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Understanding the Nucleon as a Borromean Bound-State
Jorge Segovia
Technische Universitat Munchen
Physik-Department T30f
T30fTheoretische Teilchen- und Kernphysik
Baryons 2016
Florida State University - Alumni Center
16-20 May 2016
Main collaborators (in this research line):
Craig D. Roberts (Argonne), Ian C. Cloet (Argonne), Sebastian M. Schmidt (Julich)
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 1/25
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.
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 2/25
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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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]) Understanding the Nucleon as a Borromean Bound-State 3/25
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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0 1 2 3 4 5 6 7 8 90.0
1.0
2.0
3.0
4.0
Q 2@GeV2
D
Q2
F2p�F
1p
Curve: ln2(Q2/Λ2) for Λ = 0.3GeV which is normalized to the data at 2.5GeV2.→ Λ is a soft scale parameter related to the size of the nucleon.
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 4/25
Phenomenological aspects (III)
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 5/25
Our goal
In view of these facts it is of significant interest to look for the (non-perturbative)
origin of the observed Q2-dependence of the Dirac and Pauli form factors
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 6/25
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]) Understanding the Nucleon as a Borromean Bound-State 7/25
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 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.
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 8/25
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]) Understanding the Nucleon as a Borromean Bound-State 9/25
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]) Understanding the Nucleon as a Borromean Bound-State 10/25
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
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]) Understanding the Nucleon as a Borromean Bound-State 11/25
Diquark properties
Meson BSE Diquark BSE
☞ Owing to properties of charge-conjugation, a diquark with spin-parity JP may beviewed as a partner to the analogous J−P meson:
Γqq(p;P) = −
∫
d4q
(2π)4g2Dµν(p − q)
λa
2γµ S(q + P)Γqq (q;P)S(q)
λa
2γν
Γqq(p;P)C† = −1
2
∫
d4q
(2π)4g2Dµν(p − q)
λa
2γµ S(q + P)Γqq (q;P)C†S(q)
λa
2γν
☞ Whilst no pole-mass exists, the following mass-scales express the strength andrange of the correlation:
m[ud ]0+
= 0.7−0.8GeV, m{uu}1+
= 0.9−1.1GeV, m{dd}1+
= m{ud}1+
= m{uu}1+
☞ Diquark correlations are soft, they possess an electromagnetic size:
r[ud ]0+& rπ , r{uu}1+
& rρ, r{uu}1+> r[ud ]0+
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 12/25
Remark about the 3-gluon vertex
☞ A Y-junction flux-tube picture of nucleon structure isproduced in quenched lattice QCD simulations that usestatic sources to represent the proton’s valence-quarks.
F. Bissey et al. PRD 76 (2007) 114512.
☞ This might be viewed as originating in the 3-gluonvertex which signals the non-Abelian character of QCD.
☞ These suggest a key role for the three-gluon vertex in nucleon structure if they wereequally valid in real-world QCD: finite quark masses and light dynamical quarks.
G.S. Bali, PRD 71 (2005) 114513.
The dominant effect of non-Abelian multi-gluon vertices is expressed in the formationof diquark correlations through Dynamical Chiral Symmetry Breaking.
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 13/25
The quark+diquark structure of the nucleon (I)
Faddeev equation in the quark-diquark picture
P
pd
pq
Ψa =
P
pq
pd
Ψb
Γa
Γb
Dominant piece in nucleon’s eight-componentPoincare-covariant Faddeev amplitude: s1(|p|, cos θ)
There is strong variation with respect to botharguments in the quark+scalar-diquark relativemomentum correlation.
Support is concentrated in the forward direction,cos θ > 0. Alignment of p and P is favoured.
Amplitude peaks at (|p| ∼ MN/6, cos θ = 1),whereat pq ∼ pd ∼ P/2 and hence the naturalrelative momentum is zero.
In the anti-parallel direction, cos θ < 0, support isconcentrated at |p| = 0, i.e. pq ∼ P/3, pd ∼ 2P/3.
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 14/25
The quark+diquark structure of the nucleon (II)
☞ A nucleon (and kindred baryons) can be viewedas a Borromean bound-state, the binding withinwhich has two contributions:
Formation of tight diquark correlations.
Quark exchange depicted in the shaded area.
P
pd
pq
Ψa =
P
pq
pd
Ψb
Γa
Γb
☞ The exchange ensures that diquark correlations within the nucleon are fullydynamical: no quark holds a special place.
☞ The rearrangement of the quarks guarantees that the nucleon’s wave functioncomplies with Pauli statistics.
☞ Modern diquarks are different from the old static, point-like diquarks whichfeatured in early attempts to explain the so-called missing resonance problem.
☞ The number of states in the spectrum of baryons obtained is similar to that foundin the three-constituent quark model, just as it is in today’s LQCD calculations.
☞ Modern diquarks enforce certain distinct interaction patterns for the singly- anddoubly-represented valence-quarks within the proton.
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 15/25
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]) Understanding the Nucleon as a Borromean Bound-State 16/25
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]) Understanding the Nucleon as a Borromean Bound-State 17/25
Unit-normalized ratio of Sachs electric and magnetic form factors
Both CI and QCD-kindred frameworks predict a zero crossing in µpGpE/G
pM
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0.0
0.5
1.0
Q 2@GeV2
D
ΜpG
Ep�G
Mp
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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
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 18/25
A world with only scalar diquarks (I)
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]) Understanding the Nucleon as a Borromean Bound-State 19/25
A world with only scalar diquarks (II)
The d-quark contributions to the proton form factors should be suppressedrespect the u-quark contributions
☞ Remind the experimental data...
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 20/25
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]) Understanding the Nucleon as a Borromean Bound-State 21/25
A world with scalar and axial-vector diquarks (II)
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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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0 1 2 3 4 5 6 7 8
0.0
0.2
0.4
0.6
x=Q 2�MN
2
HΚ
pdL-
1x
2F
2p
d,HΚ
puL-
1x
2F
2p
u
☞ 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]) Understanding the Nucleon as a Borromean Bound-State 22/25
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
æææææææææ
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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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æ
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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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
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 23/25
Comparison between worlds (II)
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0 1 2 3 4 5 6 7 80.0
1.0
2.0
3.0
4.0
x=Q 2�MN
2
@x
F2pD�F
1p
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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.
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]) Understanding the Nucleon as a Borromean Bound-State 24/25
Summary and conclusions
Quantum Field Theory vision of the Nucleon as a Borromean bound-state:
Poincare covariance, demands the presence of dressed-quark orbital angularmomentum in the nucleon.
The running of the strong coupling, which is expressed in e.g. the momentumdependence of the dressed-quark mass → DCSB.
Dynamical chiral symmetry breaking, and its correct implementation producespions as well as strong electromagnetically-active diquark correlations.
Proton’s electromagnetic form factors:
☞ The presence of strong diquark correlations within the nucleon is sufficient tounderstand empirical extractions of the flavour-separated form factors.
☞ The reduction of the ratios F d1 /F
u1 and F d
2 /Fu2 at high Q2 implies that F p
2 /Fp1
saturates at large momentum transfer.
☞ 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 possible existence and location of a zero in GpE/G
pM is a fairly direct measure of
the nature and shape of the quark-quark interaction.
Jorge Segovia ([email protected]) Understanding the Nucleon as a Borromean Bound-State 25/25