1. Modelling Hadron Form Factors
Egle Tomasi-Gustafsson
IRFU, SPhN-Saclay,
and
IN2P3- IPN Orsay
GDR-PH-QCD, IPNO 7/XII/2012
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

2. Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

3. Polarization experiments - Jlab
GEp collaboration
"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) QCD scaling not reached
3) Zero crossing of Gep?
4) contradiction between polarized and unpolarized measurements
A.I. Akhiezer and M.P. Rekalo, 1967
A.J.R. Puckett et al, PRL (2010)
IPNO, 7-XII-2012
Egle TOMASI-GUSTAFSSON

4. Issues
Some models (IJL 73, Di-quark, soliton..) predicted such behavior before the data appeared
BUT
Simultaneous description of the four nucleon form factors...
...in the space-like and in the time-like regions
Consequences for the light ions description
When pQCD starts to apply?
Source of the discrepancy
IPNO, 7-XII-2012
Kolomna, 11-VI-2010
Egle TOMASI-GUSTAFSSON

5. Proton form factors at large q2
L = 2  cm-2 s-1
Connection with QCD asymptotics?
100 days
Applies to NN and NN
Interaction
(Pomeranchuk theorem)
t=0 : not a QCD regime!
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)
E. T-G. e-Print: arXiv:  [nucl-th]
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

6. The nucleon: homogenous, symmetric sphere?
Analogy with Gravitation
Coulomb Potential ~ Gravitational Potential
Mass~charge
1/r
Spherical symmetric distributed mass density,
A point at a distance r<R from the center feels only the matter inside
r~0.7 fm → Q= 0.29 GeV
works for the SCALAR part,
NOT for the
VECTOR part of A=(Φ, A) → R=
R~1/Q3 is NOT the experimental behavior
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

7. The nucleon antisymmetric state of colored quarks Main assumption
3 valence quarks and
a neutral sea of qq pairs
antisymmetric state of
colored quarks
Main assumption
Does not hold in the spatial center of the nucleon: the center of the nucleon is electrically neutral, due to strong gluonic field
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

8. The nucleon
Inner region: gluonic condensate of clusters with randomly oriented chromo-magnetic field (Vainshtein, 1982):
Intensity of the gluon field in vacuum:
In the internal region of strong chromo-magnetic field, the color quantum number of quarks does not play any role, due to stochastic averaging
proton
didj
neutron
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

9. Model Colorless quarks: Antisymmetric state of colored quarks
Pauli principle
1) uu (dd) quarks are repulsed from the inner region
2) The 3rd quark is attracted by one of the identical quarks, forming a compact di-quark
3) The color state is restored
Formation of di-quark: competition between
attraction force and stochastic force of the gluon field
proton: (u) Qq=-1/3
neutron: (d) Qq=2/3
attraction force >stochastic force of the gluon field
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

10. Model Proton: r0=0.22 fm, p02 = 1.21 GeV2
attraction force >
stochastic force of the gluon field
Proton: r0=0.22 fm, p02 = 1.21 GeV2
Neutron: r0=0.31 fm, p02 = 2.43 GeV2
Applies to the scalar
part of the potential
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

11. Model Quark counting rules apply to the vector part of the potential
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

12. Model Additional suppression for the scalar part
due to colorless internal region:
“charge screening in a plasma”:
Boltzmann constant
Neutrality condition:
Additional suppression
(Fourier transform)
fitting parameter
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

13. Root mean square radius
Fourier Transform
Root mean square radius
Egle TOMASI-GUSTAFSSON
Perugia, 18-XII-2012

14. Model: generalized form factors
Definition:
space-time distribution of the
electric charge in the space-time volume
In SL- Breit frame (zero energy transfer):
In TL-(CMS):
: time evolution of the charge distribution
in the domain
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

15. The annihilation channel:
1) Creation of a pp state through
intermediate state with
2) The vacuum state transfers all the released
energy to a state of matter consisting of:
6 massless valence quarks
Set of gluons
Sea of current qq pairs of quarks with
energy q0>2Mp, J=1, dimensions
3) Pair of p and p formed by three bare quarks:
Structureless
Colorless pointlike FFs !!!
IPNO, 7-XII-2012
Egle TOMASI-GUSTAFSSON

16. The annihilation channel:
The point-like hadron pair expands and cools down:
the current quarks and antiquarks absorb
gluon and transform into constituent quarks
The residual energy turns into kinetic energy
of the motion with relative velocity
The strong chromo-EM field leads to an effective loss of color. Fermi statistics: identical quarks are
repulsed. The remaining quark of different flavor
is attracted to one of the identical quarks,
creating a compact diquark (du-state)
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

17. The annihilation channel:
The neutral plasma acts on the distribution of the electric charge (not magnetic).
Prediction: additional suppression due to the neutral plasma similar behavior in SL and TL regions
Implicit normalization at q2=4Mp2: |GE|=|GM| =1
No poles in unphysical region
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

18. The annihilation channel:
The repulsion of p and p with kinetic energy
is balanced by the confinement potential
The long range color forces create a stable
colorless state of proton and antiproton
The initial energy is dissipated from current
to constituent quarks originating on shell
separated by R.
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

19. The annihilation channel:
At larger distances, the inertial force exceeds the confinement force: p and p start to move apart with relative velocity 
p and p leave the interaction region: at large distances the integral of Q(t) must vanish.
For very small values of the velocity
FSI lead to the creation of a bound NN system .
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

20. Space-Like region GEp polarization GEp dipole GEn
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

21. Proton Form Factors GEp polarization |GMp|=|GEp| GEp dipole GMp
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

22. Neutron TL region
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

23. Time-Like region R=|GEp|/|GMp| Not a fit Ps178 BaBar Dafne E835
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

24. Point-like form factors?
S. Pacetti
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

25. Point-like form factors?
S. Pacetti
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

26. Point-like form factors?
S. Pacetti
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012

27. Hadron Form Factors: Conclusions
New, interesting results in Space-like and Time-like regions
IHEP
VEPP-Novosibirsk
Unified model in SL and TlL regions
pointlike behavior at threshold
complex FFs due to to FSI , vanishing at
asymptotics
spin one intermediate state
dynamical polarization of p and p?
Egle TOMASI-GUSTAFSSON
IPNO, 7-XII-2012