Independence of current components, polarization vectors, and reference frames in the light-front quark model analysis of meson decay constants

TL;DR

This paper demonstrates that in the light-front quark model, meson decay constants are uniquely determined regardless of the current component, polarization vector, or reference frame, ensuring consistent physical observables.

Contribution

It proves the invariance and uniqueness of meson decay constants in LFQM across different current components and reference frames, even with interactions included.

Findings

Decay constants are independent of current component used.

The approach ensures consistent physical observables across different frames.

The method confirms the validity of LFQM for meson decay calculations.

Abstract

The issue of resulting in the same physical observables with different current components, in particular from the minus current, has been challenging in the light-front quark model (LFQM) even for the computation of the two-point functions such as meson decay constants. At the level of one-body current matrix element computation, we show the uniqueness of pseudoscalar and vector meson decay constants using all available components including the minus component of the current in the LFQM consistent with the Bakamjian-Thomas construction. Regardless of the current components, the polarization vectors, and the reference frames, the meson decay constants are uniquely determined in the non-interacting constituent quark and antiquark basis while the interactions of the constituents are added to the meson mass operator in the LFQM.