The New Physics Reach of Null Tests with $D\to \pi \mathrm{\ell }\mathrm{\ell }$ and $D_s\to K\mathrm{\ell }\mathrm{\ell }$ Decays

$\mathrm{\mid }\mathrm{\Delta }c\mathrm{\mid }=\mathrm{\mid }\mathrm{\Delta }u\mathrm{\mid }=1$ processes are unique probes of flavor physics in the up-sector within and beyond the Standard Model (SM). SM tests with rare semileptonic charm meson decays are based on an approximate CP–symmetry, a superior GIM–mechanism, angular distributions, lepton-universality and lepton flavor conservation. We analyze the complete set of null test observables in $D \to \pi \ell \ell^{(\prime)}$and$D_s \to K \ell \ell^{(\prime)}$decays,$\ell^{(\prime)}=e, \mu$, and find large room for new physics safely above the SM contribution. We identify signatures of supersymmetry, leptoquarks and anomaly-free $U(1{)}^{\mathrm{\prime }}$-models with generation-dependent charges, for which we provide explicit examples. $Z^{\mathrm{\prime }}$-effects in $c \to u \ell \ell^{(\prime)}$ transitions can be sizable if both left-handed and right-handed couplings to quarks are present.