  We show that the classical scale symmetry of a particle moving in cosmic
string background is broken upon inequivalent quantization of the classical
system, leading to anomaly. The consequence of this anomaly is the formation of
single bound state in the coupling interval \gamma\in(-1,1). The inequivalent
quantization is characterized by a 1-parameter family of self-adjoint extension
parameter \omega. It has been conjectured that the formation of loosely bound
state in cosmic string background may lead to the so called anomalous
scattering cross section for the particles, which is usually seen in molecular
physics.
