Ground state pseudoscalar mesons on the light front: From the light to heavy sector

We extract the leading Fock state light-front wave functions (LF-LFWFs) of both the light and heavy pseudoscalar mesons, e.g., the pion (at masses of 130, 310, and 690 MeV), eta(c) and eta(b), from their covariant Bethe-Salpeter wave functions within the rainbow-ladder truncation. It is shown that the LF-LFWFs get narrower in x (the longitudinal momentum fraction of the meson carried by the quark) with the increasing current quark mass, and the leading twist parton distribution amplitudes inherit this feature. In the case of the pion, the LF-LFWFs only contribute about 30% of the total Fock state normalization, indicating the presence of significant higher Fock states within. In contrast, in the cases of the eta(c) and eta(b), the LF-LFWFs contribute more than 90%, suggesting the Q (Q) over bar valence Fock state truncation as a good approximation for heavy mesons. We thus study the three-dimensional parton distributions of the eta(c) and eta(b) with the unpolarized generalized parton distribution function (GPD) and the transverse momentum-dependent parton distribution function. Through the gravitational form factors in connection with the GPD, the mass radii of the eta(c) and eta(b) in the light cone frame are determined to be r(E,LC)(eta c) = 0.150 and r(E,LC)(eta b) = 0.089 fm, respectively.