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

Abstract

$|\Delta c|=|\Delta u|=1$ 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 $U(1{)}^{\prime }$-models with generation-dependent charges, for which we provide explicit examples. $Z^{\prime }$-effects in $c\to u\ell {\ell }^{(\prime )}$ transitions can be sizable if both left-handed and right-handed couplings to quarks are present.

v3: 35 pages, 12 figures; Terms involving finite m_l and C_T corrected in Eqs. (7), (17), (18), (21); q^2 integration limits in Eq.(9) adapted to LHCb analysis; benchmarks for D->pi mumu in Table II corrected; bounds on WCs in Eq. (10) and (25) corrected; further numerics and conclusions unchanged