Light top-flavoured dark matter in dark SMEFT: one-loop matching and phenomenology

We study light top-flavoured dark matter (DM) below the electroweak (EW) scale within the dark Standard Model effective field theory (DSMEFT). We perform the one-loop matching of the DSMEFT onto the dark low-energy effective field theory (DLEFT) at the EW scale for all relevant operators that couple scalar, fermionic or vector DM, as well as axion-like particles, exclusively to third-generation quarks. After QCD evolution to the relevant low-energy scales, we match the DLEFT onto the non-relativistic EFT for DM-nucleus scattering. This EFT chain provides a unified framework for phenomenological studies of rare $B$- and $K$-meson decays with missing energy, direct and indirect detection, and the thermal relic abundance. Interpreting the Belle II excess in $B^+\to K^+ν\barν$ as a decay into DM, we find that only the DSMEFT operators contributing at tree level can accommodate it with $O(1)$ couplings for a new-physics scale of $1\,\mathrm{TeV}$. The decay $B^0\to K^{*0}+\mathrm{inv}$ provides the strongest constraint over large portions of the Belle II-favoured parameter space, while $K^+\toπ^++\mathrm{inv}$ can dominate at low and $B_s\to\mathrm{inv}$, $B^+\toπ^++\mathrm{inv}$ and $Υ(1S)\to\mathrm{inv}$ become important at high DM masses, respectively. Direct-detection searches by CRESST-III and DarkSide-50 are competitive for operators involving scalar quark currents and, depending on the operator, exclude the Belle~II-favoured band for $m_{\mathrm{DM}}\gtrsim1$-$2\,\mathrm{GeV}$. We also perform detailed analyses of the thermal relic abundance and the indirect-detection constraints from the CMB and Fermi-LAT.