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

Abstract

AbstractKaon 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.