longitudinal and transverse helicity amplitudes in the hypercentral constituent quark model
DESCRIPTION
Longitudinal and transverse helicity amplitudes in the hypercentral constituent quark model. The hypercentral Constituent Quark Model Results for the longitudinal and transverse helicity amplitudes High Q 2 behaviour Meson cloud and/or quark-antiquark pair effects Conclusions. - PowerPoint PPT PresentationTRANSCRIPT
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Longitudinal and transverse helicity amplitudes in the hypercentral constituent quark model
• The hypercentral Constituent Quark Model• Results for the longitudinal and transverse helicity
amplitudes• High Q2 behaviour• Meson cloud and/or quark-antiquark pair effects• Conclusions
M. Giannini N-N* transition from factors Jlab, 13-15 october 2008
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The hypercentral Constituent Quark ModelhCQM
The description of the spectrum is the first task of a model builder:it serves to determine a quark interaction to be used for the description of other physical quantitites
LQCD (De Rújula, Georgi, Glashow, 1975) the quark interaction contains
• a long range spin-independent confinement SU(6) invariant
• a short range spin dependent term SU(6) violation
SU(6) configurations
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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)
F35
D13S11
S31S11'D15D33 D13'
(70,1-)
(56,0+)
(56,0+)'
(56,2+)(70,0+)
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x =
hyperradius
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Quark-antiquark lattice potential G.S. Bali Phys. Rep. 343, 1 (2001)
V = - b/r + c r
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7
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)
F35
D13S11
S31S11'D15D33 D13'
(70,1-)
(56,0+)
(56,0+)'
(56,2+)(70,0+)
V = x - /xc)
0+
S
0+S
0+S
1-M
1-M
0+M 1
+A
2+S 2+
M
V(x) = - /x + x P = 1 P = 1 P = -1
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hCQM & Electromagnetic properties
• Photocouplings• Helicity amplitudes (transition f.f.)• Elastic form factors of the nucleon• Structure functions
Fixed parameters predictions
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HELICITY AMPLITUDES
Definition
A1/2 = < N* Jz = 1/2 | HTem | N Jz = -1/2 > * §
A3/2 = < N* Jz = 3/2 | HTem | N Jz = 1/2 > *
§
S1/2 = < N* Jz = 1/2 | HLem | N Jz = 1/2 > *
N, N* nucleon and resonance as 3q states
HTem Hl
em model transition operator
overall sign -> problem
§ results for the negative parity resonances: M. Aiello et al. J. Phys. G24, 753 (1998)
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Photoproduction amplitude
N N
πN*
Theory: states are defined up to a phase factor N -> N eiN* -> N* ei
<N*|H|N> <N*|H|N>
the overall sign is left unchanged
Phenomenology:Overall sign relative to Born amplitude
N N
πN*
A1/2 A3/2 S1/2
In order to extract the helicity amplitudes the sign of the strong vertex is used
Need for : a definite way of extracting the photon vertex a general consensus
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Q^2 = 0values with hCQM
Ap 1/2 Ap 3/2 Sp 1/2 An 1/2 An 3/2 Sn 1/2
D13 (1520) -65.7 66.8 78.2 -1.4 -61.1 -79.6
D13 (1700) 8 -10.9 -7.9 12 70.1 8.1
D15 (1675) 1.4 1.9 0 -36.6 -51.1 -0.2 zero for
D33(1700) 80.9 70.2 78.2 no Hyp
F15 (1680) -35.4 24.1 27.4 37.7 14.8 -0.6
F35(1905) -16.6 -50.5 -4.6 10^(-5) no Hyp
F37(1950) -28 -36.2 -0.4
P11(1440) -87.7 65.4 57.9 -0.9
P11(1710) 42.5 -22.6 -21.7 18,4
P13(1720) 94.1 -17.2 -35.8 -47.6 3 13.5 identically
P33(1232) -96.9 -169 -0.6 zero
S11(1535) 108 -48.4 -81.7 49.2
S11(1650) 68.8 -27.5 -21 28.2
S31(1620) 29.7 -55.3
for a comparison with data: M. Aiello et al., Phys. Lett. B387, 215 (1996)
10-3 GeV-1/2
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13Blue curves hCQMGreen curves H.O.
m = 3/2
m = 1/2
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15
16
17
18
19
20
21
22
23
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please note• the calculated proton radius is about 0.5 fm
(value previously obtained by fitting the helicity amplitudes)
• the medium Q2 behaviour is fairly well reproduced
• there is lack of strength at low Q2 (outer region) in the e.m. transitions specially for the A 3/2 amplitudes
• emerging picture: quark core (0.5 fm) plus (meson or sea-quark) cloud
“On the other hand, the confinement radius of ≈ 0.5 fm, which is currently used in order to give reasonable results for the photocouplings, is substantially lower than the proton charge radius and this seems to indicate that other mechanisms, such as pair production and sea quark contributions may be relevant.”
M. Aiello, M. Ferraris, M.M.G, M. Pizzo, E. Santopinto, Phys.Lett.B387, 215 (1996).
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Bare vs dressed quantities
QM calculations
• the aim is the description of observables not a fit
(dressed quantities )
• with success: spectrum, magnetic moments, …
• the separation between bare and dressed quantities is meaningful within a definite theoretical approach
• CQ have a mass, some dressing is implicitly taken into account
in fact CQs are effective degrees of freedom
• something similar may occur in the spectrum e.g. the consistent inclusion of quark loops effects in the meson description does
not alter the form of the qqbar potential but renormalizes the string constant (Geiger-Isgur)
• a consistent and systematic CQM approach may be helpful in order to put in evidence explicit dressing effects
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Various approaches with mesons and baryons af effective degrees of freedomMainz-Dubna-Taiwan MAID -> 2007Sato & Lee………
e.g. MZ dynamical model
a systematic description (fit with free parameters) is obtained
with very good results
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28
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= +
tR t
RtRv
B~ ~
Explicit evaluation of the meson cloud contribution to the excitation of the nucleon resonances
(Mainz Group and coworkers)
30GE-MZ coll., EPJA 2004 (Trieste 2003)
31GE-MZ coll., EPJA 2004 (Trieste 2003)
32GE-MZ coll., EPJA 2004 (Trieste 2003)
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How to introduce dressing
hadronic approach: mesons and baryons (nucleon + resonances) (equations for amplitudes, coupled channel calculations, lagrangians, …..
hybrid models
at the quark level inclusion of higher Fock components in the baryon state
unquenching the quark modelGeiger-IsgurCapstick, BRAG 2007Santopinto-Bijker, Nstar2007
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hep-ph/0701227
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High Q^2 behaviour
• Helicity ratio
| A1/2 |2 – | A3/2 | 2
_____________________
| A1/2 |2 + | A3/2 | 2
goes to 1 for increasing Q2
(helicity conservation, Carlson 1986)
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-1
-0.5
0
0.5
1
1.5
proton neutron
D13 hCQM predictions
Q^2 GeV^2
37
0
0.10.2
0.3
0.40.5
0.6
0.7
0.80.9
1
proton neutron
F15 hCQM predictions
Q^2 GeV^2
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proton & neutron
00.10.20.30.40.50.60.70.80.9
D33 hCQM predictions
Q^2 GeV^2
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proton neutron
P33 ≈ -0.5
D13 ok ok
F15 ok ≈ 0.7
D13* ok 0.96
D33 ok
D15 1/3 ≈ 0.32
F35 -0.82
F37 -0.32
P13 ok ok
Helicity ratio
Structure effects ?
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Conclusions
• Phenomenological problems– Sign of helicity amplitudes
– PDG values (often average of quite different sets)
– Need for more data
• A comparison of systematic CQM results and data– understanding where meson cloud or (better) q-qbar
effects are important (transition and elastic ff, structure functions,…..)
– a good basis for including consistently these effects provided by (h)CQM
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Conclusions (cont.)
• Theoretical problems– Relativity (probably not important for helicity amplitudes)
[relativistic hCQM -> elastic ff (PR C 2007)]
– Consistent inclusion of quark-antiquark pair creation effects
– Contributions from higher shells
• Consequences of the inclusion of quark-antiquark pair creation effects:– Non zero width of resonances
– Consistent evaluation of strong and e.m. vertices
– Direct calculation of scattering electroproduction
– ……….
– A substantial improvement in CQM calculations!