The recent measurement of the $CP$ asymmetry in the decay $D\to K^{+}{K}^{-}$ by LHCb, combined with $\mathrm{\Delta }{A}_{CP}$, evidences a sizable $CP$ asymmetry in the decay $D\to {\pi }^{+}{\pi }^{-}$, which requires a dynamical enhancement of standard model higher-order contributions over tree-level ones by a factor of 2. The data furthermore imply huge $U$-spin breaking, about 4–5 times larger than the nominal standard model one of $\lesssim 30\%$ in charm. Enhanced breakdown of the two approximate symmetries points to models that violate $U$-spin and $CP$ and disfavors flavor singlet contributions such as chromomagnetic dipole operators as explanations of the data. We analyze the reach of flavorful $Z^{\prime }$ models for charm $CP$ asymmetries. Models generically feature explicit $U$-spin and isospin breaking, allowing for correlations with $D\to {\pi }^0{\pi }^0$ and $D^{+}\to {\pi }^{+}{\pi }^0$ decays with corresponding $CP$ asymmetries at similar level and sign as $D\to {\pi }^{+}{\pi }^{-}$, about $\mathcal{O}(1-2)\times {10}^{-3}$. Experimental and theoretical constraints very much narrow down the shape of viable models: Viable, anomaly-free models are leptophobic—or at least electron- and muophobic—with light $Z^{\prime }$ below $\mathcal{O}(20)\mathrm{GeV}$ and can be searched for in low mass dijets at the LHC or in $\mathrm{\Upsilon }$ and charmonium decays, as well as dark photon searches. A $Z^{\prime }$ around $\sim 3$ or $\sim (5–7)\mathrm{GeV}$ can relieve the tensions in the $J/\psi \to {\pi }^{+}{\pi }^{-}$ and ${\psi }^{\prime }\to {\pi }^{+}{\pi }^{-}$ branching ratios with pion form factor values from fits to BABAR and JLab data and simultaneously explain the charm $CP$ asymmetries. Models can also feature sizable branching ratios into light right-handed neutrinos or vectorlike dark fermions, which can be searched for in $e^{+}{e}^{-}\to \mathrm{hadrons}+\mathrm{invisibles}$ at Belle II and BESIII. Because of the low new physics scale, dark fermions can easily induce an early Landau pole, requiring models to be UV completed near the TeV scale.

• Received 10 November 2022
• Accepted 11 July 2023

DOI:https://doi.org/10.1103/PhysRevD.108.035005

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Published by the American Physical Society