  In this work, we analytically and numerically study the sideband transition
dynamics of the driven quantum Rabi model (QRM). We focus in particular on the
conditions when the external transverse drive fields induce first-order
sideband transitions. Inducing sideband transitions between two different
systems is an essential technique for various physical models, including the
QRM. However, despite its importance, a precise analytical study has not been
reported yet that successfully explains the sideband transition rates in a
driven QRM applicable for all system parameter configurations. In our study, we
analytically derive the sideband transition rates based on second-order
perturbation theory, not relying on the rotating wave approximation (RWA)
\cite{RWA}. Our formula are valid for all ranges of drive frequencies and
system's parameters. Our analytical derived formula agrees well with the
numerical results in a regime of moderate drive amplitudes. Interestingly, we
have found a non-trivial longitudinal drive effect derived from the transverse
drive Hamiltonian. This accounts for significant corrections to the sideband
transition rates that are expected without considering the derived longitudinal
effect. Using this approach, one can precisely estimate the sideband transition
rates in the QRM not confining themselves within specific parameter regimes.
This provides important contributions for understanding experiments described
by the driven QRM.
