The effect of electron correlation (EC) on the electronic structure in MgB$_2$, AlB$_2$ and ZrB$_2$, is studied by examining the partial density of states (PDOS) of B-2$psigma$ and $ppi$ orbitals using the polarization dependence of x-ray emission and absorption spectra. The discrepancies between observed and calculated PDOSs cannot be attributed to EC effects. The present results suggest that the EC effect is less than the experimental error ($sim$ 0.2 eV), which indirectly supports a scenario that electron-phonon interaction plays an essential role in the occurrence of superconductivity.
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