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)
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 2/25
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
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 3/25
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.
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 4/25
Theory tool: Dyson-Schwinger equations
The quantum equations of motion whose solutions are the Schwinger functions
☞ Continuum Quantum Field Theoretical Approach:
Generating tool for perturbation theory → No model-dependence.
Also nonperturbative tool → Any model-dependence should be incorporated here.
☞ Poincare covariant formulation.
☞ All momentum scales and valid from light to heavy quarks.
☞ EM gauge invariance, chiral symmetry, massless pion in chiral limit...
No constant quark mass unless NJL contact interaction.
No crossed-ladder unless consistent quark-gluon vertex.
Cannot add e.g. an explicit confinement potential.
⇒ modelling only withinthese constraints!
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 5/25
The bound-state problem in quantum field theory
Extraction of hadron properties from poles in qq, qqq, qqqq... scattering matrices
Use scattering equation (inhomogeneous BSE) toobtain T in the first place: T = K + KG0T
Homogeneous BSE forBS amplitude:
☞ Baryons. A 3-body bound state problem in quantum field theory:
Faddeev equation in rainbow-ladder truncation
Faddeev equation: Sums all possible quantum field theoretical exchanges andinteractions that can take place between the three dressed-quarks that define itsvalence quark content.
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 6/25
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
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 7/25
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
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 8/25
The γ∗N → Nucleon reaction
Work in collaboration with:
• Craig D. Roberts (Argonne)
• Ian C. Cloet (Argonne)
• Sebastian M. Schmidt (Julich)
Based on:
Phys. Lett. B750 (2015) 100-106 [arXiv: 1506.05112 [nucl-th]]
Few-Body Syst. 55 (2014) 1185-1222 [arXiv: 1408.2919 [nucl-th]]
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 9/25
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
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 10/25
Unit-normalized ratio of Sachs electric and magnetic form factors
Both CI and QCD-kindred frameworks predict a zero crossing in µpGpE/G
pM
ææææææ
æ
ææ
ææ
æ
æ
àà
à
ààààà
à à
÷÷
÷
ì
ì
ì
0 1 2 3 4 5 6 7 8 9 10
0.0
0.5
1.0
Q2@GeV
2D
ΜpG
Ep�G
Mp
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
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 11/25
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]) Flavour decomposition of EM transition FFs of nucleon resonances 12/25
A world with scalar and axial-vector diquarks (I)
The singly-represented d-quark in the proton isnot always (but often) sequestered inside a softscalar diquark correlation.
☞ Observation:
P scalar ∼ 0.62, Paxial ∼ 0.38
Contributions coming from u-quark
Ψi
Ψi
Ψf
ΨfPf Pi
PiPf
Q
Q
Contributions coming from d-quark
Ψi
Ψi
Ψf
ΨfPf Pi
PiPf
Q
Q
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 13/25
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.
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 14/25
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
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 15/25
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
ææ
ææ
æ
æ
àà
à
ààààà
à à
÷÷
÷
ì
ì
ì
0 1 2 3 4 5 6 7 8 9 10
0.0
0.5
1.0
Q2@GeV
2D
ΜpG
Ep�G
Mp
☞ Observations:
Axial-vector diquark contribution is not enough in order to explain the proton’selectromagnetic ratios.
Scalar diquark contribution is dominant and responsible of the Q2-behaviour ofthe the proton’s electromagnetic ratios.
Higher quark-diquark orbital angular momentum components of the nucleon arecritical in explaining the data.
The presence of higher orbital angular momentum components in the nucleon is aninescapable consequence of solving a realistic Poincare-covariant Faddeev equation
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 16/25
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]]
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 17/25
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]) Flavour decomposition of EM transition FFs of nucleon resonances 18/25
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]) Flavour decomposition of EM transition FFs of nucleon resonances 19/25
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.
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 20/25
Transition form factors (II)
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*
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
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 21/25
The γvp → R+ Dirac transition form factor
Diquark dissection
ææ
ææ
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*
Scatterer dissection
ææ
ææ
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.
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 22/25
The γvp → R+ Pauli transition form factor
Diquark 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*
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.
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 23/25
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*
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 24/25
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.
Jorge Segovia ([email protected]) Flavour decomposition of EM transition FFs of nucleon resonances 25/25