Flavor Non-universal Vector Leptoquark Imprints in $K\to \pi \nu\bar \nu$ and $\Delta F = 2$ Transitions

TL;DR

This paper investigates how a TeV-scale leptoquark model, designed to explain B-meson anomalies, impacts rare kaon decays and meson mixing, revealing constraints and correlations that can be tested with future experiments.

Contribution

It introduces a flavor non-universal 4321 gauge model linking B-anomalies to kaon decay constraints and predicts correlated deviations in kaon and lepton flavor universality observables.

Findings

Current $K^+ o \pi^+ u ar u$ measurements constrain the model.

Deviations in kaon decay rates correlate with $R_D$ and $R_{D^*}$ anomalies.

Future data can decisively test the model's predictions.

Abstract

We analyze $K\to \pi \nu\bar \nu$ rates in a model with a TeV-scale leptoquark addressing $B$-meson anomalies, based on the flavor non-universal 4321 gauge group featuring third-generation quark-lepton unification. We show that, together with the tight bounds imposed by $\Delta F = 2$ amplitudes, the present measurement of $\mathcal{B}(K^+ \to \pi^+ \nu \bar\nu)$ already provides a non-trivial constraint on the model parameter space. In the minimal version of the model, the deviations from the Standard Model in $\mathcal{B}(K^+ \to \pi^+ \nu \bar\nu)$ are predicted to be in close correlation with non-standard effects in the Lepton Flavor Universality ratios $R_D$ and $R_{D^*}$. With the help of future data, these correlations can provide a decisive test of the model.