Jorge Segovia - USALpuccini1.fis.usal.es/web-prints/InvitedTalk_Nstar2017.pdfnon-perturbative QCD...

Valence-Quark Structure N∗ Resonances from DSEs

Jorge Segovia

Technische Universitat Munchen

Physik-Department T30f

T30fTheoretische Teilchen- und Kernphysik

☞ With the main collaboration of Craig D. Roberts’ group.

Jorge Segovia ([email protected]) Valence-Quark Structure N∗ Resonances from DSEs 1/33

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


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, ...


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


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 cloudRapid 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.


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!


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.


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


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


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


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.


Quark-quark QCD-based interaction framework

☞ Gluon propagator: 1/k2-behaviour.

☞ 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]) Valence-Quark Structure N∗ Resonances from DSEs 12/33

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]]


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


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

1Q2 (GeV2)

G* M

,Ash

/3G

D

-7-6-5-4-3-2-1012

RE

M (

%)

-35

-30

-25

-20

-15

-10

-5

0

10-1

1Q2 (GeV2)

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


Q2-behaviour of G ∗M,Jones−Scadron

G∗

M,J−S cf. Experimental data and dynamical models

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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.


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

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æ

æ

0.1 0.2 0.5 1 2 5 10

0.01

0.1

1

x=Q 2�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.


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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òò

ò ò

ò

òò

ò

ò ò

ò

ò

òò

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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òò òò

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ò ò ò

ò

ò

òò

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


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=Q 2�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.


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]]


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.


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

-0.4-0.20.00.20.40.60.81.0

0.0 0.2 0.4 0.6 0.8 1.0|p| (GeV)

S1A2(1/3)A3+(2/3)A5

Nucleon -0.4-0.20.00.20.40.60.81.0

0.0 0.2 0.4 0.6 0.8 1.0|p| (GeV)

S1A2(1/3)A3+(2/3)A5

Roper


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=Q 2�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=Q 2�mN

2

F2*


☞ 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.


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=Q 2�mN

2

F1*


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àà

òò÷÷

0 1 2 3 4 5 6

-0.6

-0.4

-0.2

0.0

0.2

0.4

x=Q 2�mN

2F

2*


☞ 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.


The γvp → R+ Dirac transition form factor

Diquark dissection

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à

à

à

0 1 2 3 4 5 60.0

0.05

0.1

0.15

x=Q 2�mN

2

F1,p*

total

scalar-scalar

axial-axial

scalar-axial

Scatterer dissection

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à

à

à

0 1 2 3 4 5 60.0

0.05

0.1

0.15

x=Q 2�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.


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=Q 2�mN

2

F2

,p*

total

scalar-scalar

axial-axial

scalar-axial

Scatterer dissection

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àà

òò÷÷

0 1 2 3 4 5 6

-0.6

-0.4

-0.2

0.0

0.2

0.4

x=Q 2�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.


γvp → R+ .vs. γvn → R0 (I)

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0 1 2 3 4 5 60.0

0.05

0.1

0.15

x=Q 2�mN

2

F1,p*

total

scalar-scalar

axial-axial

scalar-axial

0 1 2 3 4 5 6

0.0

-0.02

-0.04

x=Q 2�mN

2

F1,n*

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à

0 1 2 3 4 5 60.0

0.05

0.1

0.15

x=Q 2�mN

2

F1,p*

total

γ-quark

γ-diquark

γ-exchange

0 1 2 3 4 5 6

0.0

-0.02

-0.04

x=Q 2�mN

2

F1,n*


γvp → R+ .vs. γvn → R0 (II)

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0 1 2 3 4 5 6

-0.6

-0.4

-0.2

0.0

0.2

0.4

x=Q 2�mN

2

F2

,p* total

scalar-scalar

axial-axial

scalar-axial

0 1 2 3 4 5 6

-0.2

0.0

0.2

0.4

x=Q 2�mN

2

F2

,n*

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0 1 2 3 4 5 6

-0.6

-0.4

-0.2

0.0

0.2

0.4

x=Q 2�mN

2

F2

,p* total

γ-quark

γ-diquark

γ-exchange

0 1 2 3 4 5 6

-0.2

0.0

0.2

0.4

x=Q 2�mN

2

F2

,n*


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=Q 2�mN

2

Κ d-

1 F2

,d*,Κ u-

1 F2

,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=Q 2�mN

2

Κ d-

1x

2F

2,d*

,Κ u-

1x

2F

2,u*

u-quark

d-quark


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


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:

Pscalar ∼ 0.621, Paxial ∼ 0.287, Pmix = 0.092

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


A world with scalar and axial-vector diquarks (II)

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àà à à

0 1 2 3 4 5 6 7 8

0.0

0.5

1.0

1.5

2.0

x=Q 2�MN

2

x2F

1p

d,

x2F

1p

u

u-quark

d-quarkææææææææææ

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à

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à

0 1 2 3 4 5 6 7 8

0.0

0.2

0.4

0.6

x=Q 2�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.


Summary

Unified study of γ∗N → ∆(1232) and γ∗N → N(1440) transition form factors thatcompares predictions made by:

Symmetry-preserving treatment of a vector⊗vector contact-interaction.

Kernels and interaction vertices that possess QCD-like momentum dependence.

☞ 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.


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Jorge Segovia - USALpuccini1.fis.usal.es/web-prints/InvitedTalk_Nstar2017.pdfnon-perturbative QCD...

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