  Vector-like quarks have been of interest for a plethora of experimentally
motivated reasons and have come under increased investigation recently due to
their inclusion to the Standard Model (SM) appreciably improving global fits to
several flavour physics and precision electroweak measurements. The addition of
vector-like quark singlets breaks the unitarity of the
Cabibbo-Kobayashi-Maskawa (CKM) matrix and enables tree-level flavour changing
neutral (FCN) vertices. The resulting radiative flavour changing decays of
these particles through the electromagnetic transition dipole moment are a key
means to study their properties and search for them at experiments like the
Large Hadron Collider (LHC). Despite these radiative decays providing such a
clean experimental signature, an explicit analytical study of the branching
ratios and $CP$ violation resulting from these loop level processes has thus
far evaded attention. We provide the formulation for the decay rates and $CP$
asymmetry resulting from a combination of the imaginary components of the loop
integrals and complex phases in the quark mixing matrix. We then apply our
analytical results to study phenomenology of these states for several global
fits pertaining to vector-like isosinglets $t'$ and $b'$. We find that clean
collider signatures and polarisation observables can be generated for both $t'$
and $b'$.
