  Spin waves in chiral magnetic materials are strongly influenced by the
Dzyaloshinskii-Moriya interaction resulting in intriguing phenomena like
non-reciprocal magnon propagation and magnetochiral dichroism. Here, we study
the non-reciprocal magnon spectrum of the archetypical chiral magnet MnSi and
its evolution as a function of magnetic field covering the field-polarized and
conical helix phase. Using inelastic neutron scattering, the magnon energies
and their spectral weights are determined quantitatively after deconvolution
with the instrumental resolution. In the field-polarized phase the imaginary
part of the dynamical susceptibility $\chi''(\varepsilon, {\bf q})$ is shown to
be asymmetric with respect to wavevectors ${\bf q}$ longitudinal to the applied
magnetic field ${\bf H}$, which is a hallmark of chiral magnetism. In the
helimagnetic phase, $\chi''(\varepsilon, {\bf q})$ becomes increasingly
symmetric with decreasing ${\bf H}$ due to the formation of helimagnon bands
and the activation of additional spinflip and non-spinflip scattering channels.
The neutron spectra are in excellent quantitative agreement with the low-energy
theory of cubic chiral magnets with a single fitting parameter being the
damping rate of spin waves.
