Z′ models with less-minimal flavor violation

TLDR: In this paper, a simplified version of the standard model with a global flavor symmetry, known as less-minimal flavor violation, was studied and the authors showed that it is possible to explain the hints for additional direct $CP$ violation in kaon decays.

Abstract: We study the phenomenology of simplified ${Z}^{\ensuremath{'}}$ 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 $\mathrm{\ensuremath{\Delta}}F=2$ processes from dangerously large new physics (NP) effects and at the same time provides a free complex phase in $b\ensuremath{\rightarrow}s$ transitions, allowing for an explanation of the hints for additional direct $CP$ violation in kaon decays (${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$) and in hadronic $B$-decays ($B\ensuremath{\rightarrow}K\ensuremath{\pi}$ puzzle). Furthermore, including the couplings of the ${Z}^{\ensuremath{'}}$ boson to the leptons, it is possible to address the intriguing hints for NP (above the $5\ensuremath{\sigma}$ level) in $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ 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 ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$, the $B\ensuremath{\rightarrow}K\ensuremath{\pi}$ puzzle and $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ data. Sizeable $CP$ violation in $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ observables, in particular ${A}_{8}$, is predicted, which can be tested in the near future, and an explanation of the $B\ensuremath{\rightarrow}K\ensuremath{\pi}$ and ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ puzzles leads to effects in dijet tails at the LHC that are not far below the current limits. If we require that also $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ anomalies are explained, cancellations in dimuon tails (possibly by a second ${Z}^{\ensuremath{'}}$) are needed to satisfy LHC data.