| \textbf{Top left:} limits on the mass and couplings of a new scalar mediator (see \cref{eq:L-scalar}), from the requirement that coherent elastic neutrino--nucleus scattering (CE$\nu$NS) mediated by this new particle shall not violate the 90\% C.L.\ constraints from PANDAX-4T (light blue) and XENONnT (blue). We show results for both the S1+S2 analysis (solid) and for the S2-only analysis, but find no significant differences in sensitivity. We also show the expected sensitivity of a hypothetical detector with an exposure of 200~tonne yrs (dark blue dotted). The green region is ruled out by measurements of CE$\nu$NS in the cesium iodide (CsI) detectors of COHERENT. We further show upper limits from the CONUS \cite{CONUS:2021dwh} and Dresden-II \cite{Coloma:2022avw} experiments. The parameter region shaded in purple is excluded by Big Bang Nucleosynthesis (BBN) \cite{Huang:2017egl}. \textbf{Top right:} analogous imits on the mass and couplings of a new scalar mediator with couplings to quarks proportional to the quark masses, see \cref{eq:q-mass-dependence}. \textbf{Bottom left:} constraints on CE$\nu$NS mediated by a light vector with interactions given by \cref{eq:L-vector}. Compared to scalar mediators, we further show bounds in shaded orange on a leptophobic vector from NA62 \cite{NA62:2019meo} and MiniBoone \cite{MiniBooNE:2017nqe}. Furthermore, the region to the left of the dotted black line is excluded by a combination of collider and beam dump experiments when the $Z^{\prime}$ can decay into electron-positron pairs \cite{Graham:2021ggy}. These constraints are significantly relaxed for vector mediators which do not couple to electrons at tree-level.\textbf{Bottom right:} constraints on neutrino--electron scattering through a new leptophilic scalar mediator (see \cref{eq:L-leptophilic}) from the PANDAX-4T S2-only analysis. We compare to limits from BBN, Borexino, CONUS, COHERENT (CsI), and Dresden-II \cite{Coloma:2022umy}. |