Braking protons at the EIC: from invisible meson decay to new physics searches

We investigate the sensitivity of the Electron-Ion Collider (EIC) to invisible final states in coherent exclusive electroproduction. The characteristic signal is a forward proton with reduced energy and little additional detector activity. Using the excellent particle detection capabilities and kinematics reconstruction at the EIC, we argue that backgrounds can be strongly suppressed. While our analysis applies to various states, we specifically focus on pseudoscalar particles: (i) neutral mesons ($\pi^0,\eta^{(\prime)}$), whose invisible Standard Model decays are extremely suppressed, and (ii) gluon-coupled axion-like particles (ALPs) decaying invisibly to a dark sector. Depending on the meson species and the achievable background rejection, the EIC could strengthen existing bounds on invisible decays of pseudoscalar mesons by up to four orders of magnitude, probing branching ratios as small as ${\rm BR}(\eta^{(\prime)}\to{\rm inv})\sim 10^{-8}$. In addition, the EIC would directly probe invisibly decaying ALPs with the couplings up to $f_a\sim 10^5\,\text{GeV}$ and masses in the range $0.1$-$2\,\text{GeV}$.