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 ({{mathcal {F}}}=g, a_{pm } and f) of Prightarrow 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 lambda =0 and ± 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 Mrightarrow M_0 relative to the traditional type-I scheme; meanwhile, the results of {{mathcal {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, i.e., [{{mathcal {F}}}]_{mathrm{SLF}}=[{{mathcal {F}}}]_{mathrm{val.}}doteq [{{mathcal {F}}}]_mathrm{full}. The numerical results for some Prightarrow 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.
Highlights
In order to treat the complete Lorentz structure of a matrix element and evaluate the zero-mode contributions, many efforts have been made in the past years [11,12,13,40,41,42,43]
We have investigated the self-consistency and Lorentz covariance of the covariant light-front quark model (CLF QM) via the matrix elements
Relevant form factors of P → V transition, which provide much stricter tests on the CLF QM and are much more complicated than the case of decay constants studied in the previous works [73,74]
Summary
In order to treat the complete Lorentz structure of a matrix element and evaluate the zero-mode contributions, many efforts have been made in the past years [11,12,13,40,41,42,43]. Between the covariant BS model and the LF QM is used in the traditional CLF QM, where the factors DV,con = M + m1 + m2 and DV,LF = M0 + m1 + m2 appear in the vertex operator Within this type-I correspondence scheme, the CLF result for fV suffers from above-mentioned self-consistency and covariance problems [72,73]. The form factors of P → V transition may present much stricter test on the self-consistency and covariance of CLF QM, as well as above-mentioned findings obtained via fV,A.
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