Leading-twist distribution amplitudes of scalar and vector mesons

Abstract

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. ≃ 0.2 GeV at an hadronic scale. In addition, it is confirmed that the dilation characterising ground-state PDAs is manifest in the PDAs of radial excitations too. The impact of SU (3)-flavour 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 flavour-dependence of dynamical chiral symmetry breaking and the PDAs are still skewed toward the heavier valence-quark in asymmetric systems.

Pseudoscalar glueball mass: a window on three-gluon interactions

“…The dashed green curve is a least-squares smoothening fit to the numerical solution, which likely delivers a more realistic picture of F 0 (k 2 ). Such a profile is typical of the amplitude for a system with significant rest-frame orbital angular momentum between the dressed-valence constituents, as can be inferred by analogy with P -wave quark-antiquark mesons [66]. In the present case, owing to the three-gluon vertex, the kernel in Eq.…”

Empirical Consequences of Emergent Mass

“…Working with this input, the authors of [203] delivered the associated leading-twist PDA, depicted in the rightmost panel of Figure 8 and whose first four moments are listed in Table 1. The prediction reveals some interesting features, e.g., the PDA of this excitation is not positive definite and there is a conspicuous locus of zeros in the lower-right section of the barycentric plot, both of which duplicate aspects of the wave function describing the first radial excitation of a quantum mechanical system that are also seen in the PDAs of meson radial excitations [236,237], and here the influence of pseudovector diquarks is contrary to that in the ground-state, viz. they shift momentum into u(x 1 ) from u(x 2 ), d(x 3 ).…”

Strong QCD from Hadron Structure Experiments

“…The prediction reveals some curious features, e.g. : the excitation's PDA is not positive definite and there is a prominent locus of zeros in the lower-right corner of the barycentric plot, both of which echo aspects of the wave function for the first radial excitation of a quantum mechanical system and have also been seen in the leading-twist PDAs of radially excited mesons [506,507]; and here the impact of pseudovector correlations is opposite to that in the ground-state, viz. they shift momentum into u(x 1 ) from u(x 2 ), d(x 3 ).…”