Measurement of upward-going milli-charged particles at the Pierre Auger Observatory

It is assumed that superheavy dark matter particles with O(EeV) mass may decay to relativistic milli-charged particles (MCPs). The upward-going MCPs passing through the Earth can be measured by the fluorescence detectors (FD) of the Pierre Auger observatory (Auger). The massless hidden photon model is taken for MCPs to interact with nuclei, so that the numbers and fluxes of expected MCPs may be evaluated at the FD of Auger. Based on the assumption that no events are observed at the FD of Auger in 14 years, the corresponding upper limits on MCP fluxes are calculated at 90% C. L. These results indicate that MCPs can be directly detected in the secondaries' energy range O(1 EeV)-O(10 EeV) at the FD of Auger, when $3\times {10}^{-13}\lesssim {ϵ}^2\lesssim {10}^{-3}$. And a new region of 0.7 GeV < $m_{MCP}$ < 10 GeV and $1.2\times {10}^{-7}$ < ϵ < $4.5\times {10}^{-3}$ is ruled out in the $m_{MCP}$-ϵ plane with 14 years of Auger data.