Low-q dispersion of transverse acoustic phonons in   YBa$_2$Cu$_3$O$_{7-\delta}$
  High-resolution ($\Delta E$=1.3 meV) inelastic X-ray scattering (IXS) in optimally doped untwinned YBa$_2$Cu$_3$O$_{7-\delta}$ single crystals show that the dispersion of transverse acoustic phonons in the a-direction remains linear with no softening due to bending modes in the long wavelength limit, down to q=0.02. The sound velocity is found to be 2700 +/- 70 m s$^{-1}$, in excellent agreement with ultrasound measurements, and unchanged upon cooling from room temperature to 98 K. These results rule out a strong coupling between bending dynamics of the CuO$_2$ planes and charge carriers in cuprates. 
Andrea Gauzzi (IMEM), Matteo D'Astuto (PMC), Francesca Licci (IMEM),   Alexei Bossak (ESRF), Michael Krisch (ESRF)