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
Outline of the talk
The Model (hCQM)
The helicity amplitudes
Relativity
The elastic nucleon form factors
The helicity amplitudes
Perspectives
The Model �(hCQM)�
hypercentral Constituent Quark Model
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)
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
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
Hyperspherical harmonics
Hasenfratz et al. 1980: Σ V(ri,rj) is approximately hypercentral
γ = 2n + lρ + lλ
hyperradius
hyperangle
Hypercentral Model
V(x) = ‐τ/x + α x
Hypercentral approximaKon of
Genoa group, 1995
Carlson et al, 1983 CapsKck‐Isgur 1986 hCQM 1995
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
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
Quark-antiquark lattice potential G.S. Bali Phys. Rep. 343, 1 (2001)
V = - b/r + c r
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
x = ρ2 + λ2
hyperradius
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
The helicity amplitudes
HELICITY AMPLITUDES
Extracted from electroproducKon of mesons
N N
γ π N*
A1/2 A3/2 S1/2
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
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)
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)
-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)
-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)
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
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
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
Relativity�
RELATIVITY
Various levels
• relaKvisKc kineKc energy
• Lorentz boosts
• RelaKvisKc dynamics
• quark‐anKquark pair effects (meson cloud)
• relaKvisKc equaKons (BS, DS)
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
calculated
Full curves: hCQM with relaKvisKc correcKons Dashed curves: hCQM in different frames
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)
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)
With quark form factors
Genoa group, Phys. Rev. C76, 062201 (2007)
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
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
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?
• 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
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
baryons
R. Bijker, E. Santopinto, Phys.Rev.C80:065210,2009
See talk by Santopinto on thursday
The good magnetic moment results of the CQM are preserved by the UCQM
Bijker, Santopinto,Phys.Rev.C80:065210,2009.
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