[-0.2] Baryon form factors in perturbative chiral quark ... · Sea-quark contributions Other...

Baryon form factors in perturbative chiral

quark model

Xuyang Liu1,2, K. Khosonthongkee2, A. Limphirat2, Y. Yan2

1. School of Mathematics and Physics, Bohai University2. School of Physics, Suranaree University of Technology

Xuyang Liu APFB 2017 August 25-30, 2017 1 / 20

http://indico.ihep.ac.cn/event/6581/

http://210.47.176.3/page/depart/slxy/index.asp

http://www.bhu.edu.cn/page/index.asp

http://physics3.sut.ac.th

http://www.sut.ac.th

OUTLINE

Perturbative chiral quark model

EM and axial form factors

Sea-quark contributions

Neutron charge form factor

Summary & Outlook


Perturbative chiral quark model

Perturbative chiral quark model (PCQM)

Linv(x) = ψ̄(x)[i∂/− γ0V (r)]ψ(x)︸︷︷︸Lq

+F 2

4Tr[∂µU∂

µU†]

︸︷︷︸LΦ

−ψ̄(x)S(r)

[U + U†

2+ γ5U − U†

2

]ψ(x)︸︷︷︸

Lint

Model potential

V (r) : vector potential, S(r) : scalar potential.

Model parameter

F = 88 MeV.

In SU(3) flavor symmetry

q− field : ψ(x) =

u(x)d(x)s(x)

, χ− field : U = exp

[iΦ̂

F

]' 1 + i

Φ̂

F+ o

(Φ̂

F

),

meson field : Φ̂ =

8∑i=1

Φiλi =

π0 + 1√3η

√2π+

√2K+

√2π− −π0 + 1√

3η√

2K0

√2K−

√2K̄0 − 2√

3η

.


Perturbative chiral quark model PCQM

Chiral symmetry

Linv(x) is invariant under the transformation

ψL → ULψL

ψR → URψR

U → URUU†L

where

ψL/R =1

2(1∓ γ5)ψ

UL = exp(− i

8∑a=1

ΘLa

λa2

)UR = exp

(− i

8∑a=1

ΘRa

λa2

)Xuyang Liu APFB 2017 August 25-30, 2017 4 / 20

Perturbative chiral quark model Previous works

Previous WorksPRC64 065203(2001); PRD63 054026(2001); PLB520 204(2001); PRC65 025202(2002); PRC66 055204(2002);PRC68 015205(2003); EPJA20 317(2004); JPG30 793(2004); JPG35 025005(2008).

V (r) and S(r) assumed being the harmonicoscillator interaction, and hence the valance quarkwave functions are in the Gaussian form.

Previous works includesElectromagnetic properties of baryonsLow-energy meson-baryon scatteringStrange nucleon form factorsElectromagnetic excitation of nucleon resonancesAxial form factor of the nucleon· · · · · ·


Perturbative chiral quark model Feymann diagrams

Feymann Diagrams

Diagrams contributing to EM form factor

Diagrams contributing to axial form factor


EM and axial form factors Quark Wavefunction

Quark WavefunctionX. Y. Liu et al, J. Phys. G: Nucl. Part. Phys. 41 (2014) 055008.

Quark WF will be determined by fitting theoretical results of pcharge form factor to the experimental data.

The radial parts g(r) and f(r) are expanded in Sturmian basis

g(r) =∑n

AnSn0(r)

r,

f(r) =∑n

BnSn0(r),

where Sturmian functions

Snl =

[n!

(n+ 2l + 1)!

]1/2

(2br)l+1e−brL2l+1n (2br),

An, Bn, and b are free expansion parameters.Xuyang Liu APFB 2017 August 25-30, 2017 7 / 20

EM and axial form factors EM form factors

Electromagnetic form factorsX. Y. Liu et al, J. Phys. G: Nucl. Part. Phys. 41 (2014) 055008.

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EM and axial form factors Axial form factors

Axial form factorsX. Y. Liu et al, Phys. Rev. D 91 (2015) 034022.

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Sea-quark contributions Magnetic moments

π, K and η mesons contribute to the µB

Meson loopsπ K η

µp 0.281 0.002 −0.006

µn −0.339 0.018 0.004

µΣ+ 0.032 0.055 −0.008

µΣ0 −0.039 −0.062 −0.004

µΣ− −0.109 0.068 0

µΛ 0 −0.052 0.004

µΞ0 −0.008 −0.055 0.012

µΞ− −0.027 −0.058 0.010

Meson cloud contributing to EM form factors is about 10%.

π-meson dominates nucleon magnetic moments.

K-meson contributions to hyperons are in the same oder.

η-meson contributions are negligible.


Sea-quark contributions Axial charge

π, K and η mesons contribute to the gBA

Meson loopsπ K η

gNA 0.375 0.045 −0.002gΣA 0.118 0.104 −0.002gΞA −0.030 −0.077 −0.001

Meson cloud contributing to axial form factor is about 30%

π-meson dominates nucleon axial charges.

K-meson contributions to hyperons axial charges are in thesame order as the π ones.

η-meson contributions are negligible.


Sea-quark contributions EM and axial form factors

EM and axial form factorsX. Y. Liu et al, SciRep. 7, 8139 (2017)

��

��

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

Q2(GeV2)

GMp(Q2)

��

��

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Q2(GeV2)

GΑΝ(Q2)

Leading order (solid) and loop (dashed) contributions to the protonmagnetic (left panel) form factor and neutron axial (right panel)form factor.


Sea-quark contributions EM and axial form factors

Meson cloud distributions

��

��

0.0 0.5 1.0 1.5 2.00.000

0.005

0.010

0.015

0.020

0.025

0.030

r [fm]

rρMp(r)

��

��

0.0 0.5 1.0 1.5 2.00.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

r [fm]rρAN(r)

Comparisons between the LO and meson cloud distributions forproton magnetic (left panel) and axial (right panel) form factors inr-space.


Sea-quark contributions Other results

Other results of meson cloud distributions

Shown as the dashed lines are the densities of nucleon chargecontributed by the pion cloud, taken from EPJA 17, 607 (2003).Left panel: r2ρ(r) for the electric form factor of the proton. Rightpanel: r2ρ(r) for the electric form factor of the neutron.


Sea-quark contributions Other results

Other results of meson cloud distributions

The densities of charge and magnetization from the pion cloudtaken from PLB 586, 291 (2004). Left panel: 4πr2ρ(r) for theisovector Pauli (upper band) and Dirac (lower band) form factors.Right panel: 4πr2ρ(r) for the isovector magnetic (upper band) andelectric (lower band) Sachs form factors.


Neutron charge form factor Wave functions of the valence quarks

Ground state wave functions of valence quarksX. Y. Liu et al, J. Phys. G: Nucl. Part. Phys. 41 (2014) 055008.

gHrLfHrL

0 2 4 6 8 10 12 140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

r @GeV-1D

gHrL

and

fHrL

Normalized radial wave function of the valence quarks for the uppercomponent g(r) and the lower component f(r), which aredetermined by fitting the theoretical results of the proton chargeform factor to the experimental data.


Neutron charge form factor Extracted PCQM potentials

Extracted PCQM potentialsX. Y. Liu et al, submitted to PRC

0 5 10 15

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

r [GeV-1 ]

Σ(r)[GeV

]

Σ(�)=�(�)+�(�)

0 5 10 15

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

r [GeV-1 ]Δ(r)[GeV

]

Δ(�)=�(�)-�(�)

The extracted PCQM potentials based on the predetermined groundstate quark wavefunction. Left panel: Σ(r) potential, right panel:∆(r) potential.


Neutron charge form factor Diagrams contributing to neutron charge form factor

Diagrams contributing to neutron charge form factor

(a) (b)

(c) (d)

Diagrams contributing to the charge form factor of neutron: mesoncloud (a), vertex correction (b), self-energy I (c) and II (d).


Neutron charge form factor Neutron charge form factor in PCQM

Neutron charge form factor

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GEn(Q2)

▽ Glazier et al., 2005△ Warren et al., 2004◇ Madey et al., 2003○ Bermuth et al., 2003□ Golak et al., 2001▼ Passchier et al., 1999▲ Ostrick et al., 1999◆ Herberg et al., 1999● Bruins et al., 1995■ Eden et al., 1994

The PCQM results on neutron charge form factor GnE(Q2) including

both the ground (1s1/2) and excited quark states (1p1/2, 1p3/2,1d3/2, 1d5/2, 1f5/2, 1f7/2, 2s1/2, 2p1/2, 2p3/2 and 3s1/2) in quarkpropagators.


Neutron charge form factor Summary

Summary

Valence quark wave functions determined by fitting the PCQM result ofproton charge form factor dictate a Conrnell-like quark-quark potential.

Sea-quark contribution to EM form factors is about 10%.

Sea-quark contribution to axial form factors is about 30%.

Axial meson cloud is smaller than the EM one.

Axial meson cloud is smaller than the axial quark core.

Contributions of quark excited states in quark propagators areconsiderable to the charge form factor of neutron.

OutlookThe PCQM result of the neutron charge form factor is still much smallerthan the experimental values. The center-of-mass correction is beingconsidered.


[-0.2] Baryon form factors in perturbative chiral quark ... · Sea-quark contributions Other...

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