  Several theories of beyond-the-standard-model physics predict light scalars
that couple to fermions. By extending classical electrodynamics to include an
electron-scalar coupling, we calculate the nonlinear Thomson scattering of
light scalars in the collision of an electron with a monochro- matic
electromagnetic background. In doing so, we identify the classical
electron-scalar current, which allows for straightforward inclusion of the
process in laser-plasma particle-in-cell simulations. Scattering of
pseudoscalar particles is found to vanish in the classical (or, equivalently,
the low-lightfront-momentum) limit. When electrons co-propagate with the laser
pulse, we demonstrate that coherence effects in the production of light scalar
particles can greatly enhance the signal for sub-eV scalars. When the electron
beams counter-propagate with the laser pulse, we demon- strate that experiments
can probe larger scalar masses due to the larger momentum transfer in the
collisions. We then discuss a possible lab-based experimental set-up to detect
this scalar signal which is similar to light-shining-through-the-wall
experiments. Using existing experimental facilities as benchmarks, we calculate
projected exclusion bounds on the couplings of light scalars in such
experiments.
