Rare $B$-meson decays, suppressed in the Standard Model (SM) by the GIM mechanism, are sensitive probes of new physics. In particular, loop-level $b \to s$ transitions can reveal effects of heavy virtual particles such as vector-like quarks (VLQs). VLQs, which do not require electroweak symmetry breaking for mass generation, can mix with SM quarks and induce flavor-changing neutral currents (FCNCs). We investigate the impact of down-type iso-singlet VLQs on the rare decay $B^+ \to K^+ \nu \bar{ \nu}$, a theoretically clean channel sensitive to new physics. The Belle-II collaboration recently reported a branching ratio of $[2.3 \pm 0.5] \times 10^{ -5}$, significantly higher than the SM prediction of $[0.45 \pm 0.07] \times 10^{ -5}$, suggesting possible new contributions. To constrain the relevant mixing parameter $U_{ sb}$, we also analyze related decays such as $B_s \to \mu^+ \mu^-$ and $B \to X_s \mu^+ \mu^-$. Incorporating VLQ effects into the effective field theory framework, we compute modified Wilson coefficients ($C_7$, $C_9$, $C_{ 10}$, $C_L$) and predict enhanced branching ratios for $B \to X_s \nu \bar{ \nu}$ and $B \to K \nu \bar{ \nu}$. $\chi^2$ contour analyses indicate that VLQs can account for observed anomalies, providing a viable and testable extension to the SM.
Categories: hep-ph