Pseudoscalar meson decay constants and distribution amplitudes up to twist-4 in the light-front quark model

In the light-front quark model (LFQM) amenable to the simultaneous study of both the mass spectroscopy and the wave function related observables, we examine the decay constants and distribution amplitudes (DAs) up to the twist-4. The analysis of the heavy pseudoscalar mesons is carried out both in the $1S$ and $2S$ states. This investigation involves calculating the local and nonlocal matrix elements $\langle 0 |{\bar q}{\Gamma} q|P \rangle$ using three distinct current operators ${\Gamma}=(\gamma^\mu\gamma_5, i\gamma_5,\sigma^{\mu\nu}\gamma_5)$. Considering a general reference frame where ${\bf P}_\perp\neq 0$ and investigating all available current components, we examine not only the frame-independence but also the component-independence of the decay constants. The explicit findings from our study provide the evidence for the equality of the three pseudoscalar meson decay constants obtained from the three distinct current operators $\Gamma$. The notable agreement in decay constants is attained by imposing the Bakamjian-Thomas construction of the LFQM, namely the meson state is constructed by the noninteracting quark and antiquark representations while the interaction is added to the mass operator, which provides the self-consistency condition replacing the physical mass $M$ with the invariant mass $M_0$ for the noninteracting quark-antiquark representation of the meson state. In addition to obtaining the process-independent pseudoscalar meson decay constant, regardless of the choice of current operators $\Gamma$, we further demonstrate its explicit Lorentz and rotation invariance. In particular, we present the analysis conducted on the twist-4 DA derived from the minus component of the axial-vector current. Finally, we discuss the various twist DAs and their $\xi$-moments associated with the $1S$ and $2S$ heavy pseudoscalar mesons.