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

Abstract

In this paper, we test the self-consistencies of the standard and the covariant light-front quark model and study the zero-mode issue via the decay constants of pseudoscalar ($P$), vector ($V$) and axial-vector ($A$) mesons, as well as the $P\to P$ weak transition form factors. With the traditional type-I correspondence 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 $\text{lbd}=0$ and $\text{lbd}=\pm$ polarization states are different from each other, which presents a challenge to the self-consistency of the covariant light-front quark model. However, such a self-consistency problem can be "resolved" within the 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 also essential for the self-consistency of the standard light-front quark model. In the type-II scheme, the valence contributions to the physical quantities~($\mathcal{Q}$) considered in this paper are alway the same as that obtained in the standard light-front quark model, $[\mathcal{Q}{]}_{val.}=[\mathcal{Q}{]}_{\mathrm{SLF}}$, and the zero-mode contributions to $f_{V{,}^{1}A{,}^{3}A}$ and $f_{-}(q^2)$ exist only formally but vanish numerically, which implies further that $[\mathcal{Q}{]}_{val.}\dot{=}[\mathcal{Q}{]}_{\mathrm{full}}$. In addition, the manifest covariance of the covariant light-front quark model is violated in the traditional type-I scheme, but can be recovered by taking the type-II scheme.

Comments: 37 pages, 5 figures, to be published in Phys. Rev. D