Strong diquark correlations inside the protonpuccini1.fis.usal.es/web-prints/2015SpanishHadron_Diquarks.pdf · Jorge Segovia Instituto ... the Sachs form factors scale as: Gp

Strong diquark correlations inside the proton

Jorge Segovia

Instituto Universitario de Fısica Fundamental y Matematicas

Universidad de Salamanca, Spain

1st Hadron Spanish Network days and Spanish-Japanese JSPS Workshop

Valencia, Valencian Community (Spain)

June 15-17, 2015

In collaboration with Ian C. Cloet and Craig D. Roberts (ANL).

Jorge Segovia ([email protected]) Strong diquark correlations inside the proton 1/26

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)

☞ Obtained by any two sensitive 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.

ææ

æ

æ

ææ æ

æ æà

à

à

à

ìì

ì

ììììì

ì ì

ò

ò

ò

ô

ô

ô

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.

æææææææææææææ

ææææ

æ

ææ

æ

æ

à

à

à

à à

à

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)

Hadron physics is dominated by non-perturbative QCD dynamics

Explain how quarks and gluons bind together to form hadrons.

Origin of the 98% of the mass of the proton ⇒ visible universe.

☞ Given QCD’s complexity:

The best promise for progress is a strong interplay between experiment and theory.

Non-perturbative phenomena

ւ ց

Quark and gluon confinement Dynamical chiral symmetry breaking

↓ ↓

Colored particleshave never been seen

isolated

Hadrons do notfollow the chiralsymmetry pattern

Neither of these phenomena is apparent in QCD’s Lagrangian

however!

They play a dominant role determining characteristics of real-world QCD


Non-perturbative QCD:Confinement and dynamical chiral symmetry breaking (II)

From a quantum field theoretical point of view: Emergent

phenomena are associated with dramatic, dynamically

driven changes in the analytic structure of QCD’s

propagators and vertices.

☞ Dressed-gluon propagator in Landau gauge:

i∆µν = −iPµν∆(q2), Pµν = gµν − qµqν/q2

An inflexion point at p2 > 0.

Breaks the axiom of reflexion positivity.

No physical observable related with.

☞ 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 i.e. the 98% of the mass of the protonand the 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


Theory tool: Dyson-Schwinger equations

Confinement and dynamical chiral symmetry breaking can be identified with propertiesof QCD’s propagators and vertices (QCD’s Schwinger functions)

Dyson-Schwinger equations (DSEs)

☞ Definition: The quantum equations of motion (of QCD)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.

☞ Nice consequences:

Allows the study of the quark-quark interaction in the whole range of momenta.

→ Analysis of the infrared behaviour is crucial to disentangle confinement anddynamical chiral symmetry breaking.

Connects quark-quark interaction with experimental observables.

→ e.g. It is via the Q2-evolution of the form factors that one gains access to therunning of QCD’s coupling and masses from the infrared into the ultraviolet.


The bound-state problem in quantum field theory

Hadrons are studied via Poincare covariant bound-state equations

☞ Mesons

A 2-body bound state problem in quantumfield theory.

Properties emerge from solutions of theBethe-Salpeter equation:

Γ(k;P) =

∫

d4q

(2π)4K(q, k;P)S(q+P) Γ(q;P) S(q)

The kernel is intimately related with that ofthe gap equation.

=

iΓ

iS

iΓ

K

iS

☞ Baryons

A 3-body bound state problem in quantumfield theory.

Properties emerge from solutions of theFaddeev equation.

The Faddeev equation sums all possiblequantum field theoretical exchanges andinteractions that can take place betweenthe three valence quarks.

=aΨ

P

pq

pd Γb

Γ−a

pd

pq

bΨP

q


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


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


Quark-quark contact-interaction framework

☞ Gluon propagator: Contact interaction.

g2Dµν(p − q) = δµν4παIR

m2G

☞ Truncation scheme: Rainbow-ladder.

Γaν(q, p) = (λa/2)γν

☞ Quark propagator: Gap equation.

S−1(p) = iγ · p +m+ Σ(p)

= iγ · p +M

Implies momentum independent constituent quarkmass (M ∼ 0.4GeV).

☞ Hadrons: Bound-state amplitudes independentof internal momenta.

☞ Form Factors: Two-loop diagrams notincorporated.

Exchange diagram

It is zero because our treatment of thecontact interaction model

i

iΨ ΨPPf

f

Q

Γ−

Γ

Seagull diagrams

They are zero

µ

i

i

X

Ψ ΨPf

f

Q

P Γ−

µi

i

X−

Ψ ΨPf

f

P

Q

Γ


Series of papers establishes its strengths and limitations

CI framework has judiciously been applied to a large body of hadron phenomena.Produces results in qualitative agreement with those obtained using

most-sophisticated interactions.

1 Features and flaws of a contact interaction treatment of the kaonC. Chen, L. Chang, C.D. Roberts, S.M. Schmidt S. Wan and D.J. WilsonPhys. Rev. C 87 045207 (2013). arXiv:1212.2212 [nucl-th]

2 Spectrum of hadrons with strangenessC. Chen, L. Chang, C.D. Roberts, S. Wan and D.J. WilsonFew Body Syst. 53 293-326 (2012). arXiv:1204.2553 [nucl-th]

3 Nucleon and Roper electromagnetic elastic and transition form factorsD.J. Wilson, I.C. Cloet, L. Chang and C.D. RobertsPhys. Rev. C 85, 025205 (2012). arXiv:1112.2212 [nucl-th]

4 π- and ρ-mesons, and their diquark partners, from a contact interactionH.L.L. Roberts, A. Bashir, L.X. Gutierrez-Guerrero, C.D. Roberts and D.J. WilsonPhys. Rev. C 83, 065206 (2011). arXiv:1102.4376 [nucl-th]

5 Masses of ground and excited-state hadronsH.L.L. Roberts, L. Chang, I.C. Cloet and C.D. RobertsFew Body Syst. 51, 1-25 (2011). arXiv:1101.4244 [nucl-th]

6 Abelian anomaly and neutral pion productionH.L.L. Roberts, C.D. Roberts, A. Bashir, L.X. Gutierrez-Guerrero and P.C. TandyPhys. Rev. C 82, 065202 (2010). arXiv:1009.0067 [nucl-th]


Weakness of the contact-interaction framework

A truncation which produces Faddeev amplitudes that are independent of relativemomentum:

Underestimates the quark orbital angular momentum content of the bound-state.

Eliminates two-loop diagram contributions in the EM currents.

Produces hard form factors.

Momentum dependence in the gluon propagator

↓

QCD-based framework

↓

Contrasting the results obtained for the same observablesone can expose those quantities which are most sensitiveto the momentum dependence of elementary quantities

in QCD.


Quark-quark QCD-based interaction framework

☞ Gluon propagator: 1/k2-behaviour.

☞ Truncation scheme: Rainbow-ladder.

Γaν(q, p) = (λa/2)γν

☞ Quark propagator: Gap equation.

S−1(p) = Z2(iγ · p +mbm) + Σ(p)

=[

1/Z(p2)] [

iγ · p +M(p2)]

Implies momentum dependent constituent quarkmass (M(p2 = 0) ∼ 0.33GeV).

☞ Hadrons: Bound-state amplitudes dependent ofinternal momenta.

☞ Form Factors: Two-loop diagramsincorporated.

Exchange diagram

Play an important role

i

iΨ ΨPPf

f

Q

Γ−

Γ

Seagull diagrams

They are less important

µ

i

i

X

Ψ ΨPf

f

Q

P Γ−

µi

i

X−

Ψ ΨPf

f

P

Q

ΓJorge Segovia ([email protected]) Strong diquark correlations inside the proton 16/26

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-normalised ratio of Sachs electric and magnetic form factors (I)

Both CI and QCD-kindred frameworks predict a zero crossing in µpGpE/G

pM

ææ

æ

æ

ææ æ

æ æà

à

à

à

ìì

ì

ììììì

ì ì

ò

ò

ò

ô

ô

ô

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

æ

æ

æ

à

à

à

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


Unit-normalised ratio of Sachs electric and magnetic form factors (II)

Our model is characterized by a particular rate of transition between theperturbative and nonperturbative domains.

If we change this rate in order to get faster the parton like quarks we movefurther the zero in the ratio of the proton but an opposite effect is found in theneutron case.

0

0.1

0.2

0.3

0.4

M(p)

(GeV)

0 1 2 3 4

p (GeV)

α = 2.0

α = 1.8

α = 1.4

α = 1.0

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

Q2@GeV2

D

ΜN

GEN�G

MN


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 ∼ 0.7, Paxial ∼ 0.3

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

ààààààààààà à à

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

æ

æææææææææ

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=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)

æææææææ

ææ

ææ

æ

æ

ààààààààààà à à

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

æææææææææææ

ææ

àààààààààà à à

à

0 1 2 3 4 5 6 7 8

0.0

0.2

0.4

0.6

0.8

1.0

x=Q 2�MN

2

HΚ

pdL-

1x

2F

2p

d,HΚ

puL-

1x

2F

2p

u

☞ Observations:

The presence of scalar diquark correlations is sufficient to explain the key featureof the flavour-separated form factors.

If only axial-vector diquarks are present inside the proton, the behaviour of theflavour-separated form factors is not reproduced.

A combination of scalar and axial-vector diquarks with being dominant the scalarone produces agreement with the empirically verified behaviour of theflavour-separated form factors.


Comparison between worlds (II)

The reduction of the ratios Fd1/F

u1 and Fd

2/Fu2 at high Q2 has the immediate

consequence that Fp2/F

p1 has its observed shape

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=Q 2�MN

2

xF

2p�F

1p


Summary and conclusions

☞ Experiments are sensitive to the momentum dependence of the running couplingsand masses in QCD.

☞ A close collaboration between experiment and theory can effectively constrain theevolution of the quark-quark interaction.

☞ New experiments using upgraded facilities will leave behind meson-cloud effects andwill gain access to the region of transition between the non-perturbative andperturbative regimes of QCD.

☞ The possible existence and location of a zero in GpE (Q

2)/GpM (Q2) are a fairly direct

measure of i.e. the nature and shape of the quark-quark interaction, the width of thetransition region.

☞ 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.


Documents

Strong diquark correlations inside the protonpuccini1.fis.usal.es/web-prints/2015SpanishHadron_Diquarks.pdf · Jorge Segovia Instituto ... the Sachs form factors scale as: Gp