Space-Like and Time-Like Form Factors Compared analysis

1
Space-Like and Time-LikeForm Factors
Compared analysis
Egle Tomasi-GustafssonSPhN-Saclay and IPN-Orsay
Varenna, June 16, 2009
2
PLAN

• Introduction
• Form factors in one photon exchange approximation

• 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 g exchange)
• Conclusions

.Model Independent Statements
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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 2S1 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 q2 probe the size of the nucleus,
• at high q2 test QCD scaling

4
Electromagnetic Interaction
The electron vertex is known, gm
The interaction is carried by a virtual photon
of mass q2
The proton vertex is parametrized in terms of
FFs Pauli and Dirac F1,F2
or in terms of Sachs FFs GEF1-t F2, GMF1F2,
t-q2/4M2
What about high order radiative corrections?
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Analyticity
Space-like
Asymptotics - QCD - analyticity
Time-like
GE(0)1
GM(0)mp
pp ? ee- p
Unphysical region
_
_
FFs are complex
FFs are real
q2
q24mp2
pp ? ee-
ep ? ep
GEGM
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The Rosenbluth separation
Q2 fixed
Linearity of the reduced cross section
e

• tan2qe dependence

• Holds for 1g exchange only

PRL 94, 142301 (2005)
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Crossing Symmetry
Scattering and annihilation channels
- Described by the same amplitude
- function of two kinematical variables, s and
t
- which scan different kinematical regions
k2 ? k2
p2 ? p2
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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!
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Experimental Status (space-like)

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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

To updatenew data!
Hohler NPB 114, 505 (1976)
Extended VDM (G.-K. 92) E.L.Lomon PRC 66,
045501 2002)

Bosted PRC 51, 409 (1995)
neutron
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Polarization Method (exp)
A.I. Akhiezer, M.P. Rekalo
The simultaneous measurement of Pt and Pl
reduces the systematic errors !
12
Statistics and Preliminary Results from GEp(III)
C. Perdrisat, V. Punjabi
New equipment worked beautifully BigCal and
FPP 8.54 GeV2 point 1.63 billion triggers
collected Analyzing power at 5.4 GeV/c close to
Dubna value 6.8 GeV2 point 160 million
triggers 5.2 GeV2 point a test of the spin
transport at 180o µpGEp/GMp1.056-0.1427
Q2
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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.

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Two-photon exchange

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

New mechanism?

• 1g-2g ae2/4p1/137
• 1970s Gunion, Lev

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Experimental Status (time-like)

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Time-Like Region
proton
VDM IJL F. Iachello..PLB43 191 (1973)
Extended VDM (G.-K. 92) E.L.Lomon PRC66
045501(2002)
neutron
QCD inspired
E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA
24, 419 (2005)
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STATUS on EM Form factors

• Time-like region
• No individual determination of GE and GM
• Assume GEGM (valid only at threshold)
• TL nucleon FFs are twice larger than SL FF

VMD or pQCD inspired parametrizations (for p
and n)
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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)
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Space-like and Time-like
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
FMsM/stot
FEeG2E/sred
5 GeV2
e0.8
----- 8 GeV2
e0.5
e0.2
FEsE/stot
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Space-like and Time-like
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
FEeG2E/sred
10
e0.8
10
e0.5
e0.2
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Radiative Return (ISR)
e e- ? p p ?
B. Aubert ( BABAR Collaboration) Phys Rev. D73,
012005 (2006)
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Results (ISR)
GE GM ?
B. Aubert Babar Collaboration, PRD 73, 012005
(2006)
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Form Factors with

pp e e-
1) Knowledge of proton form factors up to large
q2 2) Transition to QCD Asymptotics 3) Reaction
mechanism (1 or 2 photon exchange)
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Physical Background

• 3 body reactions easy to eliminate
• kinematical constraints
• PID
• 2 charged body reactions (pp-, µµ-, KK-)
• Most important background is p p-

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D. Marchand, IPN Orsay
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Expected Results(I)
L 2x1032 cm-2.s-1, 107 s (100 days)
RGE/GM
BaBAR
Individual determination of GE and GM up to
large Q2
PS170
PANDA sim
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Proton F2 /F1 and pQCD
C. Perdrisat
Brodsky and Farrar (75)
Belitsky, Ji and Yuan (03)
Q2F2/F1 constant
?
Q2F2/F1 ? ln2(Q2/?2)
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Expected Results (II)

• Asymptotic region
• Test of analytical properties

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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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Phragmèn-Lindelöf theorem
Connection with QCD asymptotics?

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

• Hadron form factors a bridge
• between perturbative
• and non perturbative QCD
• Progress in experiment
• and theory
• Next future (gt 2014)
• 12 GeV beams at JLab increase Q2 to 15 GeV2.
• Two experiment in preparation
• - Fair_at_GSI, antiprotons up to 15 GeV/c
• Precise determination of GE and GM
• Cross section measurement up to q2 to 20
  GeV2.
• Towards a unified description of form factors,
  for a better comprehension of the hadron structure

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GEp/GMp with 12 GeV at JLab
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 GeV2).
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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 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.
• The 1g-2g interference is more important in
  time-like region, as the Born amplitude is complex

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Two Photon exchange

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Fitting the angular distributions..
The form of the differential cross section
is equivalent to
Cross section at 900
Angular asymmetry
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291
(2001)
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Mpp1.877-1.9
A0.010.02
Mpp2.4-3
E. T.-G., E.A. Kuraev, S. Bakmaev, S. Pacetti,
Phys. Lett. B (2008)
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Simulations
q25.4,8.2,13.8 GeV2
Main effect odd cosq - distribution

• Approximations
• Neglect contributions to GE,GM
• Consider only real part

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Na0a2cosq sin2q a1 cos2q, a22g
2g 0.02
1g
q25.4 GeV2
2g 0.2
2g 0.05
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Two photon exchange

• The calculation of the box amplitude requires
  the
• description of intermediate nucleon excitation
  and
• of their FFs at any Q2
• Different calculations give quantitatively
  different
• results

Theory not enough constrained!
Model independent statements
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1g-2g interference
M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev.
C60, 042202 (1999)
2g
1g

1g

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Unpolarized cross section
Two Photon Exchange

• Induces four new terms
• Odd function of q
• Does not contribute at q 90

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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)
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Symmetry relations

• Differential cross section at complementary
  angles

The SUM cancels the 2g contribution
The DIFFERENCE enhances the 2g contribution
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Is there any experimental evidence of two photon
exchange?

NO
(real
part)
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(No Transcript)
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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 72, 015209 (2005)
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Linear fit to e4He scattering
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2?-Gamma Models and Data
C. Perdrisat,L. Pentchev
Expt. Jlab 04-019 measured Ratio PL/PT for
Q22.49 GeV2 at 3 values of e
PRELIMINARY
NO e-dependence at 0.01 level
NO evidence of 2g contribution
The inclusion of hard 2? exchange Chen et al
(2003) with GPDs, Blunden et al (2003) in
hadronic model
Bystriskyi et al., LSF PR C75, 015207 (2007)
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10/24/2013
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Asymptotics