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The analytic behavior of the heavy-light meson form factor is investigatedusing several relativistic examples including unconfined, weakly confined, andstrongly confined mesons. It is observed that confinement erases the anomalousthreshold singularity and also induces an essential singularity at the normalannihilation threshold. In the weak confinement limit, the "would be" anomalousthreshold contribution is identical to that of the real singularity on itsspace-like side.

Anomalous threshold, confinement, and an essential singularity in the heavy-light form factor