Proton Form Factors

1
Proton Form Factors
Q21 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
2
Hadron Electromagnetic Form Factors in
Annihilation and Scattering Reactions
Egle Tomasi-GustafssonSaclay, France
Trento,ECT, May 23, 2008
3
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.

tlt0
tgt0
Scattering
Annihilation
_
_
e- h gt e- h
e e- gt h h
Form factors are real in the space-like region
complex in the time-like
region.
4
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
5
Towards a unified description of Hadron Form
factorsto clarify - zero of GEp -
asymptotic properties - reaction mechanism
6
Comparison BABAR-LEAR
Analytical Expression for R(q2) Dispersion
Relations (S. Pacetti)
q2 (GeV2)
Space-like
Time-like
7

• Proton Form Factors

8
Proton Form Factors Ratio
SLAC Rosenbluth L. Andivahis PRD50,5491 (1994)
Jlab Super Rosenbluth I.A. Qattan et al.PRL 94
142301 (2005)
POLARIZATION Exp Jlab E93-027 , E99-007
SpokepersonsCh. Perdrisat, V. Punjabi, M.
Jones, E. Brash M. Jones et al., Phys. Rev.
Lett. 84,1398 (2000) O. Gayou et al., Phys. Rev.
Lett. 88,092301 (2002) V. Punjabi et al., Phys.
Rev. C 71, 055202 (2005)
Linear deviation from dipole mGEp?GMp
Jlab E04-108/019 , NOW running !
9
The Rosenbluth separation
Linearity of the reduced cross section

The dynamics is contained in FFs ? t, Q2 The
kinematics energies, angles The reaction
mechanism?
? Holds for 1g exchange only
10
Rosenbluth separation
Contribution of the electric term
?0.8
Before
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

After
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
11
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

12
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.

13
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 updateso many new 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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The nucleon form factors and Il Nuovo Cimento
W. Wataghin, 1968
T. Massam and A. Zichichi, 1966 - one parameter
fit! - Time-like region!
Iachello, Jackson, A. Lande, 1973 (PLB)
15

• Time-like region

16
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!
17
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)
18
STATUS on EM Form factors

• Time-like region
• No individual determination of GE and GM
• Assume GEGM (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) 77.15 GeV4

L0.3 GeV is the QCD scale parameter
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Spin Observables

• Analyzing power, A

Double spin observables
20
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)
21
Time-Like Region GE versus GM
GM 2
Cross section at 900
GE0
Asym
GEGM
GEGD
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291
(2001)
22
Perspectives in Time-Like region
Frascati
GE GM ?
Panda
23
Asymptotics
24
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)
25
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)
26
Reaction mechanism1g-2g interference
27
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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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
29
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)
30
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)
31
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!
32
How to proceed?

• Our Suggestion
• Search for model independent statements
• Exact calculation in frame of QED (pm)
• Study analytical properties of the Compton
  amplitude
• Prove that QED box is upper limit of QCD box
  diagram
• Our Conclusion
• Two photon contribution is negligible (real part)
• Radiative corrections are huge take into account
  higher order effects (Structure Functions method)

33
1g-2g interference
M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev.
C60, 042202 (1999)
2g
1g


1g
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The 1g-2g interference destroys the linearity
of the Rosenbluth plot!
35
1g-2g interference (e-d)
D/A
C/A
M. P. Rekalo, E. T-G and D. Prout, Phys. Rev.
C60, 042202 (1999)
36
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37
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)
38
Linear fit to e4He scattering
39
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.

40
TL unpolarized cross section
e e- ? p p
2g-contribution

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

E. T.-G., G. Gakh, NPA (2007)
41
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)
42
Symmetry relations

• Differential cross section at complementary
  angles

The SUM cancels the 2g contribution
The DIFFERENCE enhances the 2g contribution
43
Mpp1.877-1.9
A0.010.02
Mpp2.4-3
E. T.-G., E.A. Kuraev, S. Bakmaev, S. Pacetti,
Phys. Lett. B (2008)
44
Radiative Corrections
45
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
46
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, PRC 72, 015209 (2005)
47
Experimental correlation
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
selsmeas ? RC
RC(e)
only published values!!
Q2 gt 2 GeV2
Q2 lt 2 GeV2
48
Experimental correlation
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
Correlation (ltRCegt)
Q2 lt 2 GeV2
49
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!
50
The Structure Function Method
E. A. K. and V.S. FADIN, Sov. J. of Nucl. Phys.
41, 466 (1985)
Distinguish -leading
contributions of higher order -non leading
ones

• The SF method is based on
• Renormalization group evolution equation
• Drell-Yan parton picture of the cross section in
  QCD

Lipatov equations (1975)
51
Structure Functions 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
52
The structure function method

• Electron detected in a calorimeter?
• The cross section is integrated on the scattered
  electron energy fraction

• The cross section

• The K-factor includes all non leading
  contributions

53
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!
54
Polarization ratio
Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C
75, 015207 (2007)
Born SF SF2? exchange
q 80
q 60
q 20
2? exchange very small!
2? destroys linearity!
55
Radiative Corrections (SF method)
Yu. Bystricky, E.A.Kuraev, E. Tomasi-Gustafsson,
Phys. Rev. C75, 015207 (2007)
SLAC data
SF corrected
JLab data
SF corrected
Polarization data
Rosenbluth parameters highly correlated!
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
56
Instead of Conclusions
Towards a unified description in TL and SL
region
- Experimentalists disentangle counting
rates, acceptance, efficiency..and Radiative
Corrections
- Theoreticians think nucleon models in all
kinematical region
Model independent properties Lessons from QED
57
LSF Corrections (High orders included)
The cross section
The correction ( Leading Logarithm Approximation)
The vacuum polarization
The K-factor
58
Maximon and Tjon (2000)
The cross section
The correction ( in powers of Z) Z0 electron
emission and vacuum polarization Z1
interference 1g-2g exchange Z2
target emission
59
LSF proton
MT (Z2) proton
LSF electron (not LLA)
MT (Z) two photon
LSF LLA
LSF total
MT (Z0) electron
MT total
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MT proton
LSF proton
LSF electron (not LLA)
MT (Z0) two photon
LSF LLA
LSF total
MT (Z0) electron
MT (Z0) total
62
e4He
63
Instead of Conclusions
Towards a unified description in TL and SL
region
- Experimentalists disentangle counting
rates, acceptance, efficiency..and Radiative
Corrections
- Theoreticians think nucleon models in all
kinematical region
Model independent properties Lessons from QED
64
The Pauli and Dirac Form Factors

• The electromagnetic current in terms of the
  Pauli and Dirac FFs

Normalization F1p(0)1, F2p(0) ?p

• Related to the Sachs FFs

GEp(0)1, GMp(0)µp2.79
65
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 (2006)
66
Two Photon Exchange

• No exact calculation for ep scattering
• ( inelastic intermediate states..)
• but
• electron-muon scattering
• constitutes an upper limit!

67
QED versus QCD
Imaginary part of the 2g amplitude
proton
electron
68
QED versus QCD
Q20.05 GeV2
Q21.2 GeV2
Q22 GeV2
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Results
Q21 GeV2
Q23 GeV2
SF Born
RC Born

Polarization
Q25 GeV2
Both calculations assume dipole FFs The slope
changes (due to different RC)
E.T-G, Phys. Part. Nucl. Lett. 4, 281-288 (2007).
70
Single Spin Asymmetry for em-scattering
71
Charge asymmetry for em-scattering
72
Charge asymmetry for ee-?mm-
73
Radiative Return (ISR)
e e- ? p p ?
74
Angular distribution
Mpp1.877-1.9
Mpp2.4-3
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In presence of 2g exchange
a
a
F (q2) a0
77
Iachello, Jakson and Landé (1973)
?,?,?
?
Isoscalar and isovector FFs
78
Elastic e -4He scattering ( L.J. Kaufman)
Ayexp(4He) -13.51 1.34 (stat) 0.37(syst)
ppmq6, Q20.077 GeV2
? Im F1 (s,q2) F(q2)
1g 2g term !
If Im F1 (s,q2)
Re F1 (s,q2)