Two is better than one: The U-spin-CP anomaly in charm

Abstract

The recent measurement of the CP-asymmetry in the decay $D \to K^+ K^-$ by LHCb, combined with $\Delta A_{\text{CP}}$, evidences a sizable CP-asymmetry in $D \to \pi^+ \pi^-$ decays, which requires a dynamical enhancement of standard model higher-order contributions over tree-level ones by a factor of two. 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 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 a similar level and sign as $D \to \pi^+ \pi^-$, about $ {\cal{O}}(1-2) \cdot 10^{-3}$. Experimental and theoretical constraints narrow down the shape of viable models: anomaly-free models are leptophobic -- or at least electro- and muo-phobic -- with light $Z^\prime$ below ${\cal{O}}(20)$ GeV, and can be searched for in low mass dijets at the LHC, $\Upsilon$ and charmonium decays, and dark photon signatures. A $Z^\prime$ around $\sim 3$ GeV or $\sim (5-7)$ GeV can relieve the tensions in the $J/\psi \to \pi^+ \pi^-$ and $\psi^\prime \to \pi^+ \pi^-$ branching ratios with pion form factors from fits to Babar and JLab data, and simultaneously explain the charm CP asymmetries. Models also feature sizable branching ratios into light right-handed neutrinos or vector-like dark fermions, which can be searched for in $e^+ e^- \to$~hadrons + invisibles at Belle II and BESIII. Due to the low new physics scale dark fermions may induce an early Landau pole which requires UV-completion near the TeV-scale.