One Loop Calculations of Rare B-decays Beyond the Standard Model

TL;DR

This work investigates down-type vector-like quarks (VLQs) as a minimal extension of the SM to address anomalies in rare B decays. It formulates an EFT with VLQ-induced modifications to Wilson coefficients, including $C_7$, $C_9$, $C_{10}$ and $C_L$, and computes VLQ contributions to loop and tree-level FCNC processes such as $b\to sZ$, $b\to s\mu^+\mu^-$, and $b\to s\nu\bar{\nu}$. By fitting to $B_s\to \mu^+\mu^-$ and $B\to X_s \mu^+\mu^-$, it constrains the mixing parameter $U_{sb}$ and then predicts enhanced branching ratios for $B\to X_s \nu\bar{\nu}$ and $B\to K \nu\bar{\nu}$, potentially accounting for the Belle-II $B^+ \to K^+ \nu\bar{\nu}$ anomaly. The results demonstrate that VLQs can provide a viable, testable source of new physics in flavor, with distinctive signatures in exclusive and inclusive B decays that can be probed by Belle II and LHC experiments.

Abstract

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 $B^+ \to K^+ ν\barν$, 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 $B_s \to μ^+ μ^-$ and $B \to X_s μ^+ μ^-$. 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 $B \to X_s ν\barν$ and $B \to K ν\barν$. $χ^2$ contour analyses indicate that VLQs can account for observed anomalies, providing a viable and testable extension to the SM.

Figures (23)

• Figure 1: Potential for a complex scalar field with $\mu^2 < 0$Buras:2020xsm
• Figure 2: Feynman rules for charged W-fermion couplings
• Figure 3: Flavor changing neutral current at one loop level
• Figure 4: Loop-induced penguin diagrams for FCNC transitions. Left: effective operators with top-quark induced vertices. Right: their one-loop origin via $W$–$t$ loops emitting $Z$, $\gamma$, or gluons G.
• Figure 5: Box diagrams and their decompositions for $b\bar{b} \to d\bar{d}$ and $b \to s \nu \bar{\nu}$ transitions.