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Exposing the structure of nucleon excited states
using Dyson-Schwinger Equations
Jorge Segovia
Technische Universitat Munchen
Physik-Department T30f
T30fTheoretische Teilchen- und Kernphysik
Nanjing University and Nanjing Normal UniversityMay 2017
☞ With the main collaboration of Roberts’ group.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 1/45
Studies of N∗-electrocouplings (I)
A central goal of Nuclear Physics: understand the properties of hadrons in terms ofthe elementary excitations in Quantum Chromodynamics (QCD): quarks and gluons.
Elastic and transition form factors of N∗
ւ ցUnique window into theirquark and gluon structure
Broad range ofphoton virtuality Q2
↓ ↓Distinctive information on the
roles played by emergentphenomena in QCD
Probe the excited nucleonstructures at perturbative andnon-perturbative QCD scales
Low Q2 High Q2
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 2/45
Studies of N∗-electrocouplings (II)
A vigorous experimental program has been and is still under way worldwide
CLAS, CBELSA, GRAAL, MAMI and LEPS
☞ Multi-GeV polarized cw beam, large acceptancedetectors, polarized proton/neutron targets.
☞ Very precise data for 2-body processes in widekinematics (angle, energy): γp → πN, ηN, KY .
☞ More complex reactions needed to access highmass states: ππN, πηN, ωN, φN, ...
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 3/45
Studies of N∗-electrocouplings (III)
CEBAF Large Acceptance Spectrometer (CLAS@JLab)
☞ Most accurate results for the electro-excitationamplitudes of the four lowest excited states.
☞ They have been measured in a range of Q2 up to:
8.0GeV2 for ∆(1232)P33 and N(1535)S11 .
4.5GeV2 for N(1440)P11 and N(1520)D13 .
☞ The majority of new data was obtained at JLab.
Upgrade of CLAS up to 12GeV2 → CLAS12 (commissioning runs are under way)
☞ A dedicated experiment will aim to extract theN∗ electrocouplings at photon virtualities Q2 everachieved so far.
☞ The GlueX@JLab experiment will provide criticaldata on (exotic) hybrid mesons which explicitlymanifest the gluonic degrees of freedom.
The constituent quark-gluon research project isrelated with the last topic
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 4/45
Non-perturbative QCD:Confinement and dynamical chiral symmetry breaking (I)
Hadrons, as bound states, are dominated by non-perturbative QCD dynamics
Explain how quarks and gluons bind together ⇒ Confinement
Origin of the 98% of the mass of the proton ⇒ DCSB
Emergent phenomena
ւ ցConfinement DCSB
↓ ↓Colouredparticles
have neverbeen seenisolated
Hadrons donot followthe chiralsymmetrypattern
Neither of these phenomena is apparent in QCD’s Lagrangian
however!
They play a dominant role in determining the characteristics of real-world QCD
The best promise for progress is a strong interplay between experiment and theory
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 5/45
Non-perturbative QCD:Confinement and dynamical chiral symmetry breaking (II)
From a quantum field theoretical point of view: Emergent
phenomena could be associated with dramatic, dynamically
driven changes in the analytic structure of QCD’s
propagators and vertices.
☞ Dressed-quark propagator in Landau gauge:
S−1
(p) = Z2(iγ·p+mbm
)+Σ(p) =
(
Z (p2)
iγ · p + M(p2)
)
−1
Mass generated from the interaction of quarks withthe gluon-medium.
Light quarks acquire a HUGE constituent mass.
Responsible of the 98% of the mass of the proton andthe large splitting between parity partners.
0 1 2 3
p [GeV]
0
0.1
0.2
0.3
0.4
M(p
) [G
eV
]
m = 0 (Chiral limit)
m = 30 MeVm = 70 MeV
effect of gluon cloud
Rapid acquisition of mass is
☞ Dressed-gluon propagator in Landau gauge:
i∆µν = −iPµν∆(q2), Pµν = gµν − qµqν/q
2
An inflexion point at p2 > 0.
Breaks the axiom of reflection positivity.
No physical observable related with.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 6/45
The simplest example of DSEs: The gap equation
The quark propagator is given by the gap equation:
S−1(p) = Z2(iγ · p +mbm) + Σ(p)
Σ(p) = Z1
∫ Λ
qg2Dµν(p − q)
λa
2γµS(q)
λa
2Γν(q, p)
General solution:
S(p) =Z(p2)
iγ · p +M(p2)
Kernel involves:Dµν (p − q) - dressed gluon propagatorΓν(q, p) - dressed-quark-gluon vertex
M(p2) exhibits dynamicalmass generation
Each of which satisfies its own Dyson-Schwinger equation
↓Infinitely many coupled equations
↓Coupling between equations necessitates truncation
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 7/45
Ward-Takahashi identities (WTIs)
Symmetries should be preserved by any truncation
↓Highly non-trivial constraint → Failure implies loss of any connection with QCD
↓Symmetries in QCD are implemented by WTIs → Relate different Schwinger functions
For instance, axial-vector Ward-Takahashi identity:
These observations show that symmetries relate the kernel of the gap equation – aone-body problem – with that of the Bethe-Salpeter equation – a two-body problem –
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 8/45
Theory tool: Dyson-Schwinger equations
The quantum equations of motion whose solutions are the Schwinger functions
☞ Continuum Quantum Field Theoretical Approach:
Generating tool for perturbation theory → No model-dependence.
Also nonperturbative tool → Any model-dependence should be incorporated here.
☞ Poincare covariant formulation.
☞ All momentum scales and valid from light to heavy quarks.
☞ EM gauge invariance, chiral symmetry, massless pion in chiral limit...
No constant quark mass unless NJL contact interaction.
No crossed-ladder unless consistent quark-gluon vertex.
Cannot add e.g. an explicit confinement potential.
⇒ modelling only withinthese constraints!
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 9/45
The bound-state problem in quantum field theory
Extraction of hadron properties from poles in qq, qqq, qqqq... scattering matrices
Use scattering equation (inhomogeneous BSE) toobtain T in the first place: T = K + KG0T
Homogeneous BSE forBS amplitude:
☞ Baryons. A 3-body bound state problem in quantum field theory:
Faddeev equation in rainbow-ladder truncation
Faddeev equation: Sums all possible quantum field theoretical exchanges andinteractions that can take place between the three dressed-quarks that define itsvalence quark content.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 10/45
Diquarks inside baryons
The attractive nature of quark-antiquark correlations in a colour-singlet meson is alsoattractive for 3c quark-quark correlations within a colour-singlet baryon
☞ Diquark correlations:
A tractable truncation of the Faddeevequation.
In Nc = 2 QCD: diquarks can form coloursinglets and are the baryons of the theory.
In our approach: Non-pointlikecolour-antitriplet and fully interacting. Thanks to G. Eichmann.
Diquark composition of the Nucleon (N), Roper (R), and Delta (∆)
Positive parity states
ւ ցpseudoscalar and vector diquarks scalar and axial-vector diquarks
↓ ↓Ignored
wrong paritylarger mass-scales
Dominantright parity
shorter mass-scales
→ N, R ⇒ 0+, 1+ diquarks∆ ⇒ only 1+ diquark
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 11/45
Baryon-photon vertex
Electromagnetic gauge invariance:current must be consistent with
baryon’s Faddeev equation.
⇓
Six contributions to the current inthe quark-diquark picture
⇓
1 Coupling of the photon to thedressed quark.
2 Coupling of the photon to thedressed diquark:
➥ Elastic transition.
➥ Induced transition.
3 Exchange and seagull terms.
One-loop diagrams
i
iΨ ΨPf
f
P
Q
i
iΨ ΨPf
f
P
Q
scalaraxial vector
i
iΨ ΨPf
f
P
Q
Two-loop diagrams
i
iΨ ΨPPf
f
Q
Γ−
Γ
µ
i
i
X
Ψ ΨPf
f
Q
P Γ−
µi
i
X−
Ψ ΨPf
f
P
Q
Γ
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 12/45
Quark-quark contact-interaction framework
☞ Gluon propagator: Contact interaction.
g2Dµν(p − q) = δµν4παIR
m2G
☞ Truncation scheme: Rainbow-ladder.
Γaν(q, p) = (λa/2)γν
☞ Quark propagator: Gap equation.
S−1(p) = iγ · p +m+ Σ(p)
= iγ · p +M
Implies momentum independent constituent quarkmass (M ∼ 0.4GeV).
☞ Hadrons: Bound-state amplitudes independentof internal momenta.
mN = 1.14GeV m∆ = 1.39GeV mR = 1.72GeV
(masses reduced by meson-cloud effects)
☞ Form Factors: Two-loop diagrams notincorporated.
Exchange diagram
It is zero because our treatment of thecontact interaction model
i
iΨ ΨPPf
f
Q
Γ−
Γ
Seagull diagrams
They are zero
µ
i
i
X
Ψ ΨPf
f
Q
P Γ−
µi
i
X−
Ψ ΨPf
f
P
Q
Γ
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 13/45
Weakness of the contact-interaction framework
A truncation which produces Faddeev amplitudes that are independent of relativemomenta:
Underestimates the quark orbital angular momentum content of the bound-state.
Eliminates two-loop diagram contributions in the EM currents.
Produces hard form factors.
Momentum dependence in the gluon propagator
↓QCD-based framework
↓Contrasting the results obtained for the same observablesone can expose those quantities which are most sensitiveto the momentum dependence of elementary objects in
QCD.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 14/45
Quark-quark QCD-based interaction framework
☞ Gluon propagator: 1/k2-behaviour.
☞ Truncation scheme: Rainbow-ladder.
Γaν(q, p) = (λa/2)γν
☞ Quark propagator: Gap equation.
S−1(p) = Z2(iγ · p +mbm) + Σ(p)
=[
1/Z(p2)] [
iγ · p +M(p2)]
Implies momentum dependent constituent quarkmass (M(p2 = 0) ∼ 0.33GeV).
☞ Hadrons: Bound-state amplitudes dependent ofinternal momenta.
mN = 1.18GeV m∆ = 1.33GeV mR = 1.73GeV
(masses reduced by meson-cloud effects)
☞ Form Factors: Two-loop diagramsincorporated.
Exchange diagram
Play an important role
i
iΨ ΨPPf
f
Q
Γ−
Γ
Seagull diagrams
They are less important
µ
i
i
X
Ψ ΨPf
f
Q
P Γ−
µi
i
X−
Ψ ΨPf
f
P
Q
ΓJorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 15/45
The γ∗N → Nucleon reaction
Work in collaboration with:
Craig D. Roberts (Argonne)
Ian C. Cloet (Argonne)
Sebastian M. Schmidt (Julich)
Based on:
Phys. Lett. B750 (2015) 100-106 [arXiv: 1506.05112 [nucl-th]]
Few-Body Syst. 55 (2014) 1185-1222 [arXiv:1408.2919 [nucl-th]]
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 16/45
The Nucleon’s electromagnetic current
☞ The electromagnetic current can be generally written as:
Jµ(K ,Q) = ie Λ+(Pf ) Γµ(K ,Q) Λ+(Pi )
Incoming/outgoing nucleon momenta: P2i = P2
f = −m2N .
Photon momentum: Q = Pf − Pi , and total momentum: K = (Pi + Pf )/2.
The on-shell structure is ensured by the Nucleon projection operators.
☞ Vertex decomposes in terms of two form factors:
Γµ(K ,Q) = γµF1(Q2) +
1
2mNσµνQνF2(Q
2)
☞ The electric and magnetic (Sachs) form factors are a linear combination of the
Dirac and Pauli form factors:
GE (Q2) = F1(Q
2)− Q2
4m2N
F2(Q2)
GM(Q2) = F1(Q2) + F2(Q
2)
☞ They are obtained by any two sensible projection operators. Physical interpretation:
GE ⇒ Momentum space distribution of nucleon’s charge.
GM ⇒Momentum space distribution of nucleon’s magnetization.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 17/45
Phenomenological aspects (I)
☞ Perturbative QCD predictions for the Dirac and Pauli form factors:
F p1 ∼ 1/Q4 and F p
2 ∼ 1/Q6 ⇒ Q2F p2 /F
p1 ∼ const.
☞ Consequently, the Sachs form factors scale as:
GpE ∼ 1/Q4 and Gp
M ∼ 1/Q4 ⇒ GpE/G
pM ∼ const.
ææ
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æ æà
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ìì
ì
ììììì
ì ì
ò
ò
ò
ô
ô
ô
0 1 2 3 4 5 6 7 8 9 10
0.0
0.5
1.0
Q2@GeV
2D
ΜpG
Ep�G
Mp
• Jones et al., Phys. Rev. Lett. 84 (2000) 1398.
• Gayou et al., Phys. Rev. Lett. 88 (2002) 092301.
• Punjabi et al., Phys. Rev. C71 (2005) 055202.
• Puckett et al., Phys. Rev. Lett. 104 (2010) 242301.
• Puckett et al., Phys. Rev. C85 (2012) 045203.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 18/45
Phenomenological aspects (II)
Updated perturbative QCD prediction
Q2F p2 /F
p1 ∼ const. ➪ ➪ ➪ Q2F p
2 /Fp1 ∼ ln2
[
Q2/Λ2]
The prediction has the important feature that it includes components of thequark wave function with nonzero orbital angular momentum.
æææææææææææææ
ææææ
æ
ææ
æ
æ
à
à
à
à à
à
0 1 2 3 4 5 6 7 8 90.0
1.0
2.0
3.0
4.0
Q2@GeV
2D
Q2
F2p�F
1p
Andrei V. Belitsky, Xiang-dong Ji, Feng Yuan, Phys. Rev. Lett. 91 (2003) 092003
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 19/45
Phenomenological aspects (III)
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 20/45
Sachs electric and magnetic form factors
☞ Q2-dependence of proton form factors:
0 1 2 3 4
0.0
0.5
1.0
x=Q2�mN
2
GEp
0 1 2 3 40.0
1.0
2.0
3.0
x=Q2�mN
2
GMp
☞ Q2-dependence of neutron form factors:
0 1 2 3 40.00
0.04
0.08
x=Q2�mN
2
GEn
0 1 2 3 4
0.0
1.0
2.0
x=Q2�mN
2
GMn
QCD-based
NJL-model
Experiment
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 21/45
Unit-normalized ratio of Sachs electric and magnetic form factors
Both CI and QCD-kindred frameworks predict a zero crossing in µpGpE/G
pM
ææææææ
æ
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æ
æ
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à
ààààà
à à
÷÷
÷
ì
ì
ì
0 1 2 3 4 5 6 7 8 9 10
0.0
0.5
1.0
Q2@GeV
2D
ΜpG
Ep�G
Mp QCD-based
NJL-model æ
æ
æ
à
à
à
0 2 4 6 8 10 120.0
0.2
0.4
0.6
Q2@GeV
2D
ΜnG
En�G
Mn
QCD-based
NJL-model
The possible existence and location of the zero in µpGpE/G
pM is a fairly direct measure
of the nature of the quark-quark interaction
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 22/45
A world with only scalar diquarks
The singly-represented d-quark in the proton≡ u[ud]0+is sequestered inside a soft scalar diquark correlation.
☞ Observation:
diquark-diagram ∝ 1/Q2 × quark-diagram
Contributions coming from u-quark
Ψi
Ψi
Ψf
ΨfPf Pi
PiPf
Q
Q
Contributions coming from d-quark
Ψi
Ψi
Ψf
ΨfPf Pi
PiPf
Q
Q
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 23/45
A world with scalar and axial-vector diquarks (I)
The singly-represented d-quark in the proton isnot always (but often) sequestered inside a softscalar diquark correlation.
☞ Observation:
P scalar ∼ 0.62, Paxial ∼ 0.38
Contributions coming from u-quark
Ψi
Ψi
Ψf
ΨfPf Pi
PiPf
Q
Q
Contributions coming from d-quark
Ψi
Ψi
Ψf
ΨfPf Pi
PiPf
Q
Q
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 24/45
A world with scalar and axial-vector diquarks (II)
æææææææ
ææ
ææ
æ
æ
ààààààààà
àà à à
0 1 2 3 4 5 6 7 8
0.0
0.5
1.0
1.5
2.0
x=Q2�MN
2
x2F
1p
d,
x2F
1p
u
u-quark
d-quarkææææææææææ
æ
æ
æ
à
àààààà
àà
àà à
à
0 1 2 3 4 5 6 7 8
0.0
0.2
0.4
0.6
x=Q2�MN
2
HΚ
pdL-
1x
2F
2p
d,HΚ
puL-
1x
2F
2p
u
u-quark
d-quark
☞ Observations:
F d1p is suppressed with respect F u
1p in the whole range of momentum transfer.
The location of the zero in F d1p depends on the relative probability of finding 1+
and 0+ diquarks in the proton.
F d2p is suppressed with respect F u
2p but only at large momentum transfer.
There are contributions playing an important role in F2, like the anomalousmagnetic moment of dressed-quarks or meson-baryon final-state interactions.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 25/45
Comparison between worlds (I)
æææææææ
ææ
ææ
æ
æ
0.0
0.5
1.0
1.5
2.0
0 1 2 3 4 5 6 7x
2F
1u
æææææææææ
ææ
ææ
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 7
Κu-
1x
2F
2u
æææææææææ
ææ æ
æ
0 1 2 3 4 5 6 7
0.0
0.2
0.4
0.6
0.8
1.0
x=Q2�MN
2
x2F
1d
æææææææææ
æ æ ææ
0 1 2 3 4 5 6 7
0.0
0.2
0.4
0.6
0.8
1.0
x=Q2�MN
2
Κd-
1x
2F
2d
Only scalar
Scalar and axial
Only axial
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 26/45
Comparison between worlds (II)
æææææææææææææ
ææææ
æ
ææ
æ
æ
à
à
à
à à
0 1 2 3 4 5 6 7 80.0
1.0
2.0
3.0
4.0
x=Q2�MN
2
@x
F2pD�F
1p
Total
Scalar all-wave
Scalar S-wave
Axial all-wave
ææææææ
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æ
àà
à
ààààà
à à
÷÷
÷
ì
ì
ì
0 1 2 3 4 5 6 7 8 9 10
0.0
0.5
1.0
Q2@GeV
2D
ΜpG
Ep�G
Mp
Total
Scalar all-wave
Scalar S-wave
Axial all-wave
☞ Observations:
Axial-vector diquark contribution is not enough in order to explain the proton’selectromagnetic ratios.
Scalar diquark contribution is dominant and responsible of the Q2-behaviour ofthe the proton’s electromagnetic ratios.
Higher quark-diquark orbital angular momentum components of the nucleon arecritical in explaining the data.
The presence of higher orbital angular momentum components in the nucleon is aninescapable consequence of solving a realistic Poincare-covariant Faddeev equation
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 27/45
The γ∗N → Delta reaction
Work in collaboration with:
Craig D. Roberts (Argonne)
Ian C. Cloet (Argonne)
Sebastian M. Schmidt (Julich)
Chen Chen (Hefei)
Shaolong Wan (Hefei)
Based on:
Few-Body Syst. 55 (2014) 1185-1222 [arXiv:1408.2919 [nucl-th]]
Few-Body Syst. 54 (2013) 1-33 [arXiv:1308.5225 [nucl-th]]
Phys. Rev. C88 (2013) 032201(R) [arXiv:1305.0292 [nucl-th]]
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 28/45
The γ∗N → ∆ transtion current
☞ The electromagnetic current can be generally written as:
Jµλ(K ,Q) = Λ+(Pf )Rλα(Pf ) iγ5 Γαµ(K ,Q) Λ+(Pi )
Incoming nucleon: P2i = −m2
N , and outgoing delta: P2f = −m2
∆.
Photon momentum: Q = Pf − Pi , and total momentum: K = (Pi + Pf )/2.
The on-shell structure is ensured by the N- and ∆-baryon projection operators.
☞ Vertex decomposes in terms of three (Jones-Scadron) form factors:
Γαµ(K ,Q) = k
[
λm
2λ+(G∗
M − G∗
E )γ5εαµγδK⊥γ Qδ − G∗
ETQαγT
Kγµ − iς
λmG∗
C QαK⊥µ
]
,
called magnetic dipole, G∗
M ; electric quadrupole, G∗
E ; and Coulomb quadrupole, G∗
C .
☞ There are different conventions followed by experimentalists and theorists:
G∗
M,Ash = G∗
M,J−S
(
1 +Q2
(m∆ +mN)2
)−12
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 29/45
Experimental results and theoretical expectations
I.G. Aznauryan and V.D. Burkert Prog. Part. Nucl Phys. 67 (2012) 1-54
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
10-1
1
Q2 (GeV
2)
G*
M,A
sh/3
GD
-7
-6
-5
-4
-3
-2
-1
0
1
2
RE
M (
%)
-35
-30
-25
-20
-15
-10
-5
0
10-1
1
Q2 (GeV
2)
RS
M (
%)
☞ The REM ratio is measured to beminus a few percent.
☞ The RSM ratio does not seem to
settle to a constant at large Q2.
SU(6) predictions
〈p|µ|∆+〉 = 〈n|µ|∆0〉〈p|µ|∆+〉 = −
√2 〈n|µ|n〉
CQM predictions
(Without quark orbitalangular momentum)
REM → 0.
RSM → 0.
pQCD predictions
(For Q2 → ∞)
G∗
M → 1/Q4.
REM → +100%.
RSM → constant.
Experimental data do not support theoretical predictions
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 30/45
Q2-behaviour of G ∗M,Jones−Scadron
G∗
M,J−S cf. Experimental data and dynamical models
æ
æ
æ
æ
æææ
ææ
æææææææææææææææææææ
ææææ ææ æ æ
æ
0 0.5 1 1.50
1
2
3
x=Q2�mD
2
GM
,J-
S*
Solid-black:QCD-kindred interaction.
Dashed-blue:Contact interaction.
Dot-Dashed-green:Dynamical + no meson-cloud
☞ Observations:
All curves are in marked disagreement at infrared momenta.
Similarity between Solid-black and Dot-Dashed-green.
The discrepancy at infrared comes from omission of meson-cloud effects.
Both curves are consistent with data for Q2 & 0.75m2∆ ∼ 1.14GeV
2.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 31/45
Q2-behaviour of G ∗M,Ash
Presentations of experimental data typically use the Ash convention– G∗
M,Ash(Q2) falls faster than a dipole –
æææææææ
æ
ææ
æ
æ
æ
0.1 0.2 0.5 1 2 5 10
0.01
0.1
1
x=Q2�mD
2
GM
,Ash
*NJL-model
QCD-based
No sound reason to expect:
G∗
M,Ash/GM ∼ constant
Jones-Scadron should exhibit:
G∗
M,J−S/GM ∼ constant
Meson-cloud effects
Up-to 35% for Q2 . 2.0m2∆.
Very soft → disappear rapidly.
G∗
M,Ashvs G∗
M,J−S
A factor 1/√Q2 of difference.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 32/45
Electric and coulomb quadrupoles
☞ REM = RSM = 0 in SU(6)-symmetric CQM.
Deformation of the hadrons involved.
Modification of the structure of thetransition current. ⇔
☞ RSM : Good description of the rapid fallat large momentum transfer.
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ò
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ò
ò ò
ò
ò
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0.0 1.0 2.0 3.0 4.0
0
-5
-10
-15
-20
-25
-30
x=Q2�mD
2
RS
MH%L
☞ REM : A particularly sensitive measure oforbital angular momentum correlations.
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0.0 1.0 2.0 3.0 4.0
0
-2
-4
-6
x=Q2�mD
2
RE
MH%L
☞ Zero Crossing in the transition electric form factor:
Contact interaction → at Q2 ∼ 0.75m2∆ ∼ 1.14GeV
2
QCD-kindred interaction → at Q2 ∼ 3.25m2∆ ∼ 4.93GeV
2
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 33/45
Large Q2-behaviour of the quadrupole ratios
Helicity conservation arguments in pQCD should apply equally to both resultsobtained within our QCD-kindred framework and those produced by an
internally-consistent symmetry-preserving treatment of a contact interaction
REMQ2
→∞= 1, RSM
Q2→∞= constant
0 20 40 60 80 100
-0.5
0.0
0.5
1.0
x=Q2�m Ρ
2
RS
M,R
EM
REM
RSM
Observations:
Truly asymptotic Q2 is required before predictions are realized.
REM = 0 at an empirical accessible momentum and then REM → 1.
RSM → constant. Curve contains the logarithmic corrections expected in QCD.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 34/45
The γ∗N → Roper reaction
Work in collaboration with:
Craig D. Roberts (Argonne)
Ian C. Cloet (Argonne)
Bruno El-Bennich (Sao Paulo)
Eduardo Rojas (Sao Paulo)
Shu-Sheng Xu (Nanjing)
Hong-Shi Zong (Nanjing)
Based on:
Phys. Rev. Lett. 115 (2015) 171801 [arXiv: 1504.04386 [nucl-th]]
Phys. Rev. C94 (2016) 042201(R) [arXiv: 1607.04405 [nucl-th]]
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 35/45
bare state at 1.76GeV
-300
-200
-100
0
1400 1600 1800
Im (
E)
(Me
V)
Re (E) (MeV)
C(1820,-248)
A(1357,-76)
B(1364,-105)
πN,ππ NηN
ρN
σN
π∆
The Roper is the proton’s first radial excitation. Its unexpectedly low mass arise froma dressed-quark core that is shielded by a meson-cloud which acts to diminish its mass.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 36/45
Nucleon’s first radial excitation in DSEs
The bare N∗ states correspond to hadron structure calculations which exclude thecoupling with the meson-baryon final-state interactions
MDSERoper = 1.73GeV MEBAC
Roper = 1.76GeV
☞ Observation:Meson-Baryon final state interactions reduce dressed-quark core mass by 20%.Roper and Nucleon have very similar wave functions and diquark content.A single zero in S-wave components of the wave function ⇒ A radial excitation.
0th Chebyshev moment of the S-wave components
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
|p| (GeV)
S1A2
(1/3)A3+(2/3)A5
Nucleon -0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
|p| (GeV)
S1A2
(1/3)A3+(2/3)A5
Roper
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 37/45
Transition form factors (I)
Nucleon-to-Roper transition form factors at high virtual photon momenta penetratethe meson-cloud and thereby illuminate the dressed-quark core
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0 1 2 3 4 5 6-0.1
-0.05
0.0
0.05
0.1
0.15
x=Q2�mN
2
F1*
QCD-basedNJL-modelFitMB-FSIs
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0 1 2 3 4 5 6
-0.6
-0.4
-0.2
0.0
0.2
0.4
x=Q2�mN
2
F2*
QCD-basedNJL-modelFitMB-FSIs
☞ Observations:
Our calculation agrees quantitatively in magnitude and qualitatively in trend withthe data on x & 2.
The mismatch between our prediction and the data on x . 2 is due to mesoncloud contribution.
The dotted-green curve is an inferred form of meson cloud contribution from thefit to the data.
The Contact-interaction prediction disagrees both quantitatively and qualitativelywith the data.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 38/45
Transition form factors (II)
Including a meson-baryon Fock-space component into the baryons’ Faddeevamplitudes with a maximum strength of 20%
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à
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0 1 2 3 4 5 6-0.1
-0.05
0.0
0.05
0.1
0.15
x=Q2�mN
2
F1*
QCD-basedNJL-modelFitMB-FSIs
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0 1 2 3 4 5 6
-0.6
-0.4
-0.2
0.0
0.2
0.4
x=Q2�mN
2F
2*
QCD-basedNJL-modelFitMB-FSIs
☞ Observations:
The incorporation of a meson-baryon Fock-space component does not materiallyaffect the nature of the inferred meson-cloud contribution.
We provide a reliable delineation and prediction of the scope and magnitude ofmeson cloud effects.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 39/45
Helicity amplitudes
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0 1 2 3 4 5 6-80
-40
0
40
80
120
x=Q2�mN
2
A1 2N®
RH10-
3G
eV-
1�2L
ææææ
æ
æ
æ
æ ææ
æ
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à
à
0 1 2 3 4 5 6
0
2020
40
60
x=Q2�mN
2
S1 2N®
RH10-
3G
eV-
1�2L
QCD-basedNJL-modelFitMB-FSIsMB-FSIs EBAC
☞ Concerning A1/2:
Inferred cloud contribution and that determined by EBAC are quantitatively inagreement on x > 1.5.
Our result disputes the EBAC suggestion that a meson-cloud is solely responsible forthe x = 0 value of the helicity amplitude.
The quark-core contributes at least two-thirds of the result.
☞ Concerning S1/2:
Large quark-core contribution on x < 1 → Disagreement between EBAC and DSEs.
The core and cloud contributions are commensurate on 1 < x < 4.
The dressed-quark core contribution is dominant on x > 4.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 40/45
The γvp → R+ Dirac transition form factor
Diquark dissection
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æ
æ
æ
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à
à
à
0 1 2 3 4 5 6
0.0
0.05
0.1
0.15
x=Q2�mN
2
F1,p*
total
scalar-scalar
axial-axial
scalar-axial
Scatterer dissection
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æ
æ
æ
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à
à
à
0 1 2 3 4 5 6
0.0
0.05
0.1
0.15
x=Q2�mN
2
F1,p*
total
γ-quark
γ-diquark
γ-exchange
☞ Observations:
The Dirac transition form factor is primarily driven by a photon striking abystander dressed quark that is partnered by a scalar diquark.
Lesser but non-negligible contributions from all other processes are found.
In exhibiting these features, F∗
1,p shows marked qualitative similarities to theproton’s elastic Dirac form factor.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 41/45
The γvp → R+ Pauli transition form factor
Diquark dissection
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0 1 2 3 4 5 6
-0.6
-0.4
-0.2
0.0
0.2
0.4
x=Q2�mN
2
F2
,p*
total
scalar-scalar
axial-axial
scalar-axial
Scatterer dissection
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0 1 2 3 4 5 6
-0.6
-0.4
-0.2
0.0
0.2
0.4
x=Q2�mN
2
F2
,p*
total
γ-quark
γ-diquark
γ-exchange
☞ Observations:
A single contribution is overwhelmingly important: photon strikes a bystanderdressed-quark in association with a scalar diquark.
No other diagram makes a significant contribution.
F∗2,p shows marked qualitative similarities to the proton’s elastic Pauli form factor.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 42/45
Flavour-separated transition form factors
Obvious similarity to the analogous form factor determined in elastic scattering
The d-quark contributions of the form factors are suppressed with respect to theu-quark contributions
0.0
0.1
0.2
F1,d*
,F
1,u*
u-quark
d-quark
0 1 2 3 4 5 6
-1.0
-0.5
0.0
0.5
1.0
x=Q2�mN
2
Κ d-
1F
2,d*
,Κ u-
1F
2,u*
u-quark
d-quark
0.0
1.0
2.0
3.0
x2F
1,d*
,x
2F
1,u*
u-quark
d-quark
0 2 4 6 8 10
-3.0
-2.0
-1.0
0.0
x=Q2�mN
2
Κ d-
1x
2F
2,d*
,Κ u-
1x
2F
2,u*
u-quark
d-quark
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 43/45
Summary
Unified study of Nucleon, Delta and Roper elastic and transition form factors thatcompares predictions made by:
Contact quark-quark interaction,
QCD-kindred quark-quark interaction,
within a DSEs framework in which:
All elements employed possess an link with analogous quantities in QCD.
No parameters were varied in order to achieve success.
The comparison clearly establishes
☞ Experiments on N∗-electrocouplings are sensitive to the momentum dependence ofthe running coupling and masses in QCD.
☞ Experiment-theory collaboration can effectively constrain the evolution to infraredmomenta of the quark-quark interaction in QCD.
☞ New experiments using upgraded facilities will leave behind meson-cloud effects andthereby illuminate the dressed-quark core of baryons.
☞ CLAS12@JLAB will gain access to the transition region between nonperturbativeand perturbative QCD scales.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 44/45
Conclusions
☞ The γ∗N → Nucleon reaction:
The presence of strong diquark correlations within the nucleon is sufficient tounderstand empirical extractions of the flavour-separated form factors.
Scalar diquark dominance and the presence of higher orbital angular momentumcomponents are responsible of the Q2-behaviour of Gp
E/GpM and F p
2 /Fp1 .
☞ The γ∗N → Delta reaction:
G∗pM,J−S falls asymptotically at the same rate as Gp
M . This is compatible with
isospin symmetry and pQCD predictions.
Data do not fall unexpectedly rapid once the kinematic relation betweenJones-Scadron and Ash conventions is properly account for.
Limits of pQCD, REM → 1 and RSM → constant, are apparent in our calculationbut truly asymptotic Q2 is required before the predictions are realized.
☞ The γ∗N → Roper reaction:
The Roper is the proton’s first radial excitation. It consists on a dressed-quarkcore augmented by a meson cloud that reduces its mass by approximately 20%.
Our calculation agrees quantitatively in magnitude and qualitatively in trend withthe data on x & 2. The mismatch on x . 2 is due to meson cloud contribution.
Flavour-separated versions of transition form factors reveal that, as in the case ofthe elastic form factors, the d-quark contributions are suppressed with respect theu-quark ones.
Jorge Segovia ([email protected]) Exposing the structure of nucleon excited states using DSEs 45/45