Transversity Form Factors and Generalized Parton Distributions of the Pion in Chiral Quark Models

Broniowski, Wojciech; Dorokhov, A.E.; Arriola, E. Ruiz

doi:10.1007/s00601-011-0265-2

“…In those works, different approaches have been employed. They include the chiral quark models employing the Nambu-Jona-Lasinio model, the spectral quark model [16,28,29], the covariant constituent quark models (CCQMs) [17,18,30], the Dyson-Schwinger equation approach [19], the AdS/QCD inspired light-front wave functions [22], and some empirical parametrizations as already mentioned above. Among those phenomenological approaches, the light-cone constituent quark model (LCCQM), one of the CCQMs, is a quite suitable and successful approach to be applied for the studies of the quark-hadron vertex and of the hadron properties, as has been pointed out by Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Many endeavors have been made to study the GPDs of simple hadrons in the literature, like the studies of a pion [4,[16][17][18][19]; of a proton and neutron [10][11][12][20][21][22], and of the light nuclei, 3 He [13,23] or deuteron [8,[24][25][26][27]. In those works, different approaches have been employed.…”

Section: Introductionmentioning

confidence: 99%

ρ meson unpolarized generalized parton distributions with a light-front constituent quark model

Sun

¹

,

Dong

²

2017

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We study ρ meson unpolarized generalized parton distributions based on a light-front constituent quark model where the quark-antiquark-meson vertex is constructed under the symmetric loop momentum convention. The form factors and some other low-energy observables of the ρ meson are calculated. Moreover, the contributions to the form factors and generalized parton distributions from the valence and nonvalence regimes are discussed and analyzed in detail. In the forward limit, the usual structure functions are estimated as well. In addition, by evolving the moments of the obtained structure functions to the scale of the lattice calculation, we give the factorization scale of our quark model. It is found that the present phenomenological model is reasonable to describe the general properties of ρ meson.

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“…Thus, several modeling frameworks have been used in the last few decades, each one having its advantages. For instance, we have the Nambu-Jona-Lasinio (NJL) model [63][64][65][66][67][68], the constituent quark model [69][70][71], the light-front holographic model [72][73][74], the light-front quark-diquark model [75][76][77], the AdS/QCD model [78][79][80], the chiral quark model [81,82] and the Dyson-Schwinger equations (DSEs) [7,8,83]. The NJL model has an effective Lagrangian of relativistic fermions interacting through local fermion-fermion couplings, and especially, it preserves one of the most important fundamental symmetries of QCD, namely, chiral symmetry.…”

Section: (): V-volmentioning

confidence: 99%

Kaon generalized parton distributions and light-front wave functions in the Nambu–Jona-Lasinio model

Zhang

¹

,

Ping

²

2021

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Kaon generalized parton distributions (GPDs) and the leading Fock state light-front wave functions are investigated in the framework of Nambu–Jona-Lasinio model with proper time regularization. In addition, we compared the form factors, parton distribution functions, and generalized form factors obtained from them, respectively. The first Mellin moments of GPDs result in the form factors of local currents. The second Mellin moments of vector GPDs are related to gravitational form factors, the quark mass distribution $$\theta _2$$ θ 2 and the quark pressure distribution $$\theta _1$$ θ 1 . When taking a Fourier transform of GPDs in impact parameter space, we can get the mean-squared impact parameter for the quarks of the kaon: $$\langle {\varvec{b}}_{\bot }^2\rangle _K^u=0.149$$ ⟨ b ⊥ 2 ⟩ K u = 0.149 fm$$^2$$ 2 , $$\langle {\varvec{b}}_{\bot }^2\rangle _K^s=0.088$$ ⟨ b ⊥ 2 ⟩ K s = 0.088 fm$$^2$$ 2 . This means that the kaon s quark is nearer to the center of transverse momentum than the u quark. We also give the light-cone energy radius for the quarks of the kaon from the mass distribution $$\theta _2$$ θ 2 : $$r_{E,LC}^{u,K}=0.187 $$ r E , L C u , K = 0.187 fm, $$ r_{E,LC}^{s,K}=0.167$$ r E , L C s , K = 0.167 fm, and the light-cone charge radius from quark form factors of the kaon: $$r_{c,LC}^{u,K}=0.390 $$ r c , L C u , K = 0.390 fm, $$r_{c,LC}^{s,K}=0.296 $$ r c , L C s , K = 0.296 fm, which means that the s quark has a smaller extent than the u quark. The light-front transverse-spin distributions $$\rho _u^1\left( {\varvec{b}}_{\bot },{\varvec{s}}_{\perp }\right) $$ ρ u 1 b ⊥ , s ⊥ and $$\rho _u^2\left( {\varvec{b}}_{\bot },{\varvec{s}}_{\perp }\right) $$ ρ u 2 b ⊥ , s ⊥ show distortions, the average shift are $$\langle b_{\bot }^y\rangle _1^u=0.116$$ ⟨ b ⊥ y ⟩ 1 u = 0.116 fm and $$\langle b_{\bot }^y\rangle _2^u=0.083$$ ⟨ b ⊥ y ⟩ 2 u = 0.083 fm. On the kinematic domain associated with the valence-quark dominance, the unpolarized Wigner distribution from light-front wave functions is sharply peaked. It extends as the transverse position variable increases in magnitude and has a domain of negative support. Through the comparison of distributions from the two methods, we find that they give the same multi-dimensional mapping of the kaon in the Nambu–Jona-Lasinio model.

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“…At present, it is impossible to determine the GPDs from QCD directly, effective models have been applied to supply estimates which should serve to direct future experiments. However, up to now, it is still a challenge to model GPDs and various methods have been developed [34][35][36][37][38][39][40][41][42][43][44][45][46]. The calculation of GPD models should satisfy the theoretical constraints required by the symmetries of QCD.…”

Section: Introductionmentioning

confidence: 99%

Regularization dependence of pion generalized parton distributions *

Zhang

¹

,

Kang

²

,

Ping

³

2022

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Pion generalised parton distributions are calculated within the framework of the Nambu--Jona-Lasinio model using different regularization schemes, including the proper time regularization scheme, the three dimensional momentum cutoff scheme, the four dimensional momentum cutoff scheme, and the Pauli-Villars regularization scheme. Furthermore, we check the theoretical constraints of pion generalised parton distributions required by the symmetries of quantum chromodynamics in different regularization schemes. The diagrams of pion parton distribution functions are plotted, in addition, we evaluate the Mellin moments of generalised parton distributions, which related to the electromagnetic and gravitational form factors of pion. Pion generalised parton distributions are continuous but not differential at $x=\pm \,\xi$, when considering the effect of the contact contribution term, generalised parton distributions become not continuous at $x=\pm \,\xi$ in all the four regularization schemes. Generalised parton distributions in impact parameter space are considered, the width distribution of $u$ quark in the pion and the mean-squared $\langle \bm{b}_{\bot}^2\rangle_{\pi}^u$ are calculated. The light-front transverse-spin distributions are studied, when quark polarized in the light-front-transverse $+\,x$ direction, the transverse-spin density is no longer symmetric around $(b_x=0,b_y=0)$, the peaks shift to $(b_x=0,b_y>0)$, we compare the average transverse shift $\langle b_{\bot}^y\rangle_1^u$ and $\langle b_{\bot}^y\rangle_2^u$ in different regularization schemes. The light-cone energy radius $r_{E,LC}$ and the light-cone charge radius $r_{c,LC}$ are also evaluated, we find that in the proper time regularization scheme the values of these quantities are the largest, in the three dimensional momentum cutoff scheme they are the smallest. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd

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Transversity Form Factors and Generalized Parton Distributions of the Pion in Chiral Quark Models

Cited by 4 publications

References 46 publications

ρ meson unpolarized generalized parton distributions with a light-front constituent quark model

ρ meson unpolarized generalized parton distributions with a light-front constituent quark model

Kaon generalized parton distributions and light-front wave functions in the Nambu–Jona-Lasinio model

Regularization dependence of pion generalized parton distributions *

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