A symmetry-preserving truncation of the two-body light-quark bound-state problem in relativistic quantum field theory is used to calculate the leading-twist parton distribution amplitudes (PDAs) of scalar systems, both ground-state and radial excitations, and the radial excitations of vector mesons. Owing to the fact that the scale-independent leptonic decay constant of a scalar meson constituted from equal-mass valence constituents vanishes, it is found that the PDA of a given scalar system possesses one more zero than that of an analogous vector meson. Consequently, whereas the mean light-front relative momentum of the valence constituents within a vector meson is zero, that within a scalar meson is large, an outcome which hints at a greater role for light-front angular momentum in systems classified as $P$-wave in quantum mechanical models. Values for the scale-dependent decay constants of ground-state scalar and vector systems are a by-product of this analysis, and they turn out to be roughly equal, viz. $\simeq 0.2\mathrm{GeV}$ at an hadronic scale. In addition, it is confirmed that the dilation characterizing ground-state PDAs is manifest in the PDAs of radial excitations too. The impact of $SU(3)$-flavor symmetry breaking is also considered. When compared with pseudoscalar states, it is a little stronger in scalar systems, but the size is nevertheless determined by the flavor dependence of dynamical chiral symmetry breaking and the PDAs are still skewed toward the heavier valence quark in asymmetric systems.

• Received 16 August 2016

DOI:https://doi.org/10.1103/PhysRevD.94.094014