Spatial and Momentum Imaging of the Pion and Kaon

Abstract: We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multi-dimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. Highlights from this study include predictions that the mean-squared impact parameter for the quarks in the pion and kaon are: $\langle \vec{b}T^2\rangle{u}^\pi=0.11$fm$^2$, $\langle \vec{b}T^2\rangle{s}^K=0.08$fm$^2$, and $\langle \vec{b}T^2\rangle{u}^K=0.13$fm$^2$, and therefore the $s$ quark in the kaon is much closer to the center of transverse momentum than the $u$ quark. From the electromagnetic and gravitational form factors we find that the light-cone energy radii are about 60\% smaller than the light-cone charge radii for each quark sector in the pion and kaon. A quantitative measure of the importance of the leading Fock state is obtained via comparison with a full DSE calculation (containing an infinite tower of Fock states) for the pion form factor.