Raman scattering from a superconductivity-induced bound state in $MgB_2$

It is shown that the sharp peak in the $E_{2g}$ Raman spectrum of superconducting $MgB_2$ is due to a bound state caused by the electron-phonon coupling. Our theory explains why this peak appears only in the spectra with $E_{2g}$ symmetry and only in the $\sigma$ but not $\pi$ bands. The properties of the bound state and the Raman spectrum are investigated, also in the presence of impurity scattering.