Pseudoscalar charmonium and bottomonium: light-front wave functions, distribution amplitudes and distribution functions

Abstract

Light-front wave functions play a central role in the program of understanding the structure of hadrons as QCD bound states. Using continuum Schwinger methods, based on Dyson-Schwinger and Bethe-Salpeter equations, they can be computed directly within a framework connected to QCD. For light pseudoscalar mesons, previous studies revealed an approximate separability of longitudinal and transverse lightcone momentum dependences in the LFWFs, leading to a simple relation between distribution functions and amplitudes. In this work, we extend those previous studies to the case of pseudoscalar charmonium and bottomonium, using the fictitious $π_s$ meson as a benchmark. Motivated by the observed deviations, we propose a modified non-separable LFWF ansatz that successfully reproduces the properties of heavy pseudoscalar quarkonia and allows the calculation of zero-skewness generalised parton distribution functions, electromagnetic and gravitational form factors, and transverse charge and mass distributions.