  This paper explores the renormalization of scale-free quadratic gravity
coupled to the bumblebee field and its potential for dynamically breaking
Lorentz symmetry. We conduct one-loop renormalization of the model and
calculate the associated renormalization group functions. Additionally, we
compute the one-loop effective potential for the bumblebee field, revealing
that it acquires a non-trivial vacuum expectation value induced by radiative
corrections - a phenomenon known as the Coleman-Weinberg mechanism. This
spontaneous breaking of scale invariance arises from the non-vanishing vacuum
expectation value of the bumblebee field, implicating Lorentz symmetry
violation. Consequently, the non-minimal coupling between the bumblebee and
gravitational fields results in a spontaneous generation of the
Einstein-Hilbert term due to radiative corrections, thereby linking the Planck
scale to Lorentz violation phenomena.
