Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low...

42
Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations Jorge Segovia Technische Universit¨ at M¨ unchen Physik-Department T30f T30f Theoretische Teilchen- und Kernphysik Seminar Theoretical Hadron Physics Justus-Liebig-Universit¨ at Giessen Wednesday, February 3rd 2016 Main collaborators (in this research line): Craig D. Roberts (Argonne), Ian C. Cl¨ oet (Argonne), Sebastian M. Schmidt (J¨ ulich) Jorge Segovia ([email protected]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 1/42

Transcript of Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low...

Page 1: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

Nucleon Resonance Electro-couplings

in Dyson-Schwinger Equations

Jorge Segovia

Technische Universitat Munchen

Physik-Department T30f

T30fTheoretische Teilchen- und Kernphysik

Seminar Theoretical Hadron PhysicsJustus-Liebig-Universitat Giessen

Wednesday, February 3rd 2016

Main collaborators (in this research line):

Craig D. Roberts (Argonne), Ian C. Cloet (Argonne), Sebastian M. Schmidt (Julich)

Jorge Segovia ([email protected]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 1/42

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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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 2/42

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Studies of N∗-electrocouplings (II)

A vigorous experimental program has been and is still underway 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, ...

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Studies of N∗-electrocouplings (III)

CEBAF Large Acceptance Spectrometer (CLAS@JLab)

☞ Most accurate results for the electroexcitation amplitudesof 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 underway)

☞ 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.

My Humboldt research project within theBrambilla’s group is related with the last topic

Jorge Segovia ([email protected]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 4/42

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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

↓ ↓Coloredparticles

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

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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 reflexion positivity.

No physical observable related with.

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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

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Ward-Takahashi identities (WTIs)

Symmetries should be preserved by any truncation

↓Highly nontrivial 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 –

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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!

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Bethe-Salpeter and Faddeev equations

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 quantumfield theory.

Structure comes from solving the Faddeevequation.

P

pd

pq

Ψa =

P

pq

pd

Ψb

Γa

Γb

Faddeev equation: Sums all possible quantum field theoretical exchanges andinteractions that can take place between the three dressed-quarks that define itsvalence quark content.

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Diquarks inside baryons

The attractive nature of quark-antiquark correlations in a color-singlet meson is alsoattractive for 3c quark-quark correlations within a color-singlet baryon

☞ Diquark correlations:

A dynamical prediction of Faddeev equationstudies.

Empirical evidence in support of strong diquarkcorrelations inside the nucleon.

In our approach: Non-pointlike color-antitripletand 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

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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

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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

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Page 14: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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.

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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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 15/42

Page 16: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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]]

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Page 17: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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.

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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.

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ì ì

ò

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ò

ô

ô

ô

0 1 2 3 4 5 6 7 8 9 10

0.0

0.5

1.0

Q 2@GeV2

D

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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 18/42

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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.

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1.0

2.0

3.0

4.0

Q 2@GeV2

D

Q2

F2p�F

1p

Andrei V. Belitsky, Xiang-dong Ji, Feng Yuan, Phys. Rev. Lett. 91 (2003) 092003

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Phenomenological aspects (III)

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Page 21: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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

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Page 22: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

Unit-normalized ratio of Sachs electric and magnetic form factors

Both CI and QCD-kindred frameworks predict a zero crossing in µpGpE/G

pM

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ì

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ì

0 1 2 3 4 5 6 7 8 9 10

0.0

0.5

1.0

Q 2@GeV2

D

ΜpG

Ep�G

Mp

æ

æ

æ

à

à

à

0 2 4 6 8 10 120.0

0.2

0.4

0.6

Q 2@GeV2

D

ΜnG

En�G

Mn

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

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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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 23/42

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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

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

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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=Q 2�MN

2

x2F

1p

d,

x2F

1p

u

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à

àààààà

àà

àà à

à

0 1 2 3 4 5 6 7 8

0.0

0.2

0.4

0.6

x=Q 2�MN

2

pdL-

1x

2F

2p

d,HΚ

puL-

1x

2F

2p

u

☞ 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.

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Comparison between worlds (I)

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0.0

0.5

1.0

1.5

2.00 1 2 3 4 5 6 7

x2F

1u

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ææ

ææ

0.0

0.2

0.4

0.6

0.8

1.00 1 2 3 4 5 6 7

Κu-

1x

2F

2u

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ææ æ

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0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

1.0

x=Q 2�MN

2

x2F

1d

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æ æ ææ

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

1.0

x=Q 2�MN

2

Κd-

1x

2F

2d

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Page 27: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

Comparison between worlds (II)

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2

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0 1 2 3 4 5 6 7 8 9 10

0.0

0.5

1.0

Q 2@GeV2

D

ΜpG

Ep�G

Mp☞ 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.

Jorge Segovia ([email protected]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 27/42

Page 28: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 28/42

Page 29: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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/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 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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 29/42

Page 30: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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

Jorge Segovia ([email protected]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 30/42

Page 31: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

Q2-behaviour of G ∗M,Jones−Scadron

G∗

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

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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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 31/42

Page 32: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

Q2-behaviour of G ∗M,Ash

Presentations of experimental data typically use the Ash convention– G∗

M,Ash(Q2) falls faster than a dipole –

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0.1 0.2 0.5 1 2 5 10

0.01

0.1

1

x=Q 2�mD

2

GM

,Ash

*

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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 32/42

Page 33: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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

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

-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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 33/42

Page 34: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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

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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 34/42

Page 35: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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]]

Jorge Segovia ([email protected]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 35/42

Page 36: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 36/42

Page 37: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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

-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

Jorge Segovia ([email protected]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 37/42

Page 38: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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*

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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.

Jorge Segovia ([email protected]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 38/42

Page 39: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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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-0.05

0.0

0.05

0.1

0.15

x=Q 2�mN

2

F1*

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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

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.

Jorge Segovia ([email protected]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 39/42

Page 40: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

Helicity amplitudes

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0 1 2 3 4 5 6-80

-40

0

40

80

120

x=Q 2�mN

2

A1 2N®

RH1

0-

3G

eV-

1�2L

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0 1 2 3 4 5 6

0

2020

40

60

x=Q 2�mN

2

S1 2N®

RH1

0-

3G

eV-

1�2L

☞ 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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 40/42

Page 41: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

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]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 41/42

Page 42: Nucleon Resonance Electro-couplings in Dyson-Schwinger ...€¦ · non-perturbative QCD scales Low Q 2High Q Jorge Segovia (jorge.segovia@tum.de) Nucleon Resonance Electro-couplings

Conclusions

☞ The γ∗N → Nucleon reaction:

The possible existence and location of a zero in GpE (Q

2)/GpM (Q2) is a fairly direct

measure of the nature and shape of the quark-quark interaction.

The presence of strong diquark correlations within the nucleon is sufficient tounderstand empirical extractions of the flavour-separated form factors.

☞ 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.

Strong diquark correlations within baryons produce a zero in the transitionelectric quadrupole at Q2 ∼ 5GeV

2.

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.

Jorge Segovia ([email protected]) Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations 42/42