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