$Z^{\mathrm{\prime }}$ models with less-minimal flavour violation

We study the phenomenology of simplified $Z^{\mathrm{\prime }}$ models with a global $U(2{)}^3$ flavour symmetry in the quark sector, broken solely by the Standard Model Yukawa couplings. This flavour symmetry, known as less-minimal flavour 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 (${ϵ}^{\mathrm{\prime }}\mathrm{/}ϵ$) and in hadronic $B$-decays ($B\to K\pi$ puzzle). Furthermore, once the couplings of the $Z^{\mathrm{\prime }}$ boson to the leptons are included, it is possible to address the intriguing hints for NP (above the 5$\sigma$ level) in $b\to s{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ transitions. Taking into account all flavour observables in a global fit, we find that ${ϵ}^{\mathrm{\prime }}\mathrm{/}ϵ$, the $B\to K\pi$ puzzle and $b\to s \ell^+\ell^-$datacanbeexplainedsimultaneously\mathrm{.}SizeableCPviolationin$b\to s \ell^+\ell^-$observables,inparticular$A_8$, is predicted, which can be tested in the near future, and an explanation of the $B\to K\pi$ and ${ϵ}^{\mathrm{\prime }}\mathrm{/}ϵ$ puzzles leads to effects in di-jet tails at the LHC, that are not far below the current limits. Once $b\to s{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ is included, cancellations in di-muon tails, possibly by a second $Z^{\mathrm{\prime }}$, are required by LHC data.