Scaling anomaly in string defect background

We show that the classical scale symmetry of a particle moving in string defect background is broken due to inequivalent quantization of the classical system, which leads to scaling anomaly. The consequence of this anomaly is the formation of single bound state in the coupling constant interval γ∈(-1,1). The inequivalent quantization is characterized by a 1-parameter family of self-adjoint extension parameter ω.It has been conjectured that the formation of loosely bound state in string defect background may lead to the so called anomalous scattering cross section for the particles, which has been experimentally observed in molecular physics. A plausible laboratory test for the anomalous scattering could be devised in condensed matter system. PACS  03.65.-w; 03.65.Db; 98.80.Cq; 11.27.+d