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