Modelling Hadron Form Factors · 2013. 2. 20. · Eduard A. KURAEV 32 Hadron Electromagnetic Form...
Transcript of Modelling Hadron Form Factors · 2013. 2. 20. · Eduard A. KURAEV 32 Hadron Electromagnetic Form...
Eduard A. KURAEV JINR-BLTP
Dubna-Russia
Modelling Hadron Form
Factors
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E.A.K., E. Tomasi-Gustafsson, A. Dbeyssi Phys.Lett. B712 (2012) 240-244
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Proton Form Factors ...before
Rosenbluth separation/ Polarization observables
Dipole approximation: GD=(1+Q2/0.71 GeV2)-2
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Dipole Approximation
• Classical approach – Nucleon FF (in non relativistic
approximation or in the Breit system) are Fourier transform of the charge or magnetic distribution.
• The dipole approximation corresponds to an exponential density distribution.
– ρ = ρ0 exp(-r/r0), – r0
2= (0.24 fm)2, <r2> ~(0.81 fm) 2 m2D =0.71 GeV2
GD=(1+Q2/0.71 GeV2)-2
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Breit system
Fourier Transform
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Root mean square radius
Polarization experiments - Jlab A.I. Akhiezer and M.P. Rekalo, 1967 GEp collaboration 1) "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
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A.J.R. Puckett et al, PRL (2010), PRC (2012)
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Issues • Some models (IJL 73, Di-quark, soliton..) predicted such behavior before the data appeared
• Simultaneous description of the four nucleon form factors : GE, GM, proton and neutron
• ...in the space-like and in the time-like regions
BUT
Kolomna, 11-VI-2010 Trento, 19-II-2013
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Time-like observables: | GE| 2 and | GM| 2 .
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!
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). S. Bilenki, S. Ryndin, (1965). G. Gakh, E.T-G., Nucl. Phys. A761,120 (2005).
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Individual determination of GE and GM up to large Q2
Expected Results
R=GE/GM
BaBAR
PS170 PANDA sim
M. Sudol et al, EPJA 2010
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L = 2 10 32 cm-2 s-1
100 days
The nucleon: homogenous, symmetric sphere?
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r~0.7 fm → Q= 0.29 GeV
works for the SCALAR part, NOT for the VECTOR part of A=(Φ, A)
→
• Spherical symmetric distributed mass density,
• A point at a distance r<R from the center feels only the matter inside
Analogy with Gravitation Coulomb Potential ~ Gravitational Potential Mass~charge
1/r
R~1/Q3 is NOT the experimental behavior
R=
The nucleon
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antisymmetric state of colored quarks
3 valence quarks and a neutral sea of qq pairs
Does not hold in the spatial center of the nucleon: the center of the nucleon is electrically neutral, due to strong gluonic field
Main assumption
The nucleon
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In the internal region of strong chromo-magnetic field, the color quantum number of quarks does not play any role, due to stochastic averaging
Intensity of the gluon field in vacuum:
Inner region: gluonic condensate of clusters with randomly oriented chromo-magnetic field (Vainshtein, 1982):
didj proton neutron
Colorless quarks: Pauli principle
Model
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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
Antisymmetric state of colored quarks
Colorless quarks: Pauli principle
attraction force >stochastic force of the gluon field
proton: (u) Qq=-1/3 neutron: (d) Qq=2/3
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Proton: r0=0.22 fm, p02 = 1.21 GeV2
Neutron: r0=0.31 fm, p02 = 2.43 GeV2
Model
attraction force > stochastic force of the gluon field
Applies to the scalar part of the potential
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Quark counting rules apply to the vector part of the potential
Model
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Nature does not like empty place: Additional suppression for the scalar part due to colorless internal region: “charge screening in a plasma”:
Additional suppression (Fourier transform)
fitting parameter
Model
Neutrality condition: Boltzmann constant
Fourier Transform
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Root mean square radius
space-time distribution of the electric charge in the space-time volume
Model: generalized form factors
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Definition:
In SL- Breit frame (zero energy transfer):
In TL-(CMS): : time evolution of the charge distribution in the domain
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
The annihilation channel:
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3) Pair of p and p formed by three bare quarks: • Structureless • Colorless pointlike FFs !!!
1) Creation of a pp state through intermediate state with
The annihilation channel:
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• 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)
The annihilation channel:
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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
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• 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.
The annihilation channel:
The repulsion of p and p with kinetic energy is balanced by the confinement potential
At larger distances, the inertial force exceeds the confinement force: p and p start to move apart with relative velocity
The annihilation channel:
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For very small values of the velocity FSI lead to the creation of a bound NN system .
p and p leave the interaction region: at large distances the integral of Q(t) must vanish.
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Space-Like region
GEn
GEp polarization
GEp dipole
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Proton Form Factors
GMp
GEp Akhiezer-Rekalo
GEp Rosenbluth |GMp|=|GEp|
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Neutron TL region
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Time-Like region
R=|GEp|/|GMp|
Not a fit Ps178 BaBar Dafne E835
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Point-like form factors?
S. Pacetti
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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?
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Point-like form factors?
S. Pacetti
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Point-like form factors?
S. Pacetti
Antiprotons at FAIR
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HESR
SIS 100/300
SIS18
RESR/CR
30 GeV Protons 50 MeV
p-Linac
Cu Target 107 p/s @ 3 GeV
Collecting Accumulating
Precooling
Accelerating Cooling
100m
PANDA
pbar production • proton Linac 50 MeV • accelerate p in SIS18/SIS100 • produce pbar on target • collect pbar in CR, • cooling in RESR
http://www-panda.gsi.de/ http://www.fair-center.eu/
Parameters of HESR • Injection of pbar at 3.7 GeV • Slow synchrotron (1.5-14.5 GeV/c) • Storage ring for internal target operation • Luminosity up to L~ 2x1032 cm-2s-1
• Beam cooling (stochastic & electron) Trento, 19-II-2013 31
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Hadron Electromagnetic Form factors Characterize the internal structure of
a particle ( point-like) Elastic form factors contain
information on the hadron ground state.
In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors.
Neutron and proton form factors are different.
Deuteron: 2 structure functions, but 3 form factors.
Playground for theory and experiment at low q2 probe the size of the
nucleus, at high q2 test QCD scaling
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The proton vertex is parametrized in terms of FFs: Pauli and Dirac F1,F2
Electromagnetic Interaction
q2<0
e- e-
p p
)2q(2FM2qi
)2q(1Fνµνσ
µγµΓ +=
or in terms of Sachs FFs: GE=F1-t F2, GM=F1+F2, t=-q2/4M2
The electron vertex is known,gm The interaction is carried by a virtual photon of mass q2
What about high order
radiative corrections?
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Crossing Symmetry Scattering and annihilation channels:
- Described by the same amplitude :
- function of two kinematical variables, s and t
k2 → – k2 - which scan different kinematical regions
p2 → – p2
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Analyticity
_ _
q2<0
e- e-
p p
q2>0
e-
e+ p
p
q2 q2=4mp2
FFs are complex FFs are real Unp
hysi
cal r
egio
n
GE=GM
Space-like
Time-like GE(0)=1
GM(0)=mp
Asymptotics - QCD - analyticity
p+p ↔ e++e- e+p e+p
p+p ↔
e++
e- +p
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Dipole Approximation and pQCD
V. A. Matveev, R. M. Muradian, and A. N. Tavkhelidze (1973), Brodsky and Farrar (1973), Politzer (1974), Chernyak & Zhitnisky (1984), Efremov & Radyuskin (1980)…
Dimensional scaling
– Fn (Q2)= Cn [1/( 1+Q2/mn) n-1], • mn=n2 , <quark momentum squared> • n is the number of constituent quarks
– Setting 2 =(0.471±.010) GeV2 (fitting pion data)
• pion: F (Q2)= C [1/ (1+Q2/0.471 GeV2)1],
• nucleon: FN (Q2)= CN [1/( 1+Q2/0.71 GeV2)2], • deuteron: Fd (Q2)= Cd [1/( 1+Q2/1.41GeV2)5]
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The Rosenbluth separation
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟
⎠
⎞⎜⎜
⎝
⎛++Ω
=Ω )2(2)2(2)1(1 QMGQEG
Mottdd
dd
ετ
τσσ
2M4
2Q,1
2e2)tan1(21 =
−++=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
⎟⎠⎞⎜
⎝⎛ τθ
τε
® Holds for 1g exchange only
Linearity of the reduced cross section
PRL 94, 142301 (2005)
® tan2qe dependence e
Q2 f
ixed
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The polarization induces a term in the cross section proportional to GE GM Polarized beam and target or polarized beam and recoil proton polarization
The polarization method (1967)
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The simultaneous measurement of Pt and Pl reduces the systematic errors
The polarization method (exp)
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C. Perdrisat et al, JLab-GEp collaboration
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Proton form factors at large q2
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)
Applies to NN and NN Interaction (Pomeranchuk theorem) t=0 : not a QCD regime!
Connection with QCD asymptotics?
Eduard A. KURAEV
E. T-G. e-Print: arXiv:0907.4442 [nucl-th]
L = 2 10 32 cm-2 s-1
100 days