  Many superconducting devices rely on the finite gap in the excitation
spectrum of a superconductor: thanks to this gap, at temperatures much smaller
than the critical one the number of excitations (quasiparticles) that can
impact the device's behavior is exponentially small. Nevertheless, experiments
at low temperature usually find a finite, non-negligible density of
quasiparticles whose origin has been attributed to various non-equilibrium
phenomena. Here, we investigate the role of photons with energy exceeding the
pair-breaking threshold $2\Delta$ as a possible source for these quasiparticles
in superconducting resonators. Modeling the interacting system of
quasiparticles, phonons, sub-gap and pair-breaking photons using a kinetic
equation approach, we find analytical expressions for the quasiparticles'
density and their energy distribution. Applying our theory to measurements of
quality factor as function of temperature and for various readout powers, we
find they could be explained by assuming a small number of photons above the
pair-breaking threshold. We also show that frequency shift data can give
evidence of quasiparticle heating.
