flavour decomposition of electromagnetic transition form...

Flavour decomposition of electromagnetic transition

form factors of nucleon resonances

Jorge Segovia

Technische Universitat Munchen

Physik-Department T30f

T30fTheoretische Teilchen- und Kernphysik

XII Quark Confinement and Hadron Spectrum

Thessaloniki (Greece)

September 2nd, 2016

Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 1/25

Studies of N∗-electrocouplings

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 ց

Unique window into theirquark and gluon structure

Broad range ofphoton virtuality Q2

↓ ↓

Distinctive information on theroles played by DCSB and

confinement in QCD

Probe the excited nucleonstructures at perturbative andnon-perturbative QCD scales

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)


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 ց

Confinement 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


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 reflexion 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 color-singlet meson is alsoattractive for 3c quark-quark correlations within a color-singlet baryon

☞ Diquark correlations:

A tractable truncation of the Faddeevequation.

In Nc = 2 QCD: diquarks can form colorsinglets with are the baryons of the theory.

In our approach: Non-pointlike color-antitripletand fully interacting. Thanks to G. Eichmann.

Diquark composition of the Nucleon and Roper

Positive parity state

ւ ց

pseudoscalar and vector diquarks scalar and axial-vector diquarks

↓ ↓

Ignoredwrong parity

larger mass-scales

Dominantright parity

shorter mass-scales


Baryon-photon vertex

One must specify how the photoncouples to the constituents within

the baryon.

⇓

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


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]]


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


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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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

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

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


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:

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


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

ææææææææææ

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

☞ 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.


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


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

ææææææ

æ

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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

☞ 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


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]]

Submitted to Phys. Rev. C (rapid communications) [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

-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


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

ææ

ææ

æ

æ

æ

ææ

æ æ

àààà

à

àà

0 1 2 3 4 5 6-0.1

-0.05

0.0

0.05

0.1

0.15

x=Q2�mN

2

F1*

ææ

æææ

æ ææ

æ ææ

à

à

àà

à

àà

òò÷÷

0 1 2 3 4 5 6

-0.6

-0.4

-0.2

0.0

0.2

0.4

x=Q2�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)

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æ

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æ æ

àààà

à

àà

0 1 2 3 4 5 6-0.1

-0.05

0.0

0.05

0.1

0.15

x=Q2�mN

2

F1*

ææ

æææ

æ ææ

æ ææ

à

à

àà

à

àà

òò÷÷

0 1 2 3 4 5 6

-0.6

-0.4

-0.2

0.0

0.2

0.4

x=Q2�mN

2

F2*

ææ

ææ

æ

æ æ

æ

ææ

æ

à

à

àà

à

àà

òò÷÷

0 1 2 3 4 5 6-80

-40

0

40

80

120

x=Q2�mN

2

A1 2N®

RH1

0-

3G

eV-

1�2L

ææææ

æ

æ

æ

æ ææ

æ

ààààà

à

à

0 1 2 3 4 5 6

0

2020

40

60

x=Q2�mN

2

S1 2N®

RH1

0-

3G

eV-

1�2L


The γvp → R+ Dirac transition form factor

Diquark dissection

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æ

æ

ææ

àààà

à

à

à

0 1 2 3 4 5 6

0.0

0.05

0.1

0.15

x=Q2�mN

2

F1,p*

Scatterer dissection

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æ

æ

æ

æ

æ

ææ

àààà

à

à

à

0 1 2 3 4 5 6

0.0

0.05

0.1

0.15

x=Q2�mN

2

F1,p*

☞ 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

ææ

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æ ææ

æ ææ

à

à

àà

à

àà

òò÷÷

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*

Scatterer dissection

ææ

æææ

æ ææ

æ ææ

à

à

àà

à

àà

òò÷÷

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*

☞ 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.


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*

0 1 2 3 4 5 6

-1.0

-0.5

0.0

0.5

1.0

x=Q2�mN

2

Κd-

1F

2,d*

,Κ

u-1F

2,u*

0.0

1.0

2.0

3.0

x2F

1,d*

,x

2F

1,u*

0 2 4 6 8 10

-3.0

-2.0

-1.0

0.0

x=Q2�mN

2

Κd-

1x

2F

2,d*

,Κ

u-1x

2F

2,u*


Epilogue

☞ Quantum Field Theory view of a baryon:

Poincare covariance demands the presence of dressed-quark orbital angularmomentum in the baryon.

Dynamical chiral symmetry breaking and its correct implementation producespions as well as strong electromagnetically-active diquark correlations.

☞ 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 → 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.


flavour decomposition of electromagnetic transition form...

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