Self-consistent $M1$ radiative transitions of excited $B_c$ and heavy quarkonia with different polarizations in the light-front quark model

TL;DR

This paper uses the light-front quark model to analyze M1 radiative transitions in heavy quarkonia and Bc mesons, providing theoretical predictions consistent with existing data and offering new testable results.

Contribution

It introduces a self-consistent method for calculating M1 radiative transitions with different polarizations in the light-front quark model, including predictions for Bc mesons.

Findings

Results agree with experimental data, lattice QCD, and other theories.

The model captures the hierarchy of mass spectra and decay constants.

Predictions for Bc meson radiative transitions are provided.

Abstract

In this study, we investigate the properties of pseudoscalar and vector charmonia, bottomonia, and $B_c$ mesons using the light-front quark model, focusing on the $M1$ radiative transition. For that purpose, we conduct a variational analysis with a QCD-motivated effective Hamiltonian, employing a trial wave function expanded in the harmonic oscillator basis functions up to the $3S$ state. We fit the model parameters to mass spectra and decay constants, obtaining reasonable agreement with experimental data and correctly reflecting the hierarchy of mass spectra and decay constants. In analyzing the $M1$ radiative transition, we consider both good ($\mu=+$) and transverse ($\mu={\perp}$) current components with both longitudinal $(h=0)$ and transverse $(h=\pm1)$ polarizations, demonstrating that the results from both components of currents and polarizations are identical. Self-consistency is achieved by substituting $M$ with $M_0$ when computing the operators for decay constants and radiative transitions. We also find that the difference between longitudinal and transverse polarizations of the observables may quantify the anisotropy of the model wave function. Our results on radiative transitions align reasonably well with experimental data, lattice QCD, and theoretical predictions. Furthermore, we also provide predictions for $B_c$ mesons that can be tested in experiments.