We report a direct observation of a sharp Kohn-like anomaly in the doubly degenerate copper-oxygen bond-stretching phonon mode occurring at $mathbf{q}mathrm{=(0.3, 0,0)}$ in La$_{2-x}$Ba$_x$CuO$_{4+delta}$ with $mathrm{x=0.14pm0.01}$, thanks to the high $mathbf{Q}$ resolution of inelastic x-ray scattering. This anomaly is clearly seen when the inelastic signal is analysed using a single mode but is also consistent with a two mode hypothesis possibly due to a splitting of the degenerate modes due to symmetry breaking stripes. Our observation shows that the effect persists at the stripe propagation vector in a superconducting system close to optimal doping.
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