A Relativistic Model for the Electromagnetic Structure of...

A Relativistic Model for the Electromagnetic Structureof Baryons from the 3rd Resonance Region

Gilberto Ramalho

International Institute of Physics,UFRN, Federal University of Rio Grande do Norte, Brazil

[email protected]

GR and K Tsushima, PRD 89, 073010 (2014); GR, PRD 90, 033010 (2014)

Collaborators: F. Gross (Jlab), M.T. Pena (Lisbon) and K. Tsushima (UCS/Sao Paulo)

Nucleon Resonances: From Photoproduction toHigh Photon VirtualitiesECT*, Trento, Italy

October 15, 2015

Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 1 / 41

Motivation

1000 1200 1400 1600 1800 2000W (MeV)

0

10

20

30

40

50

60

σ T

∆(12

32)

P 33

N(1

710)

P11

N(1

535)

S11

∆(16

00)

P 33N

(165

0) S

11

N(1

520)

D13

γ p -> n π+

Q2 = 1 GeV

2

N(1

440)

P11


Motivation

1000 1200 1400 1600 1800 2000W (MeV)

0

10

20

30

40

50

60

σ T

∆(12

32)

P 33

N(1

710)

P11

N(1

535)

S11

∆(16

00)

P 33N

(165

0) S

11

N(1

520)

D13

γ p -> n π+

Q2 = 1 GeV

2

N(1

440)

P11

Modern accelerators(Jlab, Mainz, ...) provide accuratedata associated with N∗ stateswith increasing W (1.4–1.8 GeV)and large Q2 (2–6 GeV2)


Motivation

1000 1200 1400 1600 1800 2000W (MeV)

0

10

20

30

40

50

60

σ T

∆(12

32)

P 33

N(1

710)

P11

N(1

535)

S11

∆(16

00)

P 33N

(165

0) S

11

N(1

520)

D13

γ p -> n π+

Q2 = 1 GeV

2

N(1

440)

P11


Challenges:


Motivation

1000 1200 1400 1600 1800 2000W (MeV)

0

10

20

30

40

50

60

σ T

∆(12

32)

P 33

N(1

710)

P11

N(1

535)

S11

∆(16

00)

P 33N

(165

0) S

11

N(1

520)

D13

γ p -> n π+

Q2 = 1 GeV

2

N(1

440)

P11


Challenges:

Interpret the data(theory/models)


Motivation

1000 1200 1400 1600 1800 2000W (MeV)

0

10

20

30

40

50

60

σ T

∆(12

32)

P 33

N(1

710)

P11

N(1

535)

S11

∆(16

00)

P 33N

(165

0) S

11

N(1

520)

D13

γ p -> n π+

Q2 = 1 GeV

2

N(1

440)

P11


Challenges:

Interpret the data(theory/models)Provide predictions(higher Q2, higher W )


Motivation

1000 1200 1400 1600 1800 2000W (MeV)

0

10

20

30

40

50

60

σ T

∆(12

32)

P 33

N(1

710)

P11

N(1

535)

S11

∆(16

00)

P 33N

(165

0) S

11

N(1

520)

D13

γ p -> n π+

Q2 = 1 GeV

2

N(1

440)

P11


Challenges:

Interpret the data(theory/models)Provide predictions(higher Q2, higher W )Jlab-12 GeV–upgrade


Motivation

1000 1200 1400 1600 1800 2000W (MeV)

0

10

20

30

40

50

60

σ T

∆(12

32)

P 33

N(1

710)

P11

N(1

535)

S11

∆(16

00)

P 33N

(165

0) S

11

N(1

520)

D13

γ p -> n π+

Q2 = 1 GeV

2

N(1

440)

P11


Challenges:

Interpret the data(theory/models)Provide predictions(higher Q2, higher W )Jlab-12 GeV–upgrade

Improve description of the3rd resonance region &Extend calculations for higher Q2


Plan of the talk

Study of γ∗N → N∗ reactions

Covariant Spectator Quark ModelWave functions, quark current, transition current

Predictions for the N(1710) (2nd radial excitation of the nucleon)

Results for N(1535),N(1520) (S11 and D13)

Single Quark Transition ModelSimple relation between the helicity transition amplitudesof the same SU(6) supermultiplet

Application:Input: amplitudes for the N(1520)32

−and N(1535)12

−

Output: amplitudes for N(1650), N(1700), ∆(1620),∆(1700)


Plan of the talk







−and N(1535)12

−


Valence quark models: appropriated for large Q2


Plan of the talk







−and N(1535)12

−



May fails for small Q2 – meson cloud effects


Plan of the talk







−and N(1535)12

−



May fails for small Q2 – meson cloud effects

SQTM has SUF (2); CSQM breaks SUF (2) ⇒ react. proton targetsGilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 3 / 41

Nucleon Resonance Structure

1000 1200 1400 1600 1800 2000W (MeV)

0

10

20

30

40

50

60σ T

∆(12

32)

P 33

N(1

710)

P11

N(1

535)

S11

∆(16

00)

P 33N

(165

0) S

11

N(1

520)

D13

γ p -> n π+

Q2 = 1 GeV

2N

(144

0) P

11


Methods

Methods to study the γ∗N → N∗ reactions

QCD (only practical at high Q2)

Lattice QCD (large mπ, euclidean space ...)

(Effective) Chiral Perturbation Theory(baryons and mesons and degrees of freedom)small energy and momentum

Baryon-Meson coupled channel reaction models

Dyson-Schwinger (non-perturbative; quarks and gluons, euclidean)

Constituent quark models and chiral quark modelsquarks with structure, quark-quark interaction

Covariant Spectator Quark Model (Minkowski)Wave function determined phenomenologically (no dynamical eq.)Parametrization of the wave function by FF (MB not predicted)


Covariant Spectator Quark Model – Applications †F Gross, GR, MT Pena, K Tsushima, ...

Int. J. Mod. Phys. E 22, 1330015 (2013)– (pages 89-92); arXiv:1008.0371 [hep-ph]

Nucleon and ∆ electromagnetic form factorsPRC 77, 015202 (2008); PLB 678, 355 (2009); PLB 690, 183 (2010); JPG 36, 085004 (2009); PRD 86, 093022 (2012)

Electromagnetic transition form factors γ∗N → N∗

N∗ = ∆(1232), N∗(1440), N∗(1520), N∗(1535),∆(1600), N∗(1710), ...EPJA 36, 329 (2008); PRD 78, 114017 (2008); PRD 82, 073007 (2010); PRD 81, 074020 (2010); PRD 84, 051301

(2011); PRD 89, 073010 (2014)

Octet baryon and decuplet baryon e.m. form factors:physical regime, nuclear medium and extension to lattice QCDPRD, 033004 80 (2009); JPG 36, 115011 (2009); PRD 80, 013008 (2009); PRD 83, 054011 (2011); PRD 84, 054014

(2011); PRD 87, 093011 (2013); JPG 40, 015102 (2013)

∆(1232) mass distribution for the Dalitz decay: ∆ → Ne+e− (pp → e+e−pp)

PRD 85, 113014 (2012) Timelike regime

Nucleon – Deep Inelastic Scattering – PRC 77, 015202 (2008); PRD 85 093006 (2012)


Covariant Spectator Quark Model – Introduction

Quarks with electromagnetic structure(impulse approximation)

jµq =

(1

6f1+ +

1

2f1−τ3

)

γµ +

(1

6f2+ +

1

2f2−τ3

)iσµνqν2MN

form factors fi± parametrized according with vector meson dominancesimulate structure associated with qq and gluon dressing

Use QM symmetries to represent the structure of the wave functions

Shape (radial structure) determined phenomenologicallyby experimental data or lattice data of some ground state systems

constraints from valence quark d.o.f. ⇒ Calibrate model

Make predictions for γ∗N → N∗ form factors/helicity amplitudes


Spectator QM: Transition currents

Quark current jµq ⊕ Baryon wave function ΨB ⇒ Jµ

Transition current Jµ in spectator formalismF Gross et al PR 186 (1969); PRC 45, 2094 (1992)

Relativistic impulse approximation:

Jµ = 3∑

λ

∫

kΨf (P+, k)j

µqΨi(P−, k)

kP+ P−

N∗ N

Ψf Ψi

integrate spectator q

q = P+ − P−, P = 12(P+ + P−), Q2 = −q2






Jµ = 3∑

λ

∫

kΨf (P+, k)j

µqΨi(P−, k)

kP+ P−

N∗ N

Ψf Ψi

diquark on-shell

q = P+ − P−, P = 12(P+ + P−), Q2 = −q2






Jµ = 3∑

λ

∫

kΨf (P+, k)j

µqΨi(P−, k)

kP+ P−

N∗ N

Ψf Ψi

diquark on-shell

q = P+ − P−, P = 12(P+ + P−), Q2 = −q2

If q · J 6= 0: Landau prescription: Jµ → Jµ − q·Jq2qµ

JJ Kelly, PRC 56, 2672 (1997); Z Batiz and F Gross, PRC 58, 2963 (1998)


Spectator QM: Baryon wave functions (1)

Baryon: 3 constituent quark system




Covariant Spectator Theory: wave function Ψ defined in terms of a3-quark vertex Γ with 2 on-mass-shell quarks

Ψα(P, k3) =

(

1

mq− 6k3 − iε

)

αβ

Γβ(P, k1, k2)

Gross and Agbakpe PRC 73, 015203 (2006); Gross, GR and Pena PRC 77, 015202 (2008)





Ψα(P, k3) =

(

1

mq− 6k3 − iε

)

αβ

Γβ(P, k1, k2)


Ψ is free of singularities (3q on-shell Γ ≡ 0) ⇒ parametrize ΨStadler, Gross and Frank PRC 56, 2396 (1998); Savkli and Gross PRC 63, 035208 (2001)





Ψα(P, k3) =

(

1

mq− 6k3 − iε

)

αβ

Γβ(P, k1, k2)


Ψ is free of singularities (3q on-shell Γ ≡ 0) ⇒ parametrize ΨStadler, Gross and Frank PRC 56, 2396 (1998); Savkli and Gross PRC 63, 035208 (2001)

On-shell integration (k1, k2) ⇒ k = k1 + k2, r =12(k1 − k2)

⇒ integration in k and s = (k1 + k2)2

Gross, GR and Pena, PRC 77, 015202 (2008); PRD 85, 093005 (2012)

∫

k1

∫

k2

=π

4

∫

dΩr

∫ +∞

4m2q

ds

√

s− 4m2q

s

∫d3k

2√s+ k2

→∫

d3k

2√

m2D + k2

Mean value theorem:√s→ mD; cov. int. in diquark on-shell mom.



Effective diquark justified by the Impulse approximation

Baryon wave functions: B = diquark⊕ quarkCombination of diquark (12) and single quark (3) states,using SU(6)⊗O(3):

ΨB =∑

(color)⊗(flavor)⊗(spin-orbital)⊗ψB(P, k)

︸︷︷︸

radial

Wave function ΨB expressed at the rest frame

Covariant generalization of ΨB in terms baryon propertiesafter integration on the diquark internal variables

Phenomenology included on the quark-diquark radial wave function

ψN (χ) =N0

mD(β1 + χ)(β2 + χ), χ =

(M −mD)2 − (P − k)2

MmD

β1, β2: momentum scale parameters


Spectator QM: Nucleon wave function †

Nucleon wave function: [PRC 77,015202 (2008); EPJA 36, 329 (2008)]Simplest structure –S-state in quark-diquark system (rest frame)

ΨN (P, k) =1√2

[Φ0IΦ

0S +Φ1

IΦ1S

]ψN (P, k)

Isospin states: Φ0,1I

Spin states: defined in terms of Nucleon-Dirac spinor u(P ); diquark polarization vector ελ

Φ0S(s) ≡ u(P, s) Φ1

S(s) ≡ −(ε∗λ)αUα(P, s)

Uα(P, s) =∑

λ s′〈12s′; 1λ|1

2s〉εαλu(P, s′) →

1√3γ5

(

γα − Pα

M

)

u(P, s)

ελ = ελP function of nucleon momentumF Gross, GR and MT Pena,PRC 77, 035203 (2008)


Nucleon form factors [F Gross, GR and MT Pena, PRC 77, 015202 (2008)]

0 5 10 15 20 25 30 35Q

2(GeV

2)

0.4

0.6

0.8

1

1.2

GM

p/GD

/µp

0 10Q

2(GeV

2)

0.4

0.6

0.8

1

1.2

GM

n/GD

/µn

0 2 4 6 8 10Q

2(GeV

2)

-0.5

0

0.5

1

GE

p/GM

p/µp

0 0.5 1 1.5 2Q

2(GeV

2)

0

0.02

0.04

0.06

0.08

0.1

0.12

GE

n

Model calibrated by Nucleon form factor data

Quark current fix 4 parameters; Scalar wave function (2 parameters)

No pion cloud (explicit);


Nucleon form factors [F Gross, GR and MT Pena, PRC 77, 015202 (2008)]

0 5 10 15 20 25 30 35Q

2(GeV

2)

0.4

0.6

0.8

1

1.2

GM

p/GD

/µp

0 10Q

2(GeV

2)

0.4

0.6

0.8

1

1.2

GM

n/GD

/µn

0 2 4 6 8 10Q

2(GeV

2)

-0.5

0

0.5

1

GE

p/GM

p/µp

0 0.5 1 1.5 2Q

2(GeV

2)

0

0.02

0.04

0.06

0.08

0.1

0.12

GE

n

Model calibrated by Nucleon form factor data

Quark current fix 4 parameters; Scalar wave function (2 parameters)

No pion cloud (explicit); can be extended to the lattice QCD regimeGR and MT Pena, JPG 36, 115011 (2009); PRD 80 (2009) 013008; GR, K Tsushima and AW Thomas, JPG 40 015102 (2013)


γ∗N → R, R = radial excitation of the nucleon

N0 =NucleonN1 = N(1440) ≡ Roper, 1st radial excitationN2 = N(1710) ≈ 2nd radial excitationSame spin and isospin structure as the nucleon

States distinguished by radial wave function:ψN0, ψN1, ψN2 (and masses)

Orthogonality given at Q2 = 0 by

∫

kψN1ψN0 = 0,

∫

kψN2ψN0 = 0,

∫

kψN2ψN1 = 0,

⇒ Define ψN1, ψN2, from ψN0

with the same short-range structure: ψNj ∝ 1β2+χ

No adjustable parameters −→ predictions

GR and K Tsushima, PRD 81, 074020 (2010); PRD 89 073010 (2014)


γ∗N → R, R = radial excitation of the nucleon (2)

Radial wave functions β2 > β1 (β2 – short range)

ψN0(χN0) = N0 ×1

mD(β1 + χN )(β2 + χN )

ψN1(χN1) = N1β3 − χN1

β1 + χN1× 1

mD(β1 + χN1)(β2 + χN1)

ψN2(χN2) = N2χ2N2 − β4χN2 + β5(β1 + χN2)2

× 1

mD(β1 + χN2)(β2 + χN2)

β3, β4, β5 ⇐ Orthogonality conditions


γ∗N → N(1440): Helicity amplitudes [PRD 81, 074020 (2010)] †

0 1 2 3 4 5Q

2(GeV

2)

-80

-60

-40

-20

0

20

40

60

80

A1/

2(Q2 )

CLAS dataSpectator (valence)MAID

0 1 2 3 4 5Q

2(GeV

2)

0

10

20

30

40

50

60

S 1/2(Q

2 ) CLAS dataSpectator (valence)MAID

CLAS data - Aznauryan et al PRC 80, 055203 (2009), MAID fit

Good agreement for Q2 > 1.5 GeV2

Difference for Q2 < 1.5 GeV2 –manifestation of meson cloud

Good description also of lattice data Valence q d.o.f.


γ∗N → N(1710): Helicity amplitudes [PRD 89 073010 (2014)] (1)

0 2 4 6 8 10 12Q

2 (GeV

2)

0

20

40

60

80

A1/

2 (Q

2 ) [1

0-3 G

eV-1

/2]

N(1440)N(1710)

0 2 4 6 8 10 12Q

2 (GeV

2)

0

10

20

30

40

50

60

S 1/2 (

Q2 )

[10-3

GeV

-1/2

]

N(1440)N(1710)

Prediction of N(1710) compared with Roper amplitudes

Results similar with Roper for Q2 > 4 GeV2

Same short-range structure

Low Q2: no prediction – dominance of meson cloud



0 2 4 6 8 10 12Q

2 (GeV

2)

0

20

40

60

80

A1/

2 (Q

2 ) [1

0-3 G

eV-1

/2]

N(939)N(1440)N(1710)

0 2 4 6 8 10 12Q

2 (GeV

2)

0

10

20

30

40

50

60

S 1/2 (

Q2 )

[10-3

GeV

-1/2

]

N(939)N(1440)N(1710)

Compare with nucleon form factors (R- Roper)

R = e2

√

(MR−M)2+Q2

MRMK, K =

M2R−M2

2MR, τ → Q2

4M2

Equivalent amplitudes (extra factor√2)

A1/2 →√2RGM , S1/2 →

√2 R√

2

√1+ττ GE ,



0 2 4 6 8 10 12Q

2 (GeV

2)

0

20

40

60

80

A1/

2 (Q

2 ) [1

0-3 G

eV-1

/2]

N(939)N(1440)N(1710)

0 2 4 6 8 10 12Q

2 (GeV

2)

0

10

20

30

40

50

60

S 1/2 (

Q2 )

[10-3

GeV

-1/2

]

N(939)N(1440)N(1710)

Compare with nucleon form factors (R- Roper)

R = e2

√

(MR−M)2+Q2

MRMK, K =

M2R−M2

2MR, τ → Q2

4M2

Equivalent amplitudes (extra factor√2) Prediction

A1/2 →√2RGM , S1/2 →

√2 R√

2

√1+ττ GE ,


γ∗N → N(1710): Helicity amplitudes [PRD 89 073010 (2014)]

Amplitude A1/2: Roper, N(1710) ≈ GM (Nucleon)

0 10 20 30 40Q

2 (GeV

2)

0

20

40

60

80A

1/2 (

Q2 )

[10-3

GeV

-1/2

]

N(939)N(1440)N(1710)Nucleon data

Data: J. Arrington, W. Melnitchouk and J. A. Tjon, PRC 76, 035205 (2007)



0 2 4 6 8 10 12Q

2 (GeV

2)

0

10

20

30

40

50

A1/

2 (Q

2 ) [1

0-3 G

eV-1

/2]

N(1440)N(1710)

0 2 4 6 8 10 12Q

2 (GeV

2)

-10

0

10

20

30

40

50

60

S 1/2 (

Q2 )

[10-3

GeV

-1/2

]

N(1440)N(1710)

CLAS data: K Park et al, PRC 91, 045203 (2015)——- model predictions fail for intermediate Q2

Amplitude S1/2: difference of sign ...


γ∗N → N(1710): Helicity amplitudes [PRD 89 073010 (2014)](4)

0 2 4 6 8 10 12Q

2 (GeV

2)

0

10

20

30

40

50

A1/

2 (Q

2 ) [1

0-3 G

eV-1

/2]

N(1440)N(1710)

0 2 4 6 8 10 12Q

2 (GeV

2)

-10

0

10

20

30

40

50

60

S 1/2 (

Q2 )

[10-3

GeV

-1/2

]

N(1440)N(1710)

Possible interpretations:

Our results are valid only for larger Q2

N(1710) it is not just a radialexcitation

There are mixture of (close) states

N(1710) is a dynamically generatedresonance (EBAC): N(1820)N Suzuki et al, PRL 104, 042302 (2010)



0 2 4 6 8 10 12Q

2 (GeV

2)

0

10

20

30

40

50

A1/

2 (Q

2 ) [1

0-3 G

eV-1

/2]

N(1440)N(1710)

0 2 4 6 8 10 12Q

2 (GeV

2)

-10

0

10

20

30

40

50

60

S 1/2 (

Q2 )

[10-3

GeV

-1/2

]

N(1440)N(1710)

Discussion

We can test the if there is a dominance ofthe valence quark effects: large Q2:A1/2 ∝ 1

Q3 , S1/2 ∝ 1

Q3

Dominance of meson cloud qqq − (qq):suppression ∝ 1/Q4 – stronger falloffBaryon-meson molecule

(πN–ππN ; πN–σN ; σvN , gN , ...)

Most quark models predictA1/2 > 0, S1/2 > 0T Melde et al, PRD 77 114002 (2008);

M Ronniger et al, EPJA 49, 8 (2013)

Hyperspherical QM predicts S1/2 < 0Santopinto and Giannini, PRC 86, 065202 (2012)

good description of the data


Next ...

Results for N(1535)12

−, N(1520)3

2

−

Single Quark Transition Model

Predictions for N(1650)12

−, N(1700)3

2

−, ∆(1620)1

2

−,∆(1700)1

2

−


Wave functions N(1520), N(1535) [N2 : sq = 1/2; N4 : sq = 3/2] †

Using the SU(6)⊗O(3) structure; flavor wf: Φ0,1I ; spin wf: XS

λ,ρ, S = 12 ,

32

λ = symmetric ρ = anti− symmetric

∣∣∣∣N2,

1

2

−⟩

= N1/2

[

Φ0IX

1/2ρ +Φ1

IX1/2λ

]

ψS11∣∣∣∣N2,

3

2

−⟩

= N3/2

[

Φ0IX

3/2ρ +Φ1

IX3/2λ

]

ψD13

∣∣N4, S−⟩ = ....

diquark: kλ = k1 + k2, diquark internal momentum kρ =12(k1 − k2),

XSρ (s) =

∑

ms′

⟨1 1

2;ms′|Ss

⟩ [

Y1m(kρ) |s′〉λ + Y1m(kλ) |s′〉ρ]

XSλ (s) =

∑

ms′

⟨1 1

2;ms′|Ss

⟩ [

Y1m(kρ) |s′〉ρ − Y1m(kλ) |s′〉λ]

,

⇒ covariant generalization: k → k − k·PP 2 P ; Ylm(kρ) → ξm; |s′〉ρ,λ


γ∗N → N(1535) [GR and MT Pena, PRD 84, 033007 (2011)]12

−

Spin 1/2 dominancecos θS ≃ 0.85 → 1

|N(1535)〉 ≃∣∣∣N2, 12

−⟩

Pointlike diquark Y10(kρ) → 0kρ =

12(k1 − k2) → 0

ψS11 ≈ ψN

IS11(Q2) =∫

kkz|k|ψS11ψN

Approximated orthogonality

IS11(0) 6= 0 (⇒ F ∗

1 (0) 6= 0)

F ∗1 – good model for large Q2

F ∗2 – model fails, ...

describes EBAC data(quark core)

Data (Q2 > 1.5 GeV2): F ∗2 ≈ 0

0 1 2 3 4 5 6 7 8Q

2(GeV

2)

-0.4

-0.3

-0.2

-0.1

0

F 1* (Q2 )

CLAS dataMAID analysisDalton et alEBAC (bare)

0 1 2 3 4 5 6 7 8Q

2(GeV

2)

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

F 2* (Q2 )

CLAS dataMAID analysisDalton et alEBAC (bare)PDG


γ∗N → N(1535) [GR and MT Pena, PRD 84, 033007 (2011)] (2)

Spin 1/2 dominancecos θS ≃ 0.85 → 1

|N(1535)〉 ≃∣∣∣N2, 12

−⟩

Pointlike diquark Y10(kρ) → 0kρ =

12(k1 − k2) → 0

ψS11 ≈ ψN

IS11(Q2) =∫

kkz|k|ψS11ψN

Approximated orthogonality

IS11(0) 6= 0 (⇒ F ∗

1 (0) 6= 0)

F ∗1 – good model for large Q2

F ∗2 – model fails, ...

describes EBAC data(quark core)

Data (Q2 > 1.5 GeV2): F ∗2 ≈ 0

When F ∗2 = 0 (A1/2 ∝ F ∗

1 )

A1/2 = −2

3FS(f1+ + 2f1−τ3)IS11

0 1 2 3 4 5 6 7 8Q

2(GeV

2)

0

50

100

150

A1/

2 (10

-3G

eV-1

/2) CLAS data

MAID analysisDalton et alEBAC (bare)PDG


γ∗N → N(1535) – Updated model

No pointlike diquarkchange normalization

Orthogonality imposedIS11(0) ≡ 0Redefine ψS11(new parameter β3)

ψS11 adjustedto high Q2 data

Then F ∗1 (0) = 0

But cannotdescribe low Q2

(meson cloud !!)

When F ∗2 = 0 (A1/2 ∝ F ∗

1 )

A1/2 = −√2

3FS(f1+ + 2f1−τ3)IS11

0 1 2 3 4 5 6 7 8 9 10Q

2 (GeV

2)

0

20

40

60

80

100

A1/

2 (10

-3 G

eV-1

/2)


γ∗N → N(1520) [GR and MT Pena, PRD 89, 094016 (2014)] 32

−

Spin 1/2 dominance(cos θD ≃ 1)

Amplitudes:ID13 =

∫k

kz|k|ψD13ψN

A1/2 ∝ (f1+ + 2f1−τ3)ID13

+ (f2+ + 2f2−τ3)ID13

(valence)

ψD13 fitted to high Q2 data

Orthogonality: ID13(0) = 0

0 1 2 3 4 5

-80

-60

-40

-20

0

A1/

2 (10

-3 G

eV-1

/2)

0 1 2 3 4 5Q

2 (GeV

2)

0

30

60

90

120

150

180

A3/

2 (10

-3 G

eV-1

/2)

Meson cloud


γ∗N → N(1520) [GR and MT Pena, PRD 89, 094016 (2014)] 32

−

Spin 1/2 dominance(cos θD ≃ 1)

Amplitudes:ID13 =

∫k

kz|k|ψD13ψN

A1/2 ∝ (f1+ + 2f1−τ3)ID13

+ (f2+ + 2f2−τ3)ID13

(valence)

A3/2 =

√3

4FDG

π4

(meson cloud)

ψD13 fitted to high Q2 data

Orthogonality: ID13(0) = 0

0 1 2 3 4 5

-80

-60

-40

-20

0

A1/

2 (10

-3 G

eV-1

/2)

0 1 2 3 4 5Q

2 (GeV

2)

0

30

60

90

120

150

180

A3/

2 (10

-3 G

eV-1

/2)

Meson cloud


N ∗ radial wave function (optional)

ψR(P, k) =NR

mD(β2 + χ)

1

β1 + χ− λRβ3 + χ

New short range parameter β3 – determined by large Q2 data


Summary CSQM †

Model for N(1520), N(1535) that include diquark structure

Model describes the high Q2 regime(adding a adjustable parameter βi for resonance)

For N(1520) the amplitude A3/2 is the consequence of meson cloud(zero contribution from valence quarks)⇒ A3/2 phenomenological parametrization

Small Q2: failure of the model;no meson cloud effects included (except for AD13

3/2 )


Single Quark Transition Model

Wave function given by SU(6)⊗O(3) group:supermultiplets [SU(6), LP ] - SU(6): number of particles (inc. spin proj.)Hey and Weyers, PL 48B, 69(1974); Cottingham and Dunbar, ZPC 2, 41 (1979);

Burkert et al, PRC 67, 035204 (2003)

Photon interaction with the quarks in impulse approximationTransverse current:

J+ = AL+ +Bσ+Lz + CσzL+ +Dσ−L+L−

A,B,C,D functions of Q2 for the same [SU(6), LP ]supermultiplet [70, 1−] (negative parity):N(1520), N(1535), N(1650), N(1700), ∆(1620),∆(1700)– only 3 independent coefficients: A,B,C

SU(6) breaking: θS ≈ 31, θD ≈ 6 (1/2− = S11, 3/2− = D13)

|N(1535)〉 = cos θS

sq=1/2

︷︸︸︷∣∣∣∣∣N

2,1

2

−

⟩

− sin θS

sq=3/2

︷︸︸︷∣∣∣∣∣N

4,1

2

−

⟩

, |N(1520)〉 = cos θD

sq=1/2

︷︸︸︷∣∣∣∣∣N

2,3

2

−

⟩

− sin θD

sq=3/2

︷︸︸︷∣∣∣∣∣N

4,3

2

−

⟩

|N(1650)〉 = sin θS

∣∣∣N

2, 12

−

⟩

+ cos θS

∣∣∣N

4, 12

−

⟩

, |N(1700)〉 = sin θD

∣∣∣∣∣N

2,3

2

−

⟩

+ cos θD

∣∣∣∣∣N

4,3

2

−

⟩


SQTM: [70, 1−] amplitudes

State Amplitude

S11(1535) A1/216(A+B − C) cos θS

D13(1520) A1/21

6√2(A− 2B − C) cos θD

A3/21

2√6(A+ C) cos θD

S11(1650) A1/216(A+B − C) sin θS

S31(1620) A1/2118(3A−B + C)

D13(1700) A1/21

6√2(A− 2B − C) sin θD

A3/21

2√6(A+ C) sin θD

D33(1700) A1/21

18√2(3A+ 2B + C)

A3/21

6√6(3A− C)


SQTM: Functions A,B and C

A = 2AS11

1/2

cos θS+

√2A

D131/2 +

√6A

D133/2 , B = 2

AS111/2

cos θS− 2

√2A

D131/2 , C = −2

AS111/2

cos θS−

√2A

D131/2 +

√6A

D133/2

0 1 2 3 4 5 6 7 8 9 10Q

2 (GeV

2)

0

100

200

300

400

A (

Q2 )

0 1 2 3 4 5 6 7 8 9 10Q

2(GeV

2)

0

50

100

150

200

250

B (

Q2 )

0 1 2 3 4 5 6 7 8 9 10Q

2 (GeV

2)

-100

0

100

200

300

400

C (

Q2 )

- - - only valence quark contributions (A+ C = 0) – Model 1—— include meson cloud (AD13

3/2 ) – Model 2

Based in results for S11 and D13: ⇒ predictions for Q2 > 2 GeV2


Data

Data:

CLAS:I G Aznauryan, et al, PRC 72, 045201 (2005);M. Dugger et al. (CLAS Collaboration), PRC 79, 065206 (2009)

CLAS-2: preliminary CLAS dataV Mokeev et al, arXiv:1509.05460; V Mokeev, NSTAR 2015

MAID:D. Drechsel et al EJPA, 34, 69 (2007); L. Tiator et al, Chin. Phys. C 33,1069 (2009); Eur. Phys. J. Spec. Top. 198, 141 (2011)http://wwwkph.kph.unimainz.de/MAID//maid2007/data.html.

NSTAR:V D Burkert et al PRC 67, 035204 (2003);V. Burkert, T.-S. H. Lee, R. Gothe, and V. Mokeev, Electromagnetic N-N*Transition Form Factors Workshop, Jlab, Newport News, 2008 (unpublished)


Results for N(1650), N(1700)

A1/2 A1/2 A3/2

0 1 2 3 4 5Q

2 (GeV

2)

0

20

40

60

80

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1CLAS-2MAID

N(1650)

0 1 2 3 4 5Q

2 (GeV

2)

-35

-30

-25

-20

-15

-10

-5

0

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1

N(1700)

0 1 2 3 4 5Q

2 (GeV

2)

-30

-20

-10

0

10

20

30

A3/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1

N(1700)

Data from CLAS, preliminary CLAS (CLAS-2), MAID and PDG



A1/2 A1/2 A3/2

0 1 2 3 4 5Q

2 (GeV

2)

0

20

40

60

80

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1CLAS-2MAID

N(1650)

0 1 2 3 4 5Q

2 (GeV

2)

-35

-30

-25

-20

-15

-10

-5

0

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1

N(1700)

0 1 2 3 4 5Q

2 (GeV

2)

-30

-20

-10

0

10

20

30

A3/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1

N(1700)


Model 2: better for A3/2 – N(1700)



A1/2 A1/2 A3/2

0 1 2 3 4 5Q

2 (GeV

2)

0

20

40

60

80

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1CLAS-2MAID

N(1650)

0 1 2 3 4 5Q

2 (GeV

2)

-35

-30

-25

-20

-15

-10

-5

0

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1

N(1700)

0 1 2 3 4 5Q

2 (GeV

2)

-30

-20

-10

0

10

20

30

A3/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1

N(1700)


Model 2: better for A3/2 – N(1700)

Both models: good for N(1650): Q2 > 2 GeV2


Results for ∆(1620),∆(1700)

A1/2 A1/2 A3/2

0 1 2 3 4 5Q

2 (GeV

2)

-20

0

20

40

60

80

100

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1CLAS-2MAID

∆(1620)

0 1 2 3 4 5Q

2(GeV

2)

0

20

40

60

80

100

120

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1CLAS-2MAID

∆(1700)

0 1 2 3 4 5Q

2(GeV

2)

0

20

40

60

80

100

120

140

A3/

2 (10

-3 G

eV-1

/2)

PDGCLAS-2MAIDNSTAR

∆(1700)

Data from CLAS, preliminary CLAS (CLAS-2), MAID, PDGand NSTAR (proceedings and conferences)


Results for ∆(1620),∆(1700)

A1/2 A1/2 A3/2

0 1 2 3 4 5Q

2 (GeV

2)

-20

0

20

40

60

80

100

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1CLAS-2MAID

∆(1620)

0 1 2 3 4 5Q

2(GeV

2)

0

20

40

60

80

100

120

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1CLAS-2MAID

∆(1700)

0 1 2 3 4 5Q

2(GeV

2)

0

20

40

60

80

100

120

140

A3/

2 (10

-3 G

eV-1

/2)

PDGCLAS-2MAIDNSTAR

∆(1700)


∆(1700): both models with similar results Q2 & 1 GeV2


Results for ∆(1620),∆(1700)

A1/2 A1/2 A3/2

0 1 2 3 4 5Q

2 (GeV

2)

-20

0

20

40

60

80

100

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1CLAS-2MAID

∆(1620)

0 1 2 3 4 5Q

2(GeV

2)

0

20

40

60

80

100

120

A1/

2 (10

-3 G

eV-1

/2)

PDGCLAS-1CLAS-2MAID

∆(1700)

0 1 2 3 4 5Q

2(GeV

2)

0

20

40

60

80

100

120

140

A3/

2 (10

-3 G

eV-1

/2)

PDGCLAS-2MAIDNSTAR

∆(1700)


∆(1700): both models with similar results Q2 & 1 GeV2

∆(1620): Model 2 –good for Q2 > 2 GeV2


Simple parametrization for large Q2

Facilitate comparison with future data – powers from pQCD

A1/2(Q2) = D

(Λ2

Λ2 +Q2

)3/2

, A3/2(Q2) = D

(Λ2

Λ2 +Q2

)5/2

State Amplitude D(10−3GeV−1/2) Λ2(GeV2)

S11(1650) A1/2 68.90 3.35

S31(1620) A1/2 ... ...

D13(1700) A1/2 −8.51 2.82

A3/2 4.36 3.61

D33(1700) A1/2 39.22 2.69

A3/2 42.15 8.42


γ∗N → ∆(1620)

AS311/2 ∝

2AS11

1/2

cos θS+ 4

√2A

D131/2 + 4

√6A

D133/2

0 1 2 3 4 5Q

2 (GeV

2)

-20

0

20

40

60

80

100A

1/2 (

10-3

GeV

-1/2

)PDGCLAS-1CLAS-2MAID

∆(1620)

- - - only valence quark contributions

—— include meson cloud (AD133/2 )


γ∗N → ∆(1620)

AS311/2 ∝

2AS11

1/2

cos θS+ 4

√2A

D131/2 + 4

√6A

D133/2

6∝(

Λ2

Λ2 + Q2

)3/2

0 1 2 3 4 5Q

2 (GeV

2)

-20

0

20

40

60

80

100A

1/2 (

10-3

GeV

-1/2


∆(1620)

- - - only valence quark contributions



γ∗N → ∆(1620)

AS311/2 ∝

2AS11

1/2

cos θS+ 4

√2A

D131/2 + 4

√6A

D133/2

6∝(

Λ2

Λ2 + Q2

)3/2

0 1 2 3 4 5Q

2 (GeV

2)

-20

0

20

40

60

80

100A

1/2 (

10-3

GeV

-1/2


∆(1620)

- - - only valence quark contributions AS311/2 ∝

1

1+Q2

1GeV2

5/2



γ∗N → N(1535): Meson cloud

GR, D Jido and K Tsushima, PRD 85, 093014 (2012)

0 0.5 1 1.5 2 2.5Q

2 (GeV

2)

-0.25

-0.2

-0.15

-0.1

-0.05

0

F 1* (Q2 )

ValenceMeson cloud (Re)Meson cloud (Im)

0 0.5 1 1.5 2 2.5Q

2(GeV

2)

-0.4

-0.2

0

0.2

0.4

F 2* (Q2 )


—— Spectator quark model −→ Valence

– – – D Jido, M Doring and E Oset, PRC 77, 065207 (2008) - χ Unitary ModelResonance dynamically generated −→ Meson cloud


γ∗N → N(1535): Meson cloud

GR, D Jido and K Tsushima, PRD 85, 093014 (2012) (F ∗2 )mc ≈ −(F ∗

2 )B

0 0.5 1 1.5 2 2.5Q

2 (GeV

2)

-0.25

-0.2

-0.15

-0.1

-0.05

0

F 1* (Q2 )


0 0.5 1 1.5 2 2.5Q

2(GeV

2)

-0.4

-0.2

0

0.2

0.4

F 2* (Q2 )


—— Spectator quark model −→ Valence

– – – D Jido, M Doring and E Oset, PRC 77, 065207 (2008) - χ Unitary ModelResonance dynamically generated −→ Meson cloud


γ∗N → N(1535): Relation between A1/2 and S1/2

Implications of F ∗2 = 0 ?

τ = Q2

(MR+M)2Q2 > 1.5 GeV2

S1/2 ≃ −√1 + τ√2

M2S −M2

2MSQA1/2

GR, K TsushimaPRD 84, 051301 (2011)

GR, D Jido, K Tsushima

PRD 85, 093014 (2012)

Cancellation betweenvalence and meson cloud

0 1 2 3 4 5 6Q

2(GeV

2)

-30

-20

-10

0

S 1/2 (

10-3

GeV

-1/2

)S

1/2 data

F(Q2)x( A

1/2 data)


γ∗N → N(1520) form factors – large Q2

Q 2 (GeV 2)

Hel

icit

y as

ymm

etry

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Ah =|A1/2|2 − |A3/2|2|A1/2|2 + |A3/2|2

0 5 10 15 20Q

2 (GeV

2)

-6

-4

-2

0

2

4

GX

/GD

GM

-GE

GM

+ GE

Spectator

Ah = 1− 3(GM +GE)2

2(3G2M +G2

E)

GM +GE → 0 very slowly


Conclusions

Results for N(1710) under discussion 2nd radial excitation of N ;baryon-meson resonance; mixture of states, ...


Conclusions

Results for N(1710) under discussion 2nd radial excitation of N ;baryon-meson resonance; mixture of states, ...Combine the features of the Covariant Spectator Quark Model andSingle Quark Transition Model based in valence quark d.o.f.


Conclusions

Results for N(1710) under discussion 2nd radial excitation of N ;baryon-meson resonance; mixture of states, ...Combine the features of the Covariant Spectator Quark Model andSingle Quark Transition Model based in valence quark d.o.f.Use results from CSQM to estimate the SQTM coefficients A,B,C


Conclusions

Results for N(1710) under discussion 2nd radial excitation of N ;baryon-meson resonance; mixture of states, ...Combine the features of the Covariant Spectator Quark Model andSingle Quark Transition Model based in valence quark d.o.f.Use results from CSQM to estimate the SQTM coefficients A,B,CResults are improved if we include a parametrization of theamplitude AD13

3/2 that is dominated by meson cloud effects

(according with CSQM)


Conclusions



(according with CSQM)Predictions presented for the negative parity resonancesN(1650), N(1700), ∆(1620),∆(1700)to be tested by future experiments in the range 2− 12 GeV2 (JLab-12)


Conclusions




To facilitate the comparison with the future data we provide simpleparametrizations for the amplitudes (A1/2 ∝ 1

Q3 ;A3/2 ∝ 1Q5 )


Conclusions





Q3 ;A3/2 ∝ 1Q5 )

Amplitude A1/2 for ∆(1620): very sensitive to balance betweenvalence quarks and meson cloud effects


Conclusions





Q3 ;A3/2 ∝ 1Q5 )

Amplitude A1/2 for ∆(1620): very sensitive to balance betweenvalence quarks and meson cloud effects

Thank youGilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 41 / 41

Selected bibliography (part 1)

γ∗N → N(1710) transition at high momentum transfer,G. Ramalho and K. Tsushima, Phys. Rev. D 89, 073010 (2014)[arXiv:1402.3234 [hep-ph]].

Using the Single Quark Transition Model to predictnucleon resonance amplitudesG. Ramalho, Phys. Rev. D 90 , 033010 (2014) [arXiv:1407.0649 [hep-ph]].

γ∗N → N∗(1520) form factors in the spacelike regionG. Ramalho and M. T. Pena, Phys. Rev. D 89, 094016 (2014)[arXiv:1309.0730 [hep-ph]].

A covariant model for the γN → N(1535) transition at highmomentum transfer,G. Ramalho and M. T. Pena, Phys. Rev. D 84, 033007 (2011)[arXiv:1105.2223 [hep-ph]].

A simple relation between the γN → N(1535) helicity amplitudes,G. Ramalho and K. Tsushima, Phys. Rev. D 84, 051301 (2011)[arXiv:1105.2484 [hep-ph]].


Selected bibliography (part 2)

A covariant formalism for the N∗ electroproductionat high momentum transfer, ReviewG. Ramalho, F. Gross, M. T. Pena and K. Tsushima,Exclusive Reactions and High Momentum Transfer IV, 287 (2011)[arXiv:1008.0371 [hep-ph]].

Studies of Nucleon Resonance Structure in Exclusive MesonElectroproduction, Review (pages 87-92)I. G. Aznauryan et al, Int. J. Mod. Phys. E 22, 1330015 (2013)[arXiv:1212.4891 [nucl-th]].

A pure S-wave covariant model for the nucleon,F. Gross, G. Ramalho and M. T. Pena, Phys. Rev. C 77, 015202 (2008)[arXiv:nucl-th/0606029].

Covariant nucleon wave function with S, D, and P-state components,F. Gross, G. Ramalho and M. T. Pena, Phys. Rev. D 85, 093005 (2012)[arXiv:1201.6336 [hep-ph]].

Valence quark contributions for the γ∗NP11(1440) form factor,G. Ramalho and K. Tsushima, Phys. Rev. D 81, 074020 (2010)


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