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We address the presently reported significant flavor anomalies in the Kaonand $B$ meson systems such as the CP violating Kaon decay($\epsilon'/\epsilon$) and lepton-flavor universality violation in $B$ mesondecays ($R_{K^{(*)}},{R_{D^{(*)}}}$), by proposing flavorful and chiral vectorbosons as the new physics constitution at around TeV scale. Thechiral-flavorful vectors (CFVs) are introduced as a 63-plet of the global$SU(8)$ symmetry, identified as the one-family symmetry for left-handed quarksand leptons in the standard model (SM) forming the 8-dimensional vector. Thusthe CFVs include massive gluons, vector leptoquarks, and $W',Z'$-type bosons,which are allowed to have flavorful couplings with left-handed quarks andleptons, and flavor-universal couplings to right-handed ones, where the latterarises from mixing with the SM gauge bosons. The flavor texture is assumed topossess a "minimal" structure to be consistent with the current flavormeasurements on the $K$ and $B$ systems. Among the presently reportedsignificant 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 beinterpreted by the presence of CFVs, the ${R_{D^{(*)}}}$ anomaly is predictednot to survive, due to the approximate $SU(8)$ flavor symmetry. Remarkably, wefind 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 SMvalues, which will readily be explored by the NA62 and KOTO experiments, andthey will also be explored in new resonance searches at the Large HadronCollider.

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