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

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 ${}^3{D}_1$ and ${}^3{S}_1$ are $1^{--}$ mesons, the Lorentz structures of their vertex functions are the same. Thus when one needs to study the processes where ${}^3{D}_1$ is involved, all the corresponding formulas for ${}^3{S}_1$ states can be directly applied, only the coefficient of the vertex function should be replaced by that for ${}^3{D}_1$. 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 ${\psi }^{\prime }$ with the LFQM.

12 pages, 2 figures, some typos corrected and more discussions added. Accepted by EPJC

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