We study the phenomenology of simplified $Z^{\prime }$ models with a global $U(2{)}^3$ flavor symmetry in the quark sector, broken solely by the Standard Model Yukawa couplings. This flavor symmetry, known as less-minimal flavor violation, protects $\mathrm{\Delta }F=2$ processes from dangerously large new physics (NP) effects and at the same time provides a free complex phase in $b\to s$ transitions, allowing for an explanation of the hints for additional direct $CP$ violation in kaon decays (${\epsilon }^{\prime }/\epsilon$) and in hadronic $B$-decays ($B\to K\pi$ puzzle). Furthermore, including the couplings of the $Z^{\prime }$ boson to the leptons, it is possible to address the intriguing hints for NP (above the $5\sigma$ level) in $b\to s{\ell }^{+}{\ell }^{-}$ transitions. Taking into account all flavor observables in a global fit, we find that our model can (for the first time) provide a common explanation for ${\epsilon }^{\prime }/\epsilon$, the $B\to K\pi$ puzzle and $b\to s{\ell }^{+}{\ell }^{-}$ data. Sizeable $CP$ violation in $b\to s{\ell }^{+}{\ell }^{-}$ observables, in particular $A_8$, is predicted, which can be tested in the near future, and an explanation of the $B\to K\pi$ and ${\epsilon }^{\prime }/\epsilon$ puzzles leads to effects in dijet tails at the LHC that are not far below the current limits. If we require that also $b\to s{\ell }^{+}{\ell }^{-}$ anomalies are explained, cancellations in dimuon tails (possibly by a second $Z^{\prime }$) are needed to satisfy LHC data.

• Received 7 October 2019
• Revised 3 March 2020
• Accepted 20 April 2020

DOI:https://doi.org/10.1103/PhysRevD.101.095003

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Published by the American Physical Society