Production of Light Dark Particles from Nonlinear Compton Scattering Between Intense Laser and Muon or Proton Beam

TL;DR

The paper tackles the problem of probing light dark-sector states by merging strong-field QED with high-energy lepton and hadron beams. It develops a framework for nonlinear Compton scattering in an intense laser field, producing dark photons and axion-like particles via $n$-photon absorption, and computes the corresponding cross sections using Volkov states and Jacobi-Anger/Bessel expansions. It also analyzes SM backgrounds with missing neutrinos and presents prospective sensitivity benchmarks, showing that dark-photon limits can reach $\epsilon \sim 10^{-7}$–$10^{-6}$ and ALP couplings down to $g_{a\mu} \sim 10^{-2}$–$10^{-5}$ depending on beam energy, with current searches complementing existing bounds for $m \lesssim 1~{\rm MeV}$. The results highlight a novel, experimentally accessible path to sub-MeV invisible particles by combining intense lasers with muon or proton beams, and indicate that higher laser intensity or beam energy expands the search reach.

Abstract

The laser of an intense electromagnetic field promotes the studies of strong-field particle physics in high-intensity frontier. Particle accelerator facilities in the world produce high-quality muon and proton beams. In this work, we propose the nonlinear Compton scattering to light dark particles through the collision between intense laser pulse and muon or proton beam. We take light dark photon and axion-like particle as illustrative dark particles. The cross sections of relevant nonlinear Compton scattering to dark photon or axion-like particle are calculated. We also analyze the background processes with missing neutrinos. The prospective sensitivity shows that the laser-induced process provides a complementary and competitive search of new invisible particles lighter than about 1 MeV.

Figures (3)

• Figure 1: The cross sections for the laser-induced Compton scattering to DP as a function of $\eta_e$ with kinetic mixing $\epsilon = 1$ and DP mass $m_{\gamma_D}=10~{\rm eV}$. The individual contributions from the absorption of $n = 1$ (blue dashed line), $n = 2$ (gray dashed line), $n=3$ (purple dashed line), $n=4$ (red dashed line), $n=5$ (green dashed line) or $n=6$ (brown dashed line) laser photons are displayed, with the totally summed cross section shown as a black solid line. The top panels show the results of anti-muon beam with $E_{\rm Lab}=3.1~{\rm GeV}$ (left) and 1 TeV (right). The results of the proton beam are showed in bottom panels with $E_{\rm Lab}=8~{\rm GeV}$ (left) and 1 TeV (right).
• Figure 2: The cross sections for the laser-induced Compton scattering to ALP as a function of $\eta_e$ with ALP-fermion couplings $g_{a\mu}= g_{a\mathcal{P}} = 1$ and ALP mass $m_a=10~{\rm eV}$, as labeled in Fig. \ref{['fig:xsDP']}.
• Figure 3: Sensitivity of nonlinear Compton scattering to the kinetic mixing of DP $\epsilon$ (left panels) and the ALP coupling $g_{a\mu}$ or $g_{a\mathcal{P}}$ (right panels) from the collision between laser and muon (top panels) or proton (bottom panels) beam. We take $\eta_e=0.1$ (solid lines) or 100 (dashed lines) and $E_{\rm Lab}=3.1~{\rm GeV}$ or 8 GeV (red), 1 TeV (green) and 10 TeV (blue). The limits from other experiments are also shown. For DP, we include the exclusion limits from BaBar (light blue purple region) BaBar:2017tiz, E137 (orange region) Liu:2017htz, NA64$\mu$ (light green region) Andreev:2024yft, and the projection limits from Belle II ($20~{\rm fb}^{-1}$, cyan line) Belle-II:2018jsg, BESIII ($17~{\rm fb}^{-1}$, gray line) Zhang:2019wnz and STCF (2 GeV, $30~{\rm ab}^{-1}$, brown line) Zhang:2019wnz. For ALP coupling $g_{a\mu}$, we include exclusion limits from SN1987A (purple region) Croon:2020lrf, NA64$\mu$ ($2\times 10^{10}$ muons on target, salmon region) Li:2025yzb and $(g-2)_\mu$$2\sigma$ band (cyan region) Buen-Abad:2021fwq. For ALP coupling $g_{a\mathcal{P}}$, we include exclusion limits from SNO (light blue region) Bhusal:2020bvx and SN1987A (light green region) Lella:2023bfb.