  Utilizing resonant inelastic x-ray scattering, we report a previously
unobserved mode in the excitation spectrum of La$_{2-x}$Sr$_x$CuO$_4$ at 500
meV. The mode is peaked around the ($\pi$,0) point in reciprocal space and is
observed to soften, and broaden, away from this point. Samples with x=0, 0.01,
0.05, and 0.17 were studied. The new mode is found to be rapidly suppressed
with increasing Sr content and is absent at $x$=0.17, where it is replaced by a
continuum of excitations. The peak is only observed when the incident x-ray
polarization is normal to the CuO planes and is also present in Nd$_2$CuO$_4$.
We suggest possible explanations for this excitation.
