<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi></mml:math>-spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> anomaly in charm

Abstract

The recent measurement of the $CP$ asymmetry in the decay $D\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ by LHCb, combined with $\mathrm{\ensuremath{\Delta}}{A}_{CP}$, evidences a sizable $CP$ asymmetry in the decay $D\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, 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 $\ensuremath{\lesssim}30%$ 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 ${Z}^{\ensuremath{'}}$ models for charm $CP$ asymmetries. Models generically feature explicit $U$-spin and isospin breaking, allowing for correlations with $D\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ and ${D}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$ decays with corresponding $CP$ asymmetries at similar level and sign as $D\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, about $\mathcal{O}(1\ensuremath{-}2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. 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 ${Z}^{\ensuremath{'}}$ below $\mathcal{O}(20)\text{ }\text{ }\mathrm{GeV}$ and can be searched for in low mass dijets at the LHC or in $\mathrm{\ensuremath{\Upsilon}}$ and charmonium decays, as well as dark photon searches. A ${Z}^{\ensuremath{'}}$ around $\ensuremath{\sim}3$ or $\ensuremath{\sim}(5--7)\text{ }\mathrm{GeV}$ can relieve the tensions in the $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ 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 ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{hadrons}+\mathrm{invisibles}$ 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.

Topics & Concepts