  We find that point particles interacting with a self-dual Yang-Mills field
and self-dual gravity manifestly satisfy color-kinematics duality at the level
of action. In a similar way color-kinematics duality also holds for a scalar
field minimally coupled to a self-dual Yang-Mills field and self-dual gravity.
By applying the appropriate limiting procedure to these scalar field theories
we reproduce point particle theories we started from. This allows us to connect
worldline color-kinematics duality to amplitude color-kinematics duality in
field theory. Considering that point particles act as sources of classical
solutions, our results may be regarded as a step towards establishing a precise
relation between the amplitude and the classical double copies in the self-dual
sector. Finally, we briefly mention that the extension of this discussion to
the higher-spin case suggests that scalar point particles cannot interact with
chiral higher-spin fields.
