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

Abstract

We study the phenomenology of simplified $Z^{\prime }$ 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 $\Delta F=2$ 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, once the couplings of the $Z^{\prime }$ boson to the leptons are included, it is possible to address the intriguing hints for NP (above the 5$\sigma$ level) in $b\to s{\ell }^{+}{\ell }^{-}$ transitions. Taking into account all flavour observables in a global fit, we find that ${\epsilon }^{\prime }/\epsilon$, the $B\to K\pi$ puzzle and $b\to s{\ell }^{+}{\ell }^{-}$ data can be explained simultaneously. 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 di-jet tails at the LHC, that are not far below the current limits. Once $b\to s{\ell }^{+}{\ell }^{-}$ is included, cancellations in di-muon tails, possibly by a second $Z^{\prime }$, are required by LHC data.

11 pages, 3 figures, 1 table