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

• Published in: Physical review. D 2018-12, Vol.98 (11), p.1, Article 114018
• Main Authors: Chang, Qin, Li, Xiao-Nan, Li, Xin-Qiang, Su, Fang, Yang, Ya-Dong
• Format: Article
• Language: English
• Subjects: Consistency; Covariance; Form factors; Light; Mathematical models; Mesons; Particle decay; Quark models; Quarks
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.98.114018

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 fV as well as f1A and f3A 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 → M0 relative to the type-I case. Moreover, the replacement M → M0 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 fV,1A,3A and f− (q2) 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.