Systematic classification of one-loop models addressing the $b \to s ν\barν$ anomaly

TL;DR

The paper tackles the Belle II-driven tension in $b \to s\nu\bar{\nu}$ by systematically constructing one-loop UV completions that generate both left- and right-handed vector operators $\mathcal{O}_V^{L}$ and $\mathcal{O}_V^{R}$ without tree-level mediation. It develops a gauge-invariant topology-based classification, identifies irreducible box diagrams, and matches UV models to SMEFT operators, including DM considerations and the role of Majorana vs Dirac mediators. Two minimal benchmarks, a scalar-rich model and a fermion-rich model, are proposed and subjected to a comprehensive phenomenological analysis, linking high-scale parameters to low-energy observables such as $B \to K^{(*)}\nu\bar{\nu}$, $b \to s\tau\tau$, $\Delta M_s$, $b \to s\gamma$, and $Z$-pole observables. The global constraints imply that, although the models can enhance branching fractions, loop suppression and complementary flavor constraints prevent fully accounting for the current anomaly; only modest improvements are possible under current data, suggesting the need for either different NP dynamics or refined SM predictions to fully resolve the tension.

Abstract

The recent evidence for the decay $B^+ \to K^+ ν\barν$ reported by the Belle II collaboration, combined with the existing constraints on the neutral mode $B^0 \to K^{*0} ν\barν$, implies a deviation from the Standard Model prediction that necessitates New Physics contributions to both left- and right-handed vector currents. We perform a systematic topological classification of renormalizable one-loop completions capable of generating the required dimension-six operators while forbidding tree-level mediation. Based on this classification, we identify and construct two minimal benchmark scenarios -- a scalar-rich model and a fermion-rich model -- and perform a comprehensive phenomenological analysis. Our study demonstrates that while these one-loop models can yield enhancements in the $b \to s ν\barν$ branching fractions, the attainable magnitudes are significantly restricted by the combined effects of loop suppression and complementary flavor constraints, limiting their ability to fully accommodate the current anomaly.

Figures (9)

• Figure 1: One-loop topologies with 3- and 4-point vertices and four external legs. Topologies T1 and T2, highlighted in the red-dashed box, are renormalizable.
• Figure 2: Possible one-loop diagrams for the topologies T1 and T2, where the dashed lines denote scalars and the solid lines denote fermions. All the diagrams for T2 contain a reducible 3-point loop vertex, highlighted in red. The diagram T2-2, enclosed in the green-dashed box, possesses an ultraviolet divergent loop integral.
• Figure 3: The six distinct diagrams that can be constructed from the T1-1 diagram by permuting the external fields ($b, s, \nu, \nu$). The internal fields are fixed as fermions ($\Psi_1, \Psi_3$) and scalars ($X_2, X_4$).
• Figure 4: Illustration of the new diagrammatic contribution that becomes possible in the scalar-rich model when the mediating $\Psi$ is a Majorana particle. The box diagram ($a$) is now accompanied by a "crossed" diagram, denoted ($a^\prime$), where the internal fermion lines are exchanged. Note that this crossed diagram is topologically equivalent to the diagram ($e$).
• Figure 5: Illustration of additional diagrammatic contributions in the fermion-rich model that arise when the scalar mediator $S$ is a real field. The box diagram ($c$) is accompanied by a "crossed-scalar" diagram ($c^\prime$). This crossed diagram can be topologically rearranged to show its equivalence with diagram ($c^{\prime\prime}$), which is itself identical to the box diagram ($d$).