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In this paper, we test the self-consistencies of the standard and thecovariant light-front quark model and study the zero-mode issue via the decayconstants of pseudoscalar ($P$), vector ($V$) and axial-vector ($A$) mesons, aswell as the $P\to P$ weak transition form factors. With the traditional type-Icorrespondence between the manifestly covariant and the light-front approach,the resulting $f_{V}$ as well as $f_{^1\!A}$ and $f_{^3\!A}$ obtained with the$\lbd=0$ and $\lbd=\pm$ polarization states are different from each other,which presents a challenge to the self-consistency of the covariant light-frontquark model. However, such a self-consistency problem can be "resolved" withinthe type-II scheme, which requires an additional replacement $M\to M_0$relative to the type-I case. Moreover, the replacement $M\to M_0$ is alsoessential for the self-consistency of the standard light-front quark model. Inthe type-II scheme, the valence contributions to the physicalquantities~(${\cal Q}$) considered in this paper are alway the same as thatobtained in the standard light-front quark model, $[{\cal Q}]_{\rm val.}=[{\calQ}]_{\rm SLF}$, and the zero-mode contributions to $f_{V,^1\!A,^3\!A}$ and$f_-(q^2)$ exist only formally but vanish numerically, which implies furtherthat $[{\cal Q}]_{\rm val.}\dot{=} [{\cal Q}]_{\rm full}$. In addition, themanifest covariance of the covariant light-front quark model is violated in thetraditional type-I scheme, but can be recovered by taking the type-II scheme.

physical review. d/physical review. d.

Self-consistency and covariance of light-front quark models: testing via  $P$, $V$ and $A$ meson decay constants, and $P\to P$ weak transition form  factors