We present single-crystal neutron scattering measurements of the spin-1/2 equilateral triangular lattice antiferromagnet Ba$_3$CoSb$_2$O$_9$. Besides confirming that the Co$^{2+}$ magnetic moments lie in the ab plane for zero magnetic field, we determine all the exchange parameters of the minimal quasi-2D spin Hamiltonian, which confirms that Ba$_3$CoSb$_2$O$_9$ is an almost perfect realization of the paradigmatic model of frustrated quantum magnetism. A comparison with linear and nonlinear spin-wave theory reveals that quantum fluctuations induce a strong downward renormalization of the magnon dispersion.
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