One loop calculations of rare 𝐵-decays beyond the standard model

Rare 𝐵-meson decays provide a sensitive window into potential physics beyond the Standard Model (SM), as they occur only through loop-level processes and are heavily suppressed by the Glashow-Iliopoulos-Maiani (GIM) mechanism. These suppressed transitions, such as the 𝑏 → 𝑠 processes, are particularly useful in the investigation of new particles that may contribute through virtual effects. One compelling possibility is the existence of vector-like quarks (VLQs), which can mix with Standard Model quarks and modify flavor-changing neutral current (FCNC) processes. VLQs, being singlets under the electroweak symmetry and not requiring symmetry breaking for mass generation, can be much heavier than SM quarks. Although difficult to detect directly at colliders, their effects may be observed indirectly through precise measurements in rare decays. In this work, we explore the influence of down-type iso-singlet VLQs on rare 𝐵 decays, focusing on decay 𝐵⁺ → 𝐾⁺𝑣𝑣̄, which is both theoretically clean and sensitive to new physics. Recent results from the Belle-II collaboration report a branching ratio of [2.3 ± 0.5 (stat)] × 10⁻⁵ [43], which provides evidence at the 2.7σ level and lies significantly above the Standard Model prediction of [0.45±0.7]×10⁻⁵ [72]. This discrepancy motivates the study of VLQ contributions to this process. To constrain the new physics parameter 𝑈ₛᵦ, we also examine related decays such as 𝐵ₛ → μ⁺μ⁻ and 𝐵 → 𝑋ₛμ⁺μ⁻. Using these constraints, we compute modified Wilson coefficients (C₇, C₉, C₁₀ and CL) within an effective field theory framework, incorporating VLQ contributions. These coefficients are then used to calculate the branching ratios for 𝐵 → 𝑋ₛ𝑣𝑣̄ and 𝐵 → 𝐾𝑣𝑣̄. Our analysis shows that the inclusion of VLQs can significantly enhance these branching ratios. The resulting parameter space, illustrated by ᵪ² contour plots, highlights VLQs as a viable and testable candidate to explain anomalies in rare 𝐵-meson decays.

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