# Comparison of two Minkowski-space approaches to heavy quarkonia

## TL;DR

This paper compares two fully relativistic Minkowski-space approaches, BLFQ and CST, for calculating heavy quarkonium properties, finding good agreement in spectra, decay constants, and wave functions, enhancing understanding of quarkonium structure.

## Contribution

It provides a detailed comparison of the Hamiltonian basis light-front quantization and covariant spectator theory approaches to heavy quarkonia in Minkowski space, highlighting their similarities and differences.

## Key findings

- Good agreement in decay constants for charmonium and bottomonium states.
- Qualitative similarities in wave functions and distribution amplitudes.
- Remarkable agreement even for excited states.

## Abstract

In this work we compare mass spectra and decay constants obtained from two recent, independent, and fully relativistic approaches to the quarkonium bound-state problem: the Hamiltonian basis light-front quantization (BLFQ) approach, where light-front wave functions are naturally formulated; and, the covariant spectator theory (CST), based on a reorganization of the Bethe-Salpeter equation. Even though conceptually different, both solutions are obtained in Minkowski space. Comparisons of decay constants for more than ten states of charmonium and bottomonium show favorable agreement between the two approaches as well as with experiment where available. We also apply the Brodsky-Huang-Lepage prescription to convert the CST amplitudes into functions of light-front variables. This provides an ideal opportunity to investigate the similarities and differences at the level of the wave functions. Several qualitative features are observed in remarkable agreement between the two approaches even for the rarely addressed excited states. Leading twist distribution amplitudes as well as parton distribution functions of heavy quarkonia are also analyzed.