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

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) and the quark pressure distribution theta(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: < b(perpendicular to)(2)>(u)(K) = 0.149 fm(2), < b(perpendicular to)(2)>(s)(K) = 0.088 fm(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: r(E, LC)(u, K) = 0.187 fm, r(E, LC)(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 fm, r(c,LC)(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(1)(u) (b(perpendicular to), s(perpendicular to)) and rho(2)(u) (b(perpendicular to), s(perpendicular to)) show distortions, the average shift are < b(perpendicular to)(y)>(u)(1) = 0.116 fm and < b(perpendicular to)(y)>(u)(2) = 0.083 fm. On the kinematic domain associated with the valence-quark dominance, the unpolarizedWigner 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.

Automated summary

The study investigates the Kaon generalized parton distributions (GPDs) and leading Fock state light-front wave functions in the Nambu-Jona-Lasinio model, comparing form factors, parton distribution functions, and various other results derived from these distributions. The analysis reveals specific physical properties of the quarks in the Kaon, including impact parameter distributions and light-front energy and charge radii. The research demonstrates consistent multi-dimensional mappings of the Kaon using different methods within the Nambu-Jona-Lasinio model.