systematic study of longitudinal and transverse helicity...
TRANSCRIPT
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Systematic study of longitudinal
and transverse helicity amplitudes in the
hypercentral Constituent Quark Model
M. Giannini Physics Department and INFN
Genova
13th International Conference on Meson-Nucleon Physics
and the Structure of the Nucleon (MENU 2013)
Roma, October 2nd, 2013
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Outline of the talk
The Model (hCQM)
The helicity amplitudes
Relativity
The elastic nucleon form factors
The helicity amplitudes
Perspectives
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The Model �(hCQM)�
hypercentral Constituent Quark Model
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Constituent Quarks At variance with QCD quarks: CQ acquire mass & size are the carrier of the proton spin
Basic idea of Constituent Quark Models (CQM)
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Various CQM for bayons
GROUP Kin. Energy SU(6) inv SU(6) viol date
Isgur-Karl non rel h.o. + shift OGE 1978-9
Capstick-Isgur rel string + coul-like OGE 1986
Iachello et al. non rel U(7) Casimir group chain 1994
Genoa non rel/rel hypercentral OGE/isospin 1995
Glozman-Riska rel linear GBE 1996
Bonn rel linear 3-body instanton 2001
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From early LQCD calculations: the quark interaction contains • a long range spin-independent confinement • a short range spin dependent term
Spin-independence SU(6) configurations
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Hyperspherical harmonics
Hasenfratz et al. 1980: Σ V(ri,rj) is approximately hypercentral
γ = 2n + lρ + lλ
hyperradius
hyperangle
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Hypercentral Model
V(x) = ‐τ/x + α x
Hypercentral approximaKon of
Genoa group, 1995
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Carlson et al, 1983 CapsKck‐Isgur 1986 hCQM 1995
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Two analytical solutions�� h. o. Σi<j 1/2 k (ri - rj)2 = 3/2 k x2�� hyperCoulomb - τ/x�
�
! = 0 ! = 1 ! = 2
0+S
0+S
0+S
" = 0
" = 1
HYPERCOULOMB
" = 21-M
1-M
0+
M1+
A2+
S2+
M
" = 0
" = 1 " = 0
a)
! = 0 ! = 1
SA MM
M
! = 2
" = 0
" = 1
" = 0
" = 0
b) H. O.
0+
0+ 0
+
1-
1+
2+
2+
S
S
a b
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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)
! = 1! = 1 ! = "1
F35
D13S11
S31S11'D15D33 D13'
(70,1-)
(56,0+
)
(56,0+
) '
(56,2+
)(70,0+
)
V = x - /xc)
! = 0 ! = 1 ! = 2
" = 0
" = 1
" = 2
" = 0
" = 1
" = 0
0+
S
0+
S
0+
S
1-M
1 -M
0+
M1+
A2+
S 2+
M
# $
V(x) = - τ/x + α x P = 1 P = 1 P = -1
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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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Introducing SU(6) violation
q q
g
One Gluon Exchange
VOGE = -a/r + Hyperfine interaction
De Rujula, H. Georgi, and S. L. Glashow 1975 N. Isgur and G. Karl, 1978
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x = ρ2 + λ2
hyperradius
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Predictions with the Hypercentral Constituent Quark Model
for
Helicity amplitudes
Elastic nucleon form factors
Having fixed the three parameters (A, α, τ)
The 3-quark wave function for every baryon can be built as known superpositions of SU(6) configurations
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The helicity amplitudes
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HELICITY AMPLITUDES
Extracted from electroproducKon of mesons
N N
γ π N*
A1/2 A3/2 S1/2
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Definition A1/2 = < N* Jz = 1/2 | HT
em | N Jz = -1/2 > § A3/2 = < N* Jz = 3/2 | HT
em | N Jz = 1/2 > § S1/2 = < N* Jz = 1/2 | HL
em | N Jz = 1/2 > N, N* nucleon and resonance as 3q states
HTem Hl
em model transition operator § results for the negative parity resonances: M. Aiello, M.G., E. Santopinto J. Phys. G24, 753 (1998) Systematic predictions for transverse and longitudinal amplitudes E. Santopinto, M.G., Phys. Rev. C86, 065202 (2012)
Proton and neutron electro-excitation to 14 resonances
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0
20
40
60
80
100
120
140
160
180
0 1 2 3 4 5
A3
/2 D
13(1
520)
(10
-3 G
eV
-1/2
)
Q2 (GeV
2)
(a) hCQMPDG
Maid07Mok09Azn09FH 83
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
0 1 2 3 4 5
A1/2
D1
3(1
52
0)
(10
-3 G
eV
-1/2
)
Q2 (GeV
2)
(b) hCQMPDG
Maid07Azn09Mok09FH 83
-80
-60
-40
-20
0
20
0 1 2 3 4 5
S1
/2
D1
3(1
52
0)
(10
-3 G
eV
-1/2
)
Q2 (GeV
2)
(c) hCQMMaid07Mok09Azn09
N(1520) 3/2- transition amplitudes
E. Santopinto, M.G. Phys. Rev. C86, 065202 (2012)
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0
20
40
60
80
100
120
140
0 1 2 3 4 5
S11(1
535)
Ap
1/2
(10
-3 G
eV
-1/2
)
Q2 (GeV
2)
(a) hypercentral CQM
-60
-40
-20
0
20
40
0 1 2 3 4 5
S11(1
535)
Sp
1/2
(10
-3 G
eV
-1/2
)
Q2 (GeV
2)
(b) hypercentral CQMAzn05
Maid07Azn09
N(1535) ½ - transition amplitudes
E. Santopinto, M.G. Phys. Rev. C86, 065202 (2012)
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-50
0
50
100
150
0 1 2 3 4 5
A1/2
P11(1
440)
(10
-3 G
eV
-1/2
)
Q2 (GeV
2)
(a) hCQMPDG
Maid07Azn09Mok09
-60
-40
-20
0
20
40
0 1 2 3 4 5
S11(1
535)
Sp
1/2
(10
-3 G
eV
-1/2
)
Q2 (GeV
2)
(b) hypercentral CQMAzn05
Maid07Azn09
N1440) ½ + (Roper)
transition amplitudes
E. Santopinto, M.G. Phys. Rev. C86, 065202 (2012)
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-100
-50
0
50
0 5 10 15 20 25 30 35
A1/2
(1
0-3
Ge
V-1
/2)
A1/2 hCQMA1/2 Bonn
hCQM: E. Santopinto, M.G. Phys. Rev. C86, 065202 (2012) Bonn: A.V. Anisovich et al., EPJ A49, 67 (2013)
Neutron photocouplings
N(1440 N(1520) N(1525) N(1650) N(1675 N(1680) N(1710) N(1720)
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Blue curves hCQM rp 0.5 fm
Green curves H.O.
m = 3/2
m = 1/2
rp 0.5 fm
rp 0.86 fm
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observations • 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 (1/x potential)
• 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
Quark-antiquark pairs effects are important
for the low Q2 behavior
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With a calculated radius of about 0.5 fm�the e.m. form factors predicted by the hCQM �
are not good!
BUT
relativity is needed
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Relativity�
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RELATIVITY
Various levels
• relaKvisKc kineKc energy
• Lorentz boosts
• RelaKvisKc dynamics
• quark‐anKquark pair effects (meson cloud)
• relaKvisKc equaKons (BS, DS)
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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(Q2
eff) F = kin factor Q2
eff = Q2 (MN/EN)2
De Sanctis et al. EPJ 1998
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calculated
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Full curves: hCQM with relaKvisKc correcKons Dashed curves: hCQM in different frames
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Construction of a fully relativistic theory Relativistic Dynamics
Three forms (Dirac): Light (LF), Instant (IF), Point (PF)
Composition of angular momentum states as in the non relativistic case
Point form:
Moving three-quark states are obtained through (interaction free) Lorentz boosts (velocity states)
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GEp
GEn GM
n
GMp
Calculated values! • Boosts to initial and final states • Expansion of current to any order
• Conserved current
Relativistic theory in point form
M. De Sanctis, M.G., E. Santopinto, A. Vassallo, PR C 76, 062201(R) (2007)
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With quark form factors
Genoa group, Phys. Rev. C76, 062201 (2007)
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0
0.5
1
1.5
2
2.5
3
3.5
4
0 2 4 6 8 10 12
Q2 F
2p /F1p
Q2 (GeV/c)2
4 Mp2
Milbrath et al.Gayou et al.
Pospischil et al.Punjabi et al., Jones et al.
Puckett et al.
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12
µp G
Ep /GM
p
Q2 (GeV/c)2
Milbrath et al.Gayou et al.
Pospischil et al.Punjabi et al., Jones et al.
Puckett et al.
Santopinto et al. PR C 82, 065204 (2010)
With quark form factors
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0 1 2 3 4
Q2(GeV
2)
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
Ap
1/2(10-3GeV
-1/2)
!(1232) (a)
0 1 2 3 4
Q2(GeV
2)
-300
-250
-200
-150
-100
-50
0
Ap
3/2(10-3GeV
-1/2)
!(1232) (b)Y.B. Dong, M.G., E. Santopinto, A. Vassallo, Few-Body 22, September 2013
Relativistic hCQM In Point Form
PRELIMINARY
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Relativity is an important issue for the description of elastic and inelastic form factors
but it is not the only important issue
Possible structure of the nucleon
3-quark core (about 0.5 fm) +
Meson cloud
How to introduce it?
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• the physical nucleon N is made of a bare nucleon � dressed by a surrounding meson cloud
• Introducing higher Fock components
Two main approaches
Problems of inconsistency
Consistency ok But: how many components?
Necessity of unquenching the quark model
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Unquenching the quark model
Mesons P. Geiger, N. Isgur, Phys. Rev. D41, 1595 (1990) D44, 799 (1991)
q anti q
q loop
Note: • sum over all intermediate states necessary for OZI rule • linear interaction is preserved renormalization of the string constant
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baryons
R. Bijker, E. Santopinto, Phys.Rev.C80:065210,2009
See talk by Santopinto on thursday
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The good magnetic moment results of the CQM are preserved by the UCQM
Bijker, Santopinto,Phys.Rev.C80:065210,2009.
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Conclusions
CQM provide a good systematic frame for baryon studies
fair description of e.m. properties (specially N-N* transitions)
possibility of understanding missing mechanisms
quark antiquark pairs effects unquenching: important break through