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

TL;DR

This paper derives light front wave functions for light and heavy pseudoscalar mesons using Bethe-Salpeter equations, revealing how their internal structures vary with quark mass and providing insights into their parton distributions and mass radii.

Contribution

It provides a unified calculation of light front wave functions for both light and heavy pseudoscalar mesons from covariant Bethe-Salpeter wave functions, highlighting differences in Fock-state contributions.

Findings

LF-LFWFs narrow with increasing quark mass

Heavy mesons' LF-LFWFs dominate over 90% of normalization

Mass radii of $ ext{η}_c$ and $ ext{η}_b$ are 0.150 fm and 0.089 fm

Abstract

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 MeV, 310 MeV and 690 MeV), $\eta_c$ and $\eta_b$, from their covariant Bethe-Salpeter wave functions within the rainbow-ladder (RL) truncation. It is shown that the LF-LFWFs get narrower in $x$ (the longitudinal momentum fraction of meson carried by the quark) with the increasing current quark mass, and the leading twist parton distribution amplitudes (PDAs) inherit this feature. Meanwhile, we find in the pion the LF-LFWFs only contribute around 30\% to the total Fock-state normalization, indicating the presence of significant higher Fock-states within. In contrast, in the $\eta_c$ and $\eta_b$ the LF-LFWFs contribute more than $90$\%, suggesting the $Q\bar{Q}$ valence Fock-state truncation as a good approximation for heavy mesons. We thus study the 3-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 (TMD). 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 $r_{E,{\rm LC}}^{\eta_c} =0.150$ fm and $r_{E,{\rm LC}}^{\eta_b} =0.089$ fm respectively.