Understanding the Nucleon as a Borromean Bound-Stateeinrichtungen.ph.tum.de/T30f/Talks/Baryons2016_Jorge_Segovia.pdf · Understanding the Nucleon as a Borromean Bound-State Jorge

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.


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.


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.


Phenomenological aspects (III)


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


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 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.


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

Positive parity state

ւ ց

pseudoscalar and vector diquarks scalar and axial-vector diquarks

↓ ↓

Ignoredwrong parity

larger mass-scales

Dominantright parity

shorter mass-scales


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+


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.


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.


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.


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


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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Q 2@GeV2

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Ep�G

Mp

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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


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


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...


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)

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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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0.0

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.


Comparison between worlds (I)

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2.00 1 2 3 4 5 6 7

x2F

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0.6

0.8

1.00 1 2 3 4 5 6 7

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2F

2u

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0.0

0.2

0.4

0.6

0.8

1.0

x=Q 2�MN

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x2F

1d

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0.0

0.2

0.4

0.6

0.8

1.0

x=Q 2�MN

2

Κd-

1x

2F

2d


Comparison between worlds (II)

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2.0

3.0

4.0

x=Q 2�MN

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1p

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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


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.


Documents

Understanding the Nucleon as a Borromean Bound-Stateeinrichtungen.ph.tum.de/T30f/Talks/Baryons2016_Jorge_Segovia.pdf · Understanding the Nucleon as a Borromean Bound-State Jorge