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 $\mathcal{O}(1-2)\cdot 10^{-3}$. 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 $\mathcal{O}(20)$ GeV, and can be searched for in low mass dijets at the LHC, ${\rm Y}$ 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.

arXiv comment13 pages, 5 figures. v2: Fig.1 and discussion on U-Spin improved, minor corrections and references added, v3: match published version

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