Spatial and momentum imaging of the pion and kaon

Shi, Chao; Bednar, Kyle; Cloët, Ian C.; Freese, Adam

doi:10.1103/physrevd.101.074014

“…In Ref. [95], their ratio is 0.56 from the leading Fock state LFWF of pion using DSEs, and our former results demonstrate that the pion A 2,0 from the leading Fock state LFWF is the same as our direct calculation from the vector GPD [9]. Therefore, the values are the same, our ratio is smaller than their results.…”

Section: Polynomiality Conditionsupporting

confidence: 44%

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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“…For vector GPD, we can use the BSE to get the dressed GPD term with not only variable t, but also x and ξ. Ref. [45] has showed the process in their appendix, the inhomogeneous BSE in Fig. 1, on the right side, the first diagram is the bare vertex corresponds to the bare vector GPD H a (x, ξ, t), the second term corresponds to the dressed GPD term H c (x, ξ, t) which is plotted in Fig.…”

Section: B the Definition And Calculation Of Pion Gpdsmentioning

confidence: 99%

Regularization dependence of pion generalised parton distributions

Zhang,

Kang,

Ping

2021

Preprint

0

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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 = ± ξ, when considering the effect of D-term, generalised parton distributions become not continuous at x = ± ξ 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 b 2 ⊥ u π 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 (bx = 0, by = 0), the peaks shift to (bx = 0, by > 0), we compare the average transverse shift b y ⊥ u 1 and b y ⊥ u 2 in different regularization schemes. The light-cone energy radius rE,LC and the light-cone charge radius rc,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.

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“…The primary emphasis of model calculations has so far been on calculating various quark correlation functions, with information about the gluons either inferred indirectly or generated entirely perturbatively by QCD evolution equations [15][16][17][18]. Such approaches are not adequate to fully address several of the major open questions in hadron physics, which involve significant intrinsic gluonic contributions at all renormalization scales.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Glue and Wilson lines within Dressed Quarks

Costa,

Freese,

Cloët

et al. 2021

Preprint

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We construct a quark target model (QTM) to incorporate intrinsic glue into effective low-energy models of QCD, which often contain only quark degrees of freedom. This method guarantees the gauge invariance of observables order-by-order in the strong coupling. The quark and gluon PDFs for the dressed quarks are obtained in the QTM at leading order. We demonstrate gauge invariance of the results by comparing both covariant and light cone gauges, with the former including an explicit Wilson line contribution. A key finding is that in covariant gauges the Wilson line can carry a significant amount of the light cone momentum. With coupling strength 𝛼 𝑠 = 0.5 and dressed quark mass 𝑀 𝑞 = 0.4 GeV, we find quark and gluon momentum fractions of 𝑥 𝑞 = 0.81 and 𝑥 𝑔 = 0.19, where the Wilson line contribution to the quark momentum fraction is −0.18. We use the on-shell renormalization scheme and find that at one-loop this Wilson line contribution does not depend on the covariant gauge but does vanish in light cone gauge as expected. This result demonstrates that it is crucial to account for Wilson line contributions when calculating quantum correlation functions in covariant gauges. We also consider the impact of a gluon mass using the gauge invariant formalism proposed by Cornwall, and combine these QTM results with two quark-level models to obtain quark and gluon PDFs for the pion.

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Spatial and momentum imaging of the pion and kaon

Cited by 30 publications

References 80 publications

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

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

Regularization dependence of pion generalised parton distributions

Intrinsic Glue and Wilson lines within Dressed Quarks

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