a relativistic model for the electromagnetic structure of...
TRANSCRIPT
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
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 2 / 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
Modern accelerators(Jlab, Mainz, ...) provide accuratedata associated with N∗ stateswith increasing W (1.4–1.8 GeV)and large Q2 (2–6 GeV2)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 2 / 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
Modern accelerators(Jlab, Mainz, ...) provide accuratedata associated with N∗ stateswith increasing W (1.4–1.8 GeV)and large Q2 (2–6 GeV2)
Challenges:
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 2 / 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
Modern accelerators(Jlab, Mainz, ...) provide accuratedata associated with N∗ stateswith increasing W (1.4–1.8 GeV)and large Q2 (2–6 GeV2)
Challenges:
Interpret the data(theory/models)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 2 / 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
Modern accelerators(Jlab, Mainz, ...) provide accuratedata associated with N∗ stateswith increasing W (1.4–1.8 GeV)and large Q2 (2–6 GeV2)
Challenges:
Interpret the data(theory/models)Provide predictions(higher Q2, higher W )
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 2 / 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
Modern accelerators(Jlab, Mainz, ...) provide accuratedata associated with N∗ stateswith increasing W (1.4–1.8 GeV)and large Q2 (2–6 GeV2)
Challenges:
Interpret the data(theory/models)Provide predictions(higher Q2, higher W )Jlab-12 GeV–upgrade
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 2 / 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
Modern accelerators(Jlab, Mainz, ...) provide accuratedata associated with N∗ stateswith increasing W (1.4–1.8 GeV)and large Q2 (2–6 GeV2)
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 2 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 3 / 41
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)
Valence quark models: appropriated for large Q2
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 3 / 41
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)
Valence quark models: appropriated for large Q2
May fails for small Q2 – meson cloud effects
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 3 / 41
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)
Valence quark models: appropriated for large Q2
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 4 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 5 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 6 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 7 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 8 / 41
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
diquark on-shell
q = P+ − P−, P = 12(P+ + P−), Q2 = −q2
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 8 / 41
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
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 8 / 41
Spectator QM: Baryon wave functions (1)
Baryon: 3 constituent quark system
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 9 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 9 / 41
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)
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 9 / 41
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)
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.
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 9 / 41
Spectator QM: Baryon wave functions (2)
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 10 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 11 / 41
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);
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 12 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 12 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 13 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 14 / 41
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.
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 15 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 16 / 41
γ∗N → N(1710): Helicity amplitudes [PRD 89 073010 (2014)] (2)
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 ,
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 17 / 41
γ∗N → N(1710): Helicity amplitudes [PRD 89 073010 (2014)] (2)
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 ,
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 17 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 18 / 41
γ∗N → N(1710): Helicity amplitudes [PRD 89 073010 (2014)] (3)
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 ...
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 19 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 20 / 41
γ∗N → N(1710): Helicity amplitudes [PRD 89 073010 (2014)] (5)
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 21 / 41
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
−
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 22 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 23 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 24 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 25 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 26 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 27 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 27 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 28 / 41
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 )
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 29 / 41
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
−
⟩
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 30 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 31 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 32 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 33 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 34 / 41
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
Model 2: better for A3/2 – N(1700)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 34 / 41
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
Model 2: better for A3/2 – N(1700)
Both models: good for N(1650): Q2 > 2 GeV2
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 34 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 35 / 41
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)
∆(1700): both models with similar results Q2 & 1 GeV2
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 35 / 41
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)
∆(1700): both models with similar results Q2 & 1 GeV2
∆(1620): Model 2 –good for Q2 > 2 GeV2
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 35 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 36 / 41
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 )
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 37 / 41
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
)PDGCLAS-1CLAS-2MAID
∆(1620)
- - - only valence quark contributions
—— include meson cloud (AD133/2 )
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 37 / 41
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
)PDGCLAS-1CLAS-2MAID
∆(1620)
- - - only valence quark contributions AS311/2 ∝
1
1+Q2
1GeV2
5/2
—— include meson cloud (AD133/2 )
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 37 / 41
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 )
ValenceMeson cloud (Re)Meson cloud (Im)
—— Spectator quark model −→ Valence
– – – D Jido, M Doring and E Oset, PRC 77, 065207 (2008) - χ Unitary ModelResonance dynamically generated −→ Meson cloud
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 38 / 41
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 )
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 )
ValenceMeson cloud (Re)Meson cloud (Im)
—— Spectator quark model −→ Valence
– – – D Jido, M Doring and E Oset, PRC 77, 065207 (2008) - χ Unitary ModelResonance dynamically generated −→ Meson cloud
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 38 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 39 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 40 / 41
Conclusions
Results for N(1710) under discussion 2nd radial excitation of N ;baryon-meson resonance; mixture of states, ...
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 41 / 41
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.
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 41 / 41
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
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 41 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 41 / 41
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)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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 41 / 41
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)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)
To facilitate the comparison with the future data we provide simpleparametrizations for the amplitudes (A1/2 ∝ 1
Q3 ;A3/2 ∝ 1Q5 )
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 41 / 41
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)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)
To facilitate the comparison with the future data we provide simpleparametrizations for the amplitudes (A1/2 ∝ 1
Q3 ;A3/2 ∝ 1Q5 )
Amplitude A1/2 for ∆(1620): very sensitive to balance betweenvalence quarks and meson cloud effects
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 41 / 41
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)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)
To facilitate the comparison with the future data we provide simpleparametrizations for the amplitudes (A1/2 ∝ 1
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]].
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 42 / 41
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)
Gilberto Ramalho (IIP/UFRN, Natal, Brazil) E.M. Structure of Baryons – 3rd Resonance October 15, 2015 43 / 41