γγ → ρρ: An effective Lagrangian approach

We point out that recent results on two photon production of ρ meson pairs at low energy can put new constraints on meson effective Lagrangians. We find that the data cannot be understood unless tensor and to some extent scalar mesons are introduced. A number of coupling constants are evaluated assuming exact vector dominance. The data seems to be compatible with the value of the ρ magnetic moment predicted in current effective Lagrangians. We argue that the experimental selection rule can be explained here as an interference effect between a ρ self-interaction diagram and an s-channel tensor exchange one. Due to a relativistic description, this diagram contributes effectively to two partial waves. A semi quantitative fit to the data is possible if the tensor-vector coupling constant is assumed to be somewhat larger than its VMD value and vertex form-factors are introduced. (orig.)