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

Abstract

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 ($π^0,η^{(\prime)}$), 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 ${\rm BR}(η^{(\prime)}\to{\rm inv})\sim 10^{-8}$. 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 $0.1$-$2\,\text{GeV}$.

Figures (5)

• Figure 1: An illustration of the EIC missing-proton-energy (MPE) search in $e+p \to e' +p' +X$ events. Without relying on reconstructing $X$, its pseudorapidity $\eta_{X}$ is indirectly extracted ($\eta_{X,{\rm reco}}(p_{e'},p_{p'})$) from the kinematics of outgoing states $e'$, $p'$. The latter are reconstructed by the far-forward (FFD) and far-backward (FBD) detectors if the event's $Q^{2},E_{p'},\eta_{p'}$ fall under detectability ranges (see Tbl. \ref{['tab:selection']}). Events with $\eta_X<4$ are within the fully detector-instrumented region; thus, visible $X$ can be vetoed, leaving only invisible states. See text for details.
• Figure 2: Feynman diagrams for $e\,p \to e\,p X$ with $X=\pi^0,\,\eta^{(\prime)},\,a$: (a) proton bremsstrahlung-type emission of $X$ via the final state radiation (the similar initial-state-radiation diagram is not shown), (b) $\gamma$-$V$ fusion production of $X$.
• Figure 3: The EIC projections for invisible ALPs search (see Eq. \ref{['eq:Lagr_alp']}) in the $\{m_a,f_a^{-1}\}$ plane, for $g_{a\chi}=1\,(0.01)$ on the left (right) panel. The left (right) panel is dominated by invisible meson (ALP) decay. We use the Baseline selection under conservative (Eq. \ref{['eq:bg-conservative']}) and background-free assumptions (dash and solid red), as well as the Optimal selection (red dotted). Current bounds from invisible flavorless meson NA62:2020pwiNA64:2024mah (black), kaon NA62:2025upx (brown region) and $B$-meson decays Belle-II:2023esi (turquoise region) are also presented.
• Figure S1: The production cross section of the ALPs in the model of Eq. \ref{['eq:Lagr_alp']} with the reference choice $f_a=1\,\mathrm{GeV}$ with the two setups from Tbl. \ref{['tab:selection']}: Baseline (solid) and Optimal (dashed). We also show the $\pi^0$ and $\eta^{(\prime)}$ production cross sections for the Baseline (circle) and Optimal (square) selections.
• Figure S2: Complementarity between two contributions to the missing-proton-energy events at the EIC: decays of pseudoscalar mesons (red) and of ALPs (blue), for two ALP masses $m_{a} = 0.25\text{ GeV}$ (solid) and $1\text{ GeV}$ (dashed), in the plane $\{g_{a\chi}, f_{a}^{-1}\}$. The curves show the lower bound of the sensitivity corresponding to the Baseline selection, under the assumption of zero background.