# Revisiting the form factors of $P\to V$ transition within the light-front quark models

## TL;DR

This paper examines the consistency and covariance of the covariant light-front quark model for $P o V$ transitions, proposing a scheme that resolves previous inconsistencies and aligns results with the standard light-front model.

## Contribution

It introduces a type-II correspondence scheme that fixes covariance issues and unifies the covariant and standard light-front quark model results for $P o V$ transitions.

## Key findings

- Type-II scheme resolves covariance and consistency issues.
- Results in the standard light-front model match the full covariant calculations.
- Numerical updates for $P o V$ transitions confirm previous conclusions.

## Abstract

We investigate the self-consistency and Lorentz covariance of the covariant light-front quark model~(CLF QM) via the matrix elements and form factors~(${\cal F}=g$, $a_{\pm}$ and $f$) of $P\to V$ transition. Two types of correspondence schemes between the manifest covariant Bethe-Salpeter approach and the light-front quark model are studied. We find that, for $a_{-}(q^2)$ and $f(q^2)$, the CLF results obtained via $\lbd=0$ and $\pm$ polarization states of vector meson within the traditional type-I correspondence scheme are inconsistent with each other; and moreover, the strict covariance of the matrix element is violated due to the nonvanishing spurious contributions associated with noncovariance. We further show that such two problems have the same origin and can be resolved simultaneously by employing the type-II correspondence scheme, which advocates an additional replacement $M\to M_0$ relative to the traditional type-I scheme; meanwhile, the results of ${\cal F}(q^2)$ in the standard light-front quark model~(SLF QM) are exactly the same as the valence contributions and equal to numerally the full results in the CLF QM, {\it i.e.}, $[{\cal{F}}]_{\rm SLF}=[{\cal{F}}]_{\rm val.}\doteq[{\cal{F}}]_{\rm full}$. The numerical results for some $P\to V$ transitions are updated within the type-II scheme. Above findings confirm the conclusion obtained via the decay constants of vector and axial-vector mesons in the previous works.