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Experimental correlation
Q2 gt 2 GeV2
Q2 lt 2 GeV2
selsmeas ? RC
RC(e)
only published values
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Structure function method
Q21 GeV2
Q23 GeV2
Assumes dipole FFs Change the slope !
Q25 GeV2
SF Born
Polarization
RC Born
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Scattered electron energy
final state emission
Initial state emission
Quasi-elastic scattering
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Not so small!
Y0
Shift to LOWER Q2
All orders of PT needed ? beyond Mo Tsai
approximation!
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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
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Unpolarized Cross section
Q21 GeV2
Q23 GeV2
Born dipole FFs (unpolarized experimentMoTsai)
SF (with dipole FFs) SF2? exchange
Q25 GeV2
SF change the slope!
2? exchange very small!
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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 013003 (1076)
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Polarization ratio
Born SF SF2? exchange
q 80
q 60
q 20
2? exchange very small!
2? destroys linearity!
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Correction (SF method)
SLAC data
JLab data
Polarization data
Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C
75, 015207 (2007)
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Model independent considerations fore N
scattering
Determination of EM form factors, in presence of
2g exchange
- electron and positron beams, - longitudinally
polarized , - in identical kinematical
conditions,
Generalization of the polarization method (A.
Akhiezer and M.P. Rekalo)
Where? VEPP3 (Novosibirsk) ( cf. S.
Serednyakov), HERA..
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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

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If no positron beam
Either three T-odd polarization observables.
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If no positron beam
This ratio contains the TRUE form factors!
Very difficult experiments Three T-odd
polarization observables. Expected small, of the
order of a, triple spin correlations but
Model independent way
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If no positron beam
Either three T-odd polarization
observables. ..or five T-even polarization
observables. among ds/dW, Px(le), Pz(le), Dxx,
Dyy, Dzz, Dxz
Again very difficult experiments Only Model
independent ways (without positron beams)
M. P. Rekalo and E. T-G Nucl. Phys. A740 (2004)
271, M. P. Rekalo and E. T-G Nucl. Phys. A742
(2004) 322
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The Rosenbluth separation (1950)

• Elastic ep cross section (1-? exchange)

• point-like particle ? Mott

Linearity of the reduced cross section!
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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

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Results
Linear deviation from dipole mGEp?GMp
Jlab E93-027 , E99-007SpokepersonsCh.
Perdrisat, V. Punjabi, M. Jones, E. Brash M.
Jones et ql. Phys. Rev. Lett. 84,1398 (2000) O.
Gayou et al. Phys. Rev. Lett. 88092301 (2002) V.
Punjabi et al. Phys. Rev. C (2006)
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Two-photon exchange?

• Electric proton FF
• Different results with different
• experimental methods !!
• - Both methods based on the
• same formalism
• - Experiments repeated

New mechanism?
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Two-Photon exchange

• 1g-2g interference is of the order of
  ae2/4p1/137 (in usual calculations of
  radiative corrections, one photon is hard and
  one is soft)
• In the 70s 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.

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1g-2g interference
M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C
(1999)
2g
1g


1g
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The 1g-2g interference destroys the linearity
of the Rosenbluth plot!
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Parametrization of 2g-contribution for ep

• From the data
• deviation from linearity
• ltlt 1!

E. T.-G., G. Gakh Phys. Rev. C (2005)
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Model independent considerations for
4 spin ½ fermions ? 16 amplitudes in the general
case.

• P- and T-invariance of EM interaction,
• helicity conservation

• For one-photon exchange
• Two (complexe) EM form factors
• Functions of one variable (t)

• For two-photon exchange
• Three (complexe) amplitudes
• Functions of two variables (s,t)

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• Asymptotics

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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
  ab and f(z) ?a uniformly in the angle.

D0.05, 0.1
E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265
(2005)
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pQCD Predictions
F1 / F2 ? Q2
F1 ? 1/Q4 , F2 ? 1/Q6
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Phragmèn-Lindelöf theorem
Connection with QCD asymptotics?
GM (TL)

Applies to NN and NN Interaction (Pomeranchuk
theorem ) t0 not a QCD regime!
GM (SL)
GE (SL)
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291
(2001)