  We study the polaron quasiparticle in a one-dimensional Bose gas. In the
integrable case described by the Yang-Gaudin model, we derive an exact result
for the polaron mass in the thermodynamic limit. It is expressed in terms of
the derivative with respect to the density of the ground-state energy per
particle of the Bose gas without the polaron. This enables us to find
high-order power series for the polaron mass in the regimes of weak and strong
interaction.
