Light scalars: Coherent nonlinear Thomson scattering and detection

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 monochromatic 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 copropagate 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 counterpropagate with the laser pulses, we demonstrate that experiments can probe larger scalar masses due to the larger momentum transfer in the collisions. We then discuss a possible lab-based experimental setup 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.

Figure 1

Here we compare the classical (dashed) and quantum (solid) spectra for scalar emission for a head-on collision of electron and laser-background, with $m_{\varphi }=1\mathrm{meV}$, ${\varkappa }^0=1.55\mathrm{eV}$ and for illustrative purposes, we set $g_{\varphi e}=1$. In the first row, the harmonics $s=1$, 2, 3 are shown and in the second row: $s=50$, 100, 150, 200. (In comparison, tail-on collisions have ${\eta }_p\le {\varkappa }^0{p}^0/m^2\approx 3\times {10}^{-6}$.)

Figure 2

The classical (dashed) and quantum (solid) spectra for a head-on collision of the laser background with $\xi =10$, ${\varkappa }^0=1.55\mathrm{eV}$ and an initial electron of energy of $p^0=1.6\mathrm{MeV}$ ($\approx 2\times {10}^{-5}$). For these parameters, ${\delta }_1^{*}=1\mathrm{eV}$. As the scalar mass is increased, the first and second harmonics are seen to disappear (each plot has the same axis scale).

Figure 3

The coherence changes as one varies the bunch length of a Gaussian-shaped bunch of $10^5$ electrons, where $|\widetilde{𝚥}(k){|}^2=\mathcal{C}{N}_e|{\widetilde{𝚥}}_{1e}(k){|}^2$. The empty circles are the numbers generated from the random Gaussian distribution, and the solid lines are given by the approximating function ${\mathcal{C}}_{*}$.

Figure 4

In the upper plot, we have the total rate as a function of the polar angle of the emitted scalar particles, and in the lower plot we have the emitted scalar momentum as a function of the polar angle. We have assumed that ${\theta }_p=0$ such that the electrons and the colliding photons are co-propagating, and that the $s=1$ contribution dominates. We have also taken $g_{\varphi e}=1$, $N_e={10}^9$, ${\varkappa }^0=2.33\mathrm{eV}$, $l=1\mu \mathrm{m}$, $m_{\varphi }=1\mathrm{meV}$, and $\xi =0.1$ in this calculation.

Figure 5

In the upper plot, we have the total rate as a function of the polar angle of the emitted scalar particles, and in the lower plot we have the emitted scalar momentum as a function of the polar angle. We have assumed that ${\theta }_p=\pi$ such that the electrons and the colliding photons are counter-propagating, and that the $s=1$ contribution dominates. In this plot, we also have $g_{\varphi e}=1$, $N_e={10}^9$, ${\varkappa }^0=2.33\mathrm{eV}$, $l=1\mu \mathrm{m}$, $m_{\varphi }=1\mathrm{meV}$, and $\xi =0.1$.

Figure 6

Projected exclusion bounds from the proposed experimental setup with tail-on (top) and head-on (bottom) collisions between the electron bunch and laser pulse with an ALPS I-like detection region. The regions above the lines would be excluded, and the coherence effects are only relevant for the tail-on collisions.