Simultaneous interpretation of $K$ and $B$ anomalies in terms of chiral-flavorful vectors

We address the presently reported significant flavor anomalies in the Kaon and $B$ meson systems such as the CP violating Kaon decay ($\epsilon'/\epsilon$) and lepton-flavor universality violation in $B$ meson decays ($R_{K^{(*)}},{R_{D^{(*)}}}$), by proposing flavorful and chiral vector bosons as the new physics constitution at around TeV scale. The chiral-flavorful vectors (CFVs) are introduced as a 63-plet of the global $SU(8)$ symmetry, identified as the one-family symmetry for left-handed quarks and leptons in the standard model (SM) forming the 8-dimensional vector. Thus the CFVs include massive gluons, vector leptoquarks, and $W',Z'$-type bosons, which are allowed to have flavorful couplings with left-handed quarks and leptons, and flavor-universal couplings to right-handed ones, where the latter arises from mixing with the SM gauge bosons. The flavor texture is assumed to possess a "minimal" structure to be consistent with the current flavor measurements on the $K$ and $B$ systems. Among the presently reported significant flavor anomalies in the Kaon and $B$ meson systems ($\epsilon'/\epsilon$, $R_{K^{(*)}}, {R_{D^{(*)}}}$), the first two $\epsilon'/\epsilon$ and $R_{K^{(*)}}$ anomalies can simultaneously be interpreted by the presence of CFVs, the ${R_{D^{(*)}}}$ anomaly is predicted not to survive, due to the approximate $SU(8)$ flavor symmetry. Remarkably, we find that as long as both of the $\epsilon'/\epsilon$ and $R_{K^{(*)}}$ anomalies persist beyond the SM, the CFVs predict the enhanced $K^+ \to \pi^+ \nu \bar{\nu}$ and $K_L \to \pi^0 \nu \bar{\nu}$ decay rates compared to the SM values, which will readily be explored by the NA62 and KOTO experiments, and they will also be explored in new resonance searches at the Large Hadron Collider.