# Frame dependence of transition form factors in light-front dynamics

## TL;DR

This paper studies how the calculation of transition form factors in light-front dynamics depends on the choice of frame, especially for heavy quarkonia, and proposes optimal frames to minimize Lorentz symmetry violation effects.

## Contribution

It introduces a method to assess frame dependence as a measure of Lorentz symmetry violation in light-front calculations and suggests optimal frames for more accurate form factor computations.

## Key findings

- Frame dependence indicates Lorentz symmetry violation due to Fock-space truncation.
- Using specific frames reduces the frame dependence of form factors.
- Predictions for lepton pair mass spectrum in electromagnetic Dalitz decays.

## Abstract

We calculate the transition form factor between vector and pseudoscalar quarkonia in both the timelike and the spacelike region using light-front dynamics. We investigate the frame dependence of the form factors for heavy quarkonia with light-front wavefunctions calculated from the valence Fock sector. This dependence could serve as a measure for the Lorentz symmetry violation arising from the Fock-space truncation. We suggest using frames with minimal longitudinal momentum transfer for calculations in the valence Fock sector, namely the Drell-Yan frame for the space-like region and a specific longitudinal frame for the timelike region; at $q^2=0$ these two frames give the same result. We also use the transition form factor in the timelike region to investigate the electromagnetic Dalitz decay $\psi_A\to \psi_B l^+l^-$ ($l = e,\mu$) and predict the effective mass spectrum of the lepton pair.