INSIGHTS INTO THE ELECTROMAGNETIC N TRANSITION Jorge Segovia and - - PowerPoint PPT Presentation

INSIGHTS INTO THE ELECTROMAGNETIC γ∗N → ∆ TRANSITION

Jorge Segovia and Craig D. Roberts Argonne National Laboratory Chen Chen and Shaolong Wang University of Science and Technology of China Kent State University, Center for Nuclear Research (CNR) Kent (Ohio), May 1st, 2013

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 1/37

The ∆ baryon

Discovered more than 50 years ago ↓ By Fermi and collaborators ↓ In pion scattering off protons at the Chicago cyclotron (now Fermilab)

• E. Fermi et al., Phys. Rev. 85, 935 (1952).
• H. Anderson et al., Phys. Rev. 85, 936 (1952).

Mass of 1232 MeV and width of 120 MeV. Lightest baryon resonance ⇒ 300 MeV heavier than the nucleon. Almost an ideally elastic πN resonance ⇒ 99% of times decaying to ∆ → πN. Only other decay channel: ∆ → γN ⇒ less than 1% to the total decay width. The ∆+ and ∆0 can be viewed, respectively, as isospin- and spin-flip excitations of the proton and neutron

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 2/37

The γ∗N → ∆ reaction

Two ways in order to analyze the structure of the ∆-resonances ւ ց π-mesons as a probe photons as a probe ↓ ↓ complex relatively simple BUT: B(∆ → γN) 1% This became possible with the advent of intense, energetic electron-beam facilities Reliable data on the γ∗p → ∆+ transition: ☞ Available on the entire domain 0 ≤ Q2 8 GeV2. Isospin symmetry implies γ∗n → ∆0 is simply related with γ∗p → ∆+. γ∗p → ∆+ data has stimulated a great deal of theoretical analysis: Deformation of hadrons. The relevance of pQCD to processes involving moderate momentum transfers. The role that experiments on resonance electroproduction can play in exposing non-perturbative phenomena in QCD: ☞ The nature of confinement and Dynamical Chiral Symmetry Breaking.

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 3/37

QCD and hadron physics

Quantum Chromodynamics is generally regarded as the non-Abelian gauge quantum field theory that describes quark and gluon physics (strong interactions). Successful at high energies → perturbative calculations are allowed. Some non trivial and unexpected properties of QCD have been well understood and confirmed experimentally. The nonperturbative regime of QCD, where the hadron properties are involved, remains to be understood. A rigorous proof is still lacking that QCD works as a microscopic theory of strong interactions that gives rise to the phenomenological properties of hadron spectra. Emergent phenomena ☞ Quark and gluon confinement. No matter how hard one strikes the proton, one cannot liberate an individual quark and gluon. ☞ Dynamical chiral symmetry breaking Very unnatural pattern of bound states. Current quark mass is small and still no degeneracy between parity partners is found. Neither of these phenomena is apparent in QCD’s Lagrangian yet! they are the dominant determining characteristics of real-world QCD

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Emergent phenomena: Confinement (I)

Usual result in Lattice QCD Pure gluon dynamics Multigluon exchanges produce an attractive linearly rising potential proportional to the distance between quarks. This idea has been confirmed, but not rigorously proved, by quenched lattice gauge calculations applied to heavy valence quark systems.

G.S. Bali, Phys. Rep. 343, 1 (2001).

• 3
• 2
• 1

1 2 3 4 0.5 1 1.5 2 2.5 3 [V(r)-V(r0)]r0 r/r0 Σg

+

Πu 2 mps mps + ms quenched κ = 0.1575

Sea light quarks Sea quarks are also important ingredients of the strong interaction dynamics. Included in the lattice calculations. Contribute to the screening of the rising potential at low momenta and eventually to the breaking of the quark-antiquark binding string.

G.S. Bali, Phys. Rev. D 71, 114513 (2005).

• 0.8
• 0.6
• 0.4
• 0.2

0.2 2 4 6 8 10 12 14 16 18 [E(r) - 2 mB]a r/a

• state |1>

state |2> Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 5/37

Emergent phenomena: Confinement (II)

Another point of view ☞ Novel feature of QCD: Tree-level interactions between gauge-bosons

O(αs) cross-section cf. O(α4

em) in QED

3-gluon vertex 4-gluon vertex

(b) fermion screening (c) gluon antiscreening

g0

s

g0

s

(a) + (b) + (c) + ... = − → ¯ gs(Q2) ¯ gs(Q2) (d)

αs(Q2) = α(0)

s

• 1 − 2

3nf α(0)

s

4π ln Λ2 Q2 + 11α(0)

s

4π ln Λ2 Q2

• ☞ This momentum-dependent coupling translates

into a coupling that depends strongly on separation ☞ The interaction becomes stronger as the participants try to separate. The confinement hypothesis: Color-charged particles cannot be isolated, they clump together in color-neutral bound states.

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Emergent phenomena: Confinement (III)

Quantum field theory paradigm Dressed-propagator for a colored state Confinement is expressed through a dramatic change in the analytic structure of propagators for colored states. Real-axis mass-pole splits, moving into pair(s)

• f complex conjugate singularities.

State described by rapidly damped wave and hence state cannot exist in observable spectrum. Dressed-gluon propagator Confined gluon. IR-massive but UV-massless. mG ∼ 2 − 4ΛQCD. Modification of the quark and gluon propagators

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 7/37

Emergent phenomena: Dynamical chiral symmetry breaking (I)

In the Dirac basis, γ5 is the chiral operator and one may represent: Positive helicity (right handed) fermion: q+(x) = 1 2 (ID + γ5)q(x) = P+q(x) Negative helicity (left handed) fermion: q−(x) = 1 2 (ID − γ5)q(x) = P−q(x) A global chiral transformation is enacted by: q(x) → q′(x) = eiγ5θq(x), ¯ q(x) → ¯ q′(x) → ¯ q(x)eiγ5θ with the choice θ = π/2, this transformation maps: q+ → q+, q− → −q− helicity is conserved An example: ¯ q(x)iγ5q(x)

θ=π/4

− − − − → −¯ q(x)IDq(x) It turns a pseudoscalar into a scalar Spectrum of a theory invariant under chiral transformations ↓ should exhibit degenerate parity doublets π JP = 0− m = 140 MeV cf. σ JP = 0+ m = 500 MeV ρ JP = 1− m = 775 MeV cf. a1 JP = 1+ m = 1260 MeV N JP = 1/2+ m = 938 MeV cf. N(1535) JP = 1/2− m = 1535 MeV

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Emergent phenomena: Dynamical chiral symmetry breaking (II)

Current quark mass should be the responsible since it is the only piece in the QCD Lagrangian that breaks chiral symmetry This appears to suggest that the quarks are quite massive ↓ but quarks are very light: mu/md ∼ 0.5 md = 4 MeV ↓ splitting between parity partners is greater than 100-times this mass scale Dynamical chiral symmetry breaking

Mass generated from the interaction of quarks with the gluon-medium. Quarks acquire a HUGE constituent mass. Responsible of the 98% of the mass of the proton.

(Not) spontaneous chiral symmetry breaking

Higgs mechanism. Quarks acquire a TINY current mass. Responsible of the 2% of the mass of the proton.

1 2 3 p [GeV] 0.1 0.2 0.3 0.4 M(p) [GeV]

m = 0 (Chiral limit) m = 30 MeV m = 70 MeV

effect of gluon cloud Rapid acquisition of mass is

Modification of the quark propagator

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Theory tool: Dyson-Schwinger equations

The extraordinary phenomena of confinement and DCSB: Can be identified with properties of dressed-quark and -gluon propagators. Are expressed through QCD’s vertices. Dyson-Schwinger equations (DSEs) Well suited to Relativistic Quantum Field Theory. Generating tool for perturbation theory → No model-dependence. Nonperturbative tool for the study of continuum strong QCD → any model-dependence should be incorporated here. Allows the study of the interaction between light quarks in the whole range of momenta Analysis of the infrared behaviour of the strong coupling constant → β-function. The β-function behaviour at infrared momenta is crucial to disentangle confinement and DCSB. DSEs connect β-function to experimental observables Solutions of DSEs are Schwinger functions. All cross sections can be constructed from such n-point functions. Comparison between computations and observations of

Hadron mass spectrum. Elastic and transition form factors ...

can be used to illuminate QCD (at infrared momenta).

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 10/37

The gap equation

The dressed-quark propagator is given by the gap equation: Sf (p)−1 = Z2(iγ · p + mbm

f

) + Σf (p) Σf (p) = Z1 Λ

q

g2Dµν(p − q)λa 2 γµSf (q)λa 2 Γf

ν(q, p)

General solution: S(p) = Z(p2) iγ · p + M(p2) Dynamical chiral symmetry breaking Interaction alone provides mass to the massless fermions Kernel of the equation for the quark self energy involves:

Dµν(p − q) - dressed gluon propagator Γν(q, p) - dressed-quark-gluon vertex

Σ γ S Γ D

=

1 2 3 p [GeV] 0.1 0.2 0.3 0.4 M(p) [GeV]

m = 0 (Chiral limit) m = 30 MeV m = 70 MeV

effect of gluon cloud Rapid acquisition of mass is

each of which satisfies its own Dyson-Schwinger equation ↓ Infinitely many coupled equations ↓ Coupling between equations necessitates truncation → Rainbow-Ladder truncation

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Vector and Axial-vector Ward-Takahashi identities

Symmetries should be preserved by any truncation ↓ Highly nontrivial constraint → failure implies loss of any connection with QCD ↓ Symmetries associated with conservation of vector and axial-vector currents For instance, axial-vector Ward-Takahashi identity: These observations show that symmetries relate the kernel of the gap equation – a

• ne-body problem – with that of the Bethe-Salpeter equation – a two-body problem –

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 12/37

Bethe-Salpeter and Faddeev equations

Hadrons are studied via covariant bound-state equations ☞ Mesons A 2-body bound state problem in quantum field theory. Properties emerge from solutions of Bethe-Salpeter equation: Γ(k; P) =

• d4q

(2π)4 K(q, k; P) Sf (q+P) Γ(q; P) Sf (q) → The kernel is that of the gap equation

= iΓ iS iΓ K iS

☞ Baryons A 3-body bound state problem in quantum field theory. Structure comes from solving the Faddeev equation. Faddeev equation: Sums all possible quantum field theoretical interactions that can take place between the three quarks that define its valence quark content.

=

a

Ψ P pq pd Γb Γ −a pd pq

b

Ψ P

q

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Diquarks inside baryons

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

☞ Diquark correlations: A dynamical prediction of Faddeev equation studies. Non-pointlike color-antitriplet. Fully interacting. Empirical evidence in support of diquarks.

=

a

Ψ P pq pd Γb Γ −a pd pq

b

Ψ P

q

Diquark composition of the nucleon and ∆ Positive parity states ւ ց pseudoscalar and vector diquarks scalar and axial-vector diquarks ↓ ↓ Ignored wrong parity larger mass-scales Dominant right parity shorter mass-scales → N ⇒ 0+, 1+ diquarks ∆ ⇒ only 1+ diquark

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Return to the γ∗N → ∆ reaction

Do you remember ... ☞ It is sensible to exploit the relative simplicity of virtual photons in order to study the ∆-resonance’s structure. ☞ The problem is that B(∆ → γN) 1% but this became possible with the advent of intense, energetic electron-beam facilities. ☞ Reliable data for the γ∗p → ∆+ transition on the entire domain 0 ≤ Q2 8 GeV2. ☞ Isospin symmetry implies γ∗n → ∆0 is simply related with γ∗p → ∆+. γ∗p → ∆+ data has stimulated a great deal of theoretical analysis: Deformation of hadrons. The relevance of pQCD to processes involving moderate momentum transfers. The role that experiments on resonance electroproduction can play in exposing non-perturbative phenomena in QCD.

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 15/37

The electromagnetic current

☞ The electromagnetic current can be generally written as: Jµλ(K, Q) = Λ+(Pf )Rλα(Pf )iγ5Γαµ(K, Q)Λ+(Pi) Incoming nucleon momentum ⇒ P2

i = −m2 N.

Outgoing ∆ momentum ⇒ P2

f = −m2 ∆.

Q = Pf − Pi and K = (Pi + Pf )/2. The on-shell structure is ensured by the N- and ∆-baryon projectors. ☞ The composition of the 4-point function Γαµ is determined by Poincar´ e covariance: Convenient to work with orthogonal momenta ↔ Simplify its structure considerably ↓ Not yet the case for K and Q ↔ ∆(m∆ − mN) = 0 ⇒ K · Q = 0 ↓ We take instead ˆ K ⊥

µ = TQ µν ˆ

Kν and ˆ Q ☞ Vertex decomposes in terms of three (Jones-Scadron) form factors Γαµ = k λm 2λ+ (G ∗

M − G ∗ E )γ5εαµγδ ˆ

K ⊥

γ ˆ

Qδ − G ∗

E TQ αγTK γµ − iς

λm G ∗

C ˆ

Qα ˆ K ⊥

µ

• ,

Magnetic dipole ⇒ G ∗

M

Electric quadrupole ⇒ G ∗

E

Coulomb quadrupole ⇒ G ∗

C

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Extraction of the form factors

The Jones-Scadron form factors are:

G ∗

M = 3(s2 + s1),

G ∗

E = s2 − s1,

G ∗

C = s3.

G ∗

M,Ash vs G ∗p M,J−S

G ∗

M,Ash = G ∗ M,J−S

• 1 +

Q2 (m∆ + mN)2 − 1

2

The scalars are obtained from the following Dirac traces and momentum contractions: s1 = n

• ς(1 + 2d )

d − ς

TK

µν ˆ

K ⊥

λ Tr[γ5Jµλγν],

s2 = n λ+ λm TK

µλTr[γ5Jµλ],

s3 = 3n λ+ λm (1 + 2d )

d − ς

ˆ K ⊥

µ ˆ

K ⊥

λ Tr[γ5Jµλ].

We have used the following notation:

n =

• 1 − 4d 2

4ik λm , λ± = (m∆±mN )2+Q2

2(m2 ∆+m2 N )

, ς = Q2 2(m2

∆ + m2 N) ,

d =

m2

∆ − m2 N

2(m2

∆ + m2 N) ,

λm =

• λ+λ−,

k =

• 3

2

• 1 + m∆

mN

• .
• G. Eichman et al., Phys. Rev. D 85, 093004 (2012).

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 17/37

Experimental data

I.G. Aznauryan and V.D. Burkert Prog. Part. Nucl Phys. 67, 1-54 (2012)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10

• 1

1

Q2 (GeV2) G*M,Ash/3GD

• 7
• 6
• 5
• 4
• 3
• 2
• 1

1 2

REM (%)

• 35
• 30
• 25
• 20
• 15
• 10
• 5

10

• 1

1

Q2 (GeV2) RSM (%)

CLAS data: . MAMI: △. MIT/Bates: Open crosses. JLab/Hall C: and . JLab/ Hall A: . Old experiments from NINA and DESY: . MAID2007:Blue Dotted curve. Others: theoretical calculations.

Historically the electromagnetic transition amplitudes for the γ∗N → ∆ have been presented in terms of: G ∗

M in the Ash convention.

REM = − G∗

E

G∗

M .

RSM = − |

Q| 2m∆ G∗

C

G∗

M .

Observations ☞ G ∗

M,Ash decays faster than a dipole form

factor ∼ 1/Q4. ☞ The REM ratio is measured to be minus a few percent. ☞ The RSM ratio does not seem to settle to a constant at large Q2.

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Theoretical expectations in SU(6)-symmetric constituent quark models

In analyses of baryon electromagnetic properties, using a quark model framework which implements a current that transforms according to the adjoint representation of spin flavor SU(6), one finds: p|µ|∆+ = − n|µ|∆0 p|µ|∆+ = − √ 2 n|µ|n ☞ Magnetic components of the γ∗p → ∆+ and γ∗n → ∆0 are equal in magnitude. ☞ Simply proportional to the neutron’s magnetic form factor ∼ 1/Q4. ☞ Nucleon and ∆ in S-wave. ☞ Neither is deformed. ☞ Hence G ∗

E = G ∗ C = 0.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10

• 1

1

Q2 (GeV2) G*M,Ash/3GD

• 7
• 6
• 5
• 4
• 3
• 2
• 1

1 2

REM (%)

• 35
• 30
• 25
• 20
• 15
• 10
• 5

10

• 1

1

Q2 (GeV2) RSM (%)

☞ The G∗

M,Ash is not 1/Q4.

☞ The REM ratio is not zero. ☞ The RSM ratio is not zero.

↓ Deformation of hadrons

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 19/37

Theoretical expectations in perturbative QCD

The electro-excitation of the ∆ provides a famous test for perturbative QCD ☞ Based on conserved quark helicities. ☞ Scaling and selection rules for dominant helicity amplitudes have been derived. ☞ Expected to be valid at sufficiently high momentum transfers. For Q2 → ∞ G ∗

M → 1/Q4.

REM → +100%. RSM → cte.

q q q g g q N* N q q q γ∗ q

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10

• 1

1

Q2 (GeV2) G*M,Ash/3GD

• 7
• 6
• 5
• 4
• 3
• 2
• 1

1 2

REM (%)

• 35
• 30
• 25
• 20
• 15
• 10
• 5

10

• 1

1

Q2 (GeV2) RSM (%)

☞ The G∗

M,Ash is not 1/Q4.

☞ The REM ratio is not +100%. ☞ The RSM ratio is not a constant.

↓ Validity of pQCD within the experimental range of transfer momentum

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 20/37

Motivation

☞ Technical “narrow” perspective: Experimental data do not support the constituent quark model and pQCD predictions. The nucleon and ∆ deformation is tightly connected to the understanding of their internal structure. The high-Q2 reach makes possible the idea of being probed the nucleon and ∆ structure in the transition regime between perturbative and nonperturbative QCD. ☞ Broad perspective: A central goal of (the DOE Office of) Nuclear Physics is to understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD. The excitation of nucleon resonances in electromagnetic interactions has long been recognize as an important source of information for understanding strong interactions. The high-Q2 reach by experiments makes possible to probe the excited nucleon structures at perturbative and non-perturbative QCD scales.

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CLAS and CLAS12

CEBAF Large Acceptance Spectrometer (CLAS) ☞ The most accurate results have been obtained for the electroexcitation amplitudes of the four lowest excited states. ☞ They have been measured in a range of Q2 up to: 8.0 GeV2 for ∆(1232)P33 and N(1535)S11. 4.5 GeV2 for N(1440)P11 and N(1520)D13. ☞ The majority of new data was obtained at JLab. High enough Q2 that people began to ask about the pQCD Upgrade of CLAS up to 12 GeV → CLAS12 ☞ Upgrade underway. ☞ Construction cost $310-million. ☞ New generation experiments in 2015. ☞ In particular, a dedicated experiment will aim to extract the N∗ electrocouplings at photon virtualities Q2 ever achieved so far.

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Electromagnetic current description in the quark-diquark picture

To compute the electromagnetic properties of the γ∗N∆ reaction in a given framework, one must specify how the photon couples to its constituents. ☞ There are six contributions to the current. The picture shows the one-loop diagrams

1

Coupling of the photon to the dressed quark.

2

Coupling of the photon to the dressed diquark: ➫ Elastic transition. ➫ Induced transition. scalar diquark correlations are absent from the ∆-resonance ↓ Only axial-vector diquark correlations contribute in the top and middle diagrams ☞ Each diagram can be expressed like the electromagnetic current: Γµλ = Λ+(Pf )Rλα(Pf )Jµα(K, Q)Λ+(Pi)

i i

Ψ Ψ P

f f

P Q

i i

Ψ Ψ P

f f

P Q

scalar axial vector i i

Ψ Ψ P

f f

P Q

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Elastic form factor of the proton in the quark-diquark picture

☞ Each diagram can be expressed in a similar way: Γµ = Λ+(Pf )Jµ(K, Q)Λ+(Pi) Photon coupling directly to a dressed-quark with the diquark acting as a bystander

Initial state and final state: Proton Two axial-vector diquark isospin states: (I, Iz) = (1, 1) → flavor content: {uu} (I, Iz) = (1, 0) → flavor content: {ud} In the isospin limit, they appear with relative weighting: (−

• 2/3) : (
• 1/3)

Therefore

J scalar

µ

=

• 1

3

• 1

3 eu I {ud}

µ

= 0

J axial

µ

=

• 2

3

• 2

3 ed I {uu}

µ

+

• 1

3

• 1

3 eu I {ud}

µ

= 0

Ψi Ψf Pf Pi Q Pf Pi Q Ψi Ψf axial − vector scalar

Hard contributions appear in the microscopic description of the elastic form factor of the proton

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Elastic form factor of the proton in the quark-diquark picture (continuation)

Remaining diagrams: Photon interacting with diquarks H.L.L. Roberts et al. Phys. Rev. C 83, 065206 (2011)

Ψi Ψf Pi Pf Q Q Ψi Ψf Pf Pi axial scalar

2 4 6 8 10 0.2 0.0 0.2 0.4 0.6 0.8 1.0 Q2 GeV2 GE,M,Q

1

, GM

1GQ 1

2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Q2 GeV2 G0Γ 1, GΠΓΡ

Composite object ↓ Electromagnetic radius is nonzero (rqq rπ) ↓ Softer contribution to the form factors Soft contributions appear in the microscopic description of the elastic form factor of the proton

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Transition form factor of γ∗N∆ in the quark-diquark picture

☞ Diagrams in which the photon interact with diquarks appear Photon coupling directly to a dressed-quark with the diquark acting as a bystander

Initial state: Proton Two axial-vector diquark isospin states: (I, Iz) = (1, 1) → flavor content: {uu} (I, Iz) = (1, 0) → flavor content: {ud} In the isospin limit, they appear with relative weighting: (−

• 2/3) : (
• 1/3)

Final state: ∆+ Same isospin states of axial-vector diquark. Different weighting due to I∆ = 3/2: (

• 1/3) : (
• 2/3)

Therefore

J 1,axial

µα

= −

• 2

3

• 1

3 ed I 1{uu}

µα

+

• 1

3

• 2

3 eu I 1{ud}

µα

= √ 2 3 I 1{qq}

µα

(K, Q)

Ψi Ψf Pf Pi Q Pf Pi Q Ψi Ψf axial − vector scalar

Soft and still hard contributions appear in the microscopic description of the γ∗N∆ electromagnetic reaction

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General observation

G p

M vs G ∗p M

☞ Similar contributions in both cases: G ∗p

M should fall asymptotically at the same rate as G p M.

☞ By isospin considerations: G ∗n

M should fall asymptotically at the same rate as G ∗p M .

☞ Hold SU(6): p|µ|∆+ ∝ n|µ|∆0 ∝ p|µ|p .

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Simple framework

Symmetry preserving Dyson-Schwinger equation treatment of a vector × vector contact interaction ☞ Gluon propagator: Contact interaction. g2Dµν(p − q) = δµν 4παIR m2

G

☞ Truncation scheme: Rainbow-ladder. Γa

ν(q, p) = (λa/2)γν

☞ Fermion propagator: Gap equation. S−1(p) = iγ · p + m + Σ(p) = iγ · p + M M ∼ 0.4 GeV = constant. Implies momentum independent Bethe-Salpeter and Faddeev amplitudes. ☞ Baryons: Faddeev equation. mN = 1.14 GeV m∆ = 1.39 GeV (masses reduced by pion-cloud effects) ☞ Ward-Green-Takahashi identities: Axial-vector and vector. Gap equation

Σ γ S Γ D

=

Bethe-Salpeter equation

= iΓ iS iΓ K iS

Faddeev equation

=

a

Ψ P pq pd Γb Γ −a pd pq

b

Ψ P

q

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Series of papers establishes strengths and limitations

Used judiciously, produces results indistinguishable from most-sophisticated Rainbow-ladder interactions Spectrum of hadrons with strangeness Chen Chen, L. Chang, C.D. Roberts, Shaolong Wang and D.J. Wilson Few Body Syst. 53 293-326 (2012). arXiv:1204.2553 [nucl-th] Nucleon and Roper electromagnetic elastic and transition form factors D.J. Wilson, I.C. Clo¨ et, L. Chang and C.D. Roberts

• Phys. Rev. C 85, 025205 (2012). arXiv:1112.2212 [nucl-th]

π- and ρ-mesons, and their diquark partners, from a contact interaction H.L.L. Roberts, A. Bashir, L.X. Gutierrez-Guerrero, C.D. Roberts and D.J. Wilson

• Phys. Rev. C 83, 065206 (2011). arXiv:1102.4376 [nucl-th]

Masses of ground and excited-state hadrons H.L.L. Roberts, L. Chang, I.C. Clo¨ et and C.D. Roberts Few Body Syst. 51, 1-25 (2011). arXiv:1101.4244 [nucl-th] Abelian anomaly and neutral pion production H.L.L. Roberts, C.D. Roberts, A. Bashir, L.X. Gutierrez-Guerrero and P.C. Tandy

• Phys. Rev. C 82, 065202 (2010). arXiv:1009.0067 [nucl-th]

Pion form factor from a contact interaction L.X. Gutierrez-Guerrero, A. Bashir, I.C. Clo¨ et and C.D. Roberts

• Phys. Rev. C 81, 065202 (2010). arXiv:1002.1968 [nucl-th]

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 29/37

Magnetic dipole form factor

Weakness of contact-interaction ☞ Truncation which produces Faddeev amplitudes that are independent of relative momentum: Underestimates the quark orbital angular momentum content of the bound-state. Suppresses the two-loop diagrams. ind.-p DSE kernels dep.-p DSE kernels axial-diquark(∆)-axial-diquark(p) 0.85 0.96 axial-diquark(∆)-scalar-diquark(p) 0.18 1.27 Two sets of results

1

Original result.

2

Improved version:

Rescale the axial(∆)-scalar(p) diagram 1 + gas/aa 1 + Q2/m2

ρ

axial(∆)-scalar(p) = axial(∆)-axial(p) Incorporate dressed quark-anomalous magnetic moment ☞ Consequence of the DCSB.

Coupled-channel prediction of the dressed quark core contribution

• 1

2 3 1 2 3 xQ 2m Ρ

2

GM

• Jorge Segovia et al., jsegovia@anl.gov

Insights into the electromagnetic γ∗N → ∆ transition 30/37

Q2-behaviour of G ∗p

M,J−S G ∗p

M cf. Experimental data and dynamical models

Both computed curves are consistent with data for Q2 2m2

ρ.

They are in marked disagreement at infrared momenta. Similarity between our improved version and dressed-quark-core result determined by EBAC. The discrepancy results from the omission of meson-cloud effects.

• 1

2 3 1 2 3 xQ 2m Ρ

2

GM

• Transition cf. elastic magnetic form factors

The fall-off rate of G ∗

M(Q2) in the γ∗p → ∆+

transition must much that of GM(Q2). With isospin symmetry, p|µ|∆+ = − n|µ|∆0 is valid, so same is true of the γnn → ∆0 magnetic form factor. These are statements about the dressed quark core contributions → Outside the domain of meson-cloud effects, Q2 2 GeV2

• 2

4 6 8 10 0.8 0.9 1.0 1.1 xQ 2m Ρ

2

Μn ΜN

GM NGM n Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 31/37

Q2-behaviour of G ∗p

M,Ash ☞ Presentations of experimental data typically use the Ash convention. G ∗

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

Many have viewed this as a conundrum. There is no sound reason to expect: G ∗

M,Ash/G n M ∼ constant

Instead, the Jones-Scadron form factor should exhibit: G ∗

M,J−S/G n M ∼ constant

• 2

4 6 8 10 1 2 3 xQ 2m Ρ

2

GM,Ash

• GD

Two main reasons Meson-cloud effects ↓ Provide more than 30% for Q2 2m2

ρ

↓ These contributions are very soft ↓ They disappear rapidly G ∗

M,Ash vs G ∗p M,J−S

G ∗

M,Ash = G ∗ M,J−S

• 1 +

Q2 (m∆ + mN)2 − 1

2

↓ A factor 1/Q of difference ↓ Provides material damping for Q2 4m2

ρ

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 32/37

Electric and coulomb quadrupoles

REM and RSM Deformation of the hadrons involved. The influence of the deformation on the structure of the transition current. ☞ RSM In good agreement with the experimental data. We describe the rapid fall at large Q2 ☞ REM is a particularly sensitive measure

• f orbital angular momentum correlations.

The true amount of which is predicted poorly by the contact interaction. Dot-dashed: Same DSE truncation but with a QCD motivated momentum-dependent interaction. Zero crossing in the electric transition form factor.

• 0.0

0.5 1.0 1.5 2.0 4 8 12 xQ 2m Ρ

2

RSM

• 0.0

0.5 1.0 1.5 2.0 2 4 6 8 xQ 2m Ρ

2

REM

Even a contact interaction produces correlations between dressed-quarks within Faddeev wave-functions and related features in the current that are comparable in size with those observed empirically

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 33/37

Zero crossing in the transition electric form factor

Contact interaction predicts zero crossing for the electric form factors of the hadrons involved ☞ The existence of a zero is independent of the interaction ☞ The location of the zero depends on the interaction.

• 1

2 0.2 0.2 0.4 0.6 0.8 1.0 xQ 2m

2

GE

• 2

4 6 8 10 0.2 0.4 0.6 0.8 1 Q2 GeV2 ΜpGEpGMp Experimental data and dynamical models do not rule out the possibility of a zero crossing in the transition electric form factor. Vladimir Pascalutsa Phys. Rep. 437, 125 (2007).

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 34/37

Large Q2-behaviour of the quadrupole ratios

Helicity conservation arguments in pQCD should apply equally to an internally-consistent symmetry-preserving treatment of a contact interaction REM

Q2→∞

= 1, RSM

Q2→∞

= constant 20 40 60 80 100 0.5 0.0 0.5 1.0 xQ 2m Ρ

2

RSM,REM Take in mind that the asymptotic power-law dependence of our computed form factors is harder that in QCD. Observations: Truly asymptotic Q2 is required before predictions are realized. G ∗

E (Q2) posses a zero at an empirical accessible momentum and thereafter

REM → 1. RSM → constant. The curve we display contains the ln2Q2-growth expected in QCD but it is not a prominent feature.

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 35/37

Summary

We have explained what many still consider to be a conundrum by the judicious interpretation of the results produced by an internally-consistent nonperturbative quantum-field-theoretical treatment of the γ∗N → ∆ transition. Jones-Scadron G ∗p

M :

☞ G ∗p

M fall asymptotically at the same rate as G p M.

☞ Compatible with isospin symmetry and pQCD predictions. ☞ Data do not fall unexpectedly rapid once the kinematic relation between Jones-Scadron and Ash form factors is properly account for. G ∗p

E

☞ The presence of strong diquark correlations within baryons predicts zero crossings for the electric form factors of the baryons involve in the γ∗N → ∆ transition. ☞ This implies that there should be a zero in the transition electric form factor. ☞ Experimental data and dynamical models do not rule out this possibility for the transition electric form factor. REM and RSM: ☞ Contact interaction produces correlations between dressed-quarks within Faddeev wave functions and related features in the current that are comparable in size with those observed empirically. ☞ Limits of pQCD, REM → 1 and RSM → constant, are apparent in our calculation but truly asymptotic Q2 is required before the predictions are realized.

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 36/37

Outlook

This talk is based on a work submitted to Physical Review C ☞ Complete a detailed article, including ∆-baryon elastic form factors. ☞ Verify claims using a more sophisticated interaction. ☞ Compute transition form factors for N → N(1535)S11(parity-partner). ☞ All these projects are essential in paving the way for JLab to chart the infrared behaviour of the strong interaction.

Jorge Segovia et al., jsegovia@anl.gov Insights into the electromagnetic γ∗N → ∆ transition 37/37