Leptoquark-mediated Dirac neutrino mass and its impact on $B\to K\nu \bar{\nu }$ and $K\to \pi \nu \bar{\nu }$ decays

Right-handed neutrinos ${\nu }_R$ play a crucial role in flavor-changing neutral-current processes with missing energy, such as $b\to s+\text{slashed}E$ and $d\to s+\text{slashed}E$, where Belle-II reports unexpectedly large branching fraction in $B\to K\nu \bar{\nu }$ decays. Assuming ${\nu }_R$ is the partner of the active neutrino ${\nu }_L$ in the standard model, a Dirac-type neutrino framework emerges. We investigate a scenario of radiative Dirac neutrino mass generation in a scalar leptoquark (LQ) model with a global $U(1{)}_X$ symmetry to suppress Majorana mass, tree-level Dirac mass, and diquark couplings. The simplest LQ realization consists of two $S_1=(3,1,-1\mathrm{/}3)$ LQs with distinct $U(1{)}_X$ charges. A non-Casas-Ibarra parametrization is proposed to match neutrino data with fewer model parameters. Imposing current experimental constraints from meson mixing and lepton flavor-violating processes, we find that right-handed neutrino effects can significantly enhance $B\to K^{(\ast )}\nu \bar{\nu }$ and $K^{+}\to {\pi }^{+}\nu \bar{\nu }$. Additionally, the model predicts excesses in $R_D$ from $B\to D\tau \bar{\nu }$ that remain within $1\sigma$ of current experimental data.