[-0.2] baryon form factors in perturbative chiral quark ... · sea-quark contributions other...
TRANSCRIPT
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
OUTLINE
Perturbative chiral quark model
EM and axial form factors
Sea-quark contributions
Neutron charge form factor
Summary & Outlook
Xuyang Liu APFB 2017 August 25-30, 2017 2 / 20
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
.
Xuyang Liu APFB 2017 August 25-30, 2017 3 / 20
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· · · · · ·
Xuyang Liu APFB 2017 August 25-30, 2017 5 / 20
Perturbative chiral quark model Feymann diagrams
Feymann Diagrams
Diagrams contributing to EM form factor
Diagrams contributing to axial form factor
Xuyang Liu APFB 2017 August 25-30, 2017 6 / 20
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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Xuyang Liu APFB 2017 August 25-30, 2017 8 / 20
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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Xuyang Liu APFB 2017 August 25-30, 2017 9 / 20
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.
Xuyang Liu APFB 2017 August 25-30, 2017 10 / 20
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.
Xuyang Liu APFB 2017 August 25-30, 2017 11 / 20
Sea-quark contributions EM and axial form factors
EM and axial form factorsX. Y. Liu et al, SciRep. 7, 8139 (2017)
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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)
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����
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.
Xuyang Liu APFB 2017 August 25-30, 2017 12 / 20
Sea-quark contributions EM and axial form factors
Meson cloud distributions
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����
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)
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����
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.
Xuyang Liu APFB 2017 August 25-30, 2017 13 / 20
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.
Xuyang Liu APFB 2017 August 25-30, 2017 14 / 20
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.
Xuyang Liu APFB 2017 August 25-30, 2017 15 / 20
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.
Xuyang Liu APFB 2017 August 25-30, 2017 16 / 20
Neutron charge form factor Extracted PCQM potentials
Extracted PCQM potentialsX. Y. Liu et al, submitted to PRC
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-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.
Xuyang Liu APFB 2017 August 25-30, 2017 17 / 20
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).
Xuyang Liu APFB 2017 August 25-30, 2017 18 / 20
Neutron charge form factor Neutron charge form factor in PCQM
Neutron charge form factor
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Q2 [GeV2]
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.
Xuyang Liu APFB 2017 August 25-30, 2017 19 / 20
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.
Xuyang Liu APFB 2017 August 25-30, 2017 20 / 20