electromagnetic form factors in the relativized hypercentral cqm e. santopinto
DESCRIPTION
Electromagnetic form factors in the relativized Hypercentral CQM E. Santopinto. Trieste 22_26 May 2006. M. Ferraris, M.Giannini, M. Pizzo, E. Santopinto, L. Tiator , Phys. Lett. B 364 , 231 (1995). - PowerPoint PPT PresentationTRANSCRIPT
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Electromagnetic form factors in the relativized Hypercentral CQM
E. Santopinto
Trieste 22_26 May 2006
M. Ferraris, M.Giannini, M. Pizzo, E. Santopinto, L. Tiator,Phys. Lett. B 364, 231 (1995).
E. Santopinto, F. Iachello, M. Giannini, Eur. Phys. J. A 1, 307 (1998).
R. Bijker, E. Santopinto, F. Iachello, J. Phys. A 31, 9041 (1998).
M. Aiello, M. Ferraris, M. Giannini, M.Pizzo, E. Santopinto, Phys. Lett. B 387, 215 (1996).
M. De Sanctis, M.M. Giannini, L.Repetto, E. Santopinto, Phys. Rev. C 62,
025208 (2000).De Sanctis, M.Giannini, E.Santopinto, A.Vassallo, Nucl. Phys. A.755,294(2005)
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Introduction
The hypercentral Constituent Quark Model
The elastic nucleon form factors (relativistic effects)
Conclusion
Work done in collaboration with M. Giannini, A. Vassallo, M. De Santis
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New Jlab data on nucleon f.f.
Give rise to problems:
• compatibility with old (Rosenbluth plot) data
• why the ratio GE/GM decreases?
• is there any zero in the f.f. ?
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VMD models (fits)
FF = Fintr * VMD propagators
Mesons Fintr
JIL dipole
monopole
G K QCD-interpolation
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00
Gari-Kruempelmann
Iachello
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Skyrme Model
Holzwarth 1996,2002
ff given by soliton + VMD
dip at Q2 3 GeV2
Boosting of the solitondip at Q2 10 GeV2
Skyrmion (nucleon) mass 1648 MeV
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The Hypercentral Constituent Quark Model
M. Ferraris et al., Phys. Lett. B364, 231 (1995)
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PDG 4* & 3*
0.8
1
1.2
1.4
1.6
1.8
2
P11
P11'
P33
P33'
P11''
P31
F15P13
P33''F37
M
(GeV)
π=1π=1 π=−1
35F
13D11S
31S11S '15D33 13D D '
(70,1 -)
(56,0+)
(56,0+)'
(56,2+)(70,0+)
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Jacobi coordinates
SPACE WAVE FUNCTION
1 2
3
= r - r1 2
√ 2
=r 2 rr1 + 2 - 3
√ 6
Hyperspherical coordinates
( (x
2 2+x = (size)
arc tg
(shape)
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Quark-antiquark lattice potential G.S. Bali Phys. Rep. 343, 1 (2001)
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3-quark lattice potential G.S. Bali Phys. Rep. 343, 1 (2001)
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Electromagnetic properties
• Photocouplings M. Aiello et al., PL B387, 215 (1996)
• Helicity amplitudes (transition f.f.) M. Aiello et al., J. of Phys. G24, 753 (1998)
• Elastic form factors of the nucleon
M. De Sanctis et al., EPJ A1, 187 (1998)
• Structure functionsto be published
Fixed parameters predictions
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Dynamical model (Mainz group)
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please note
• the calculated proton radius is about 0.5 fm
(value previously obtained by fitting the helicity amplitudes)
• not good for elastic form factors
• there is lack of strength at low Q2 (outer region) in the e.m. transitions
• emerging picture: quark core (0.5 fm) plus (meson or sea-quark) cloud
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ELASTIC FORM FACTORS
1. - Relativistic corrections to the elastic form factors
2. - Results with the semirelativistic CQM
3. - Introduction of Quark form factors
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1.- Relativistic corrections to form factors
• Breit frame• Lorentz boosts applied to the initial and final state• Expansion of current matrix elements up to first
order in quark momentum• Results
Arel (Q2) = F An.rel(Q2eff)
F = kin factor Q2eff = Q2 (MN/EN)2
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calculated
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2.- Results with the semirelativisticM. De Sanctis, M. Giannini., E. Santopinto, A. Vassallo,
Nucl. Phys. A.755,294(2005)
• Relativistic kinetic energy
• Boosts to initial and final states
• Expansion of current to any order
• Conserved current
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and not much different from the NR case
V(x) = - /x + x
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Calculated values!
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QuickTime™ and aGIF decompressor
are needed to see this picture.
QuickTime™ and aGIF decompressor
are needed to see this picture.
Q2 F2p/F1
p
Q F2p/F1
p
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3.- Quark form factors M. De Sanctis, M. Giannini, E. Santopinto, A. Vassallo, Nucl. Phys. A.755,294(2005)
• Quark form factors are added into the current
ff = Fintr * quark form factors
semirelativistic hCQM input (calculated)
• Monopole + dipole form for qff
• Fit of:
– GEp/GM
p ratio (polarization data)
– GMp; GE
n ;GMn
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QuickTime™ and aGIF decompressor
are needed to see this picture.
QuickTime™ and aGIF decompressor
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Q2 F2p/F1
p
Q F2p/F1
p
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Conclusion
• The hCQM provides a consistent framework for the description of all the 4 nucleon electromagnetic form factors
• Relativity is crucial in explaining the decrease of the ratio GE/GM
• Quark form factors are necessary in order to get a good reproduction of the Q2 behaviour