Vertex functions for d-wave mesons in the light-front approach

TL;DR

This paper derives vertex functions for all d-wave mesons within the light-front quark model, facilitating studies of new resonances and mixing phenomena involving these states.

Contribution

It provides explicit vertex functions for d-wave mesons in the LFQM, enabling direct application to processes involving these states, especially for 2S-1D mixing analysis.

Findings

Derived vertex functions for all d-wave states in LFQM.

Unified Lorentz structure for $^3D_1$ and $^3S_1$ mesons.

Facilitates studies of newly observed resonances and mixing phenomena.

Abstract

While the light-front quark model (LFQM) is employed to calculate hadronic transition matrix elements, the vertex functions must be pre-determined. In this work we derive the vertex functions for all d-wave states in this model. Especially, since both of $^3D_1$ and $^3S_1$ are $1^{--}$ mesons, the Lorentz structures of their vertex functions are the same. Thus when one needs to study the processes where $^3D_1$ is involved, all the corresponding formulas for $^3S_1$ states can be directly applied, only the coefficient of the vertex function should be replaced by that for $^3D_1$. The results would be useful for studying the newly observed resonances which are supposed to be d-wave mesons and furthermore the possible 2S-1D mixing in $\psi'$ with the LFQM.