  We calculate the renormalisation of different light ray operators with one
light degree of freedom and a static heavy quark. Both $2\to2$- and
$2\to3$-kernels are considered. A comparison with the light-light case suggests
that the mixing with three-particle operators is solely governed by the light
degrees of freedom. Additionally we show that conformal symmetry is already
broken at the level of the one loop counterterms due to the additional
UV-renormalisation of a cusp in the two contributing Wilson-lines. This general
feature can be used to fix the $2\to2$-renormalisation kernels up to a
constant. Some examples for applications of our results are given.
