Self-consistency and covariance of light-front quark models: Testing via P, V, and A meson decay constants, and P→P weak transition form factors

摘要

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 → 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 A 1 and f A 3 obtained with the λ = 0 and λ = ± 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 → M 0 relative to the type-I case. Moreover, the replacement M → 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 ( Q ) considered in this paper are always the same as that obtained in the standard light-front quark model, [ Q ] val = [ Q ] SLF , and the zero-mode contributions to f V , 1 A , 3 A and f ? ( q 2 ) exist only formally but vanish numerically, which further implies that [ Q ] val = ˙ [ Q ] 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 correspondence.