A framework for missing-energy searches with anomalous light vectors

Abstract

We study light spin-1 gauge bosons coupled to electroweak-anomalous currents. For generic charge assignments, anomaly cancellation requires new fermions (anomalons) that are chiral under the new abelian symmetry and carry electroweak charges. If their masses arise from the breaking of the new gauge symmetry, integrating them out generates Wess-Zumino interactions fixed by mixed-anomaly matching, providing the infrared description of the theory. We classify minimal anomalon spectra, derive the corresponding effective interactions, and combine experimental constraints with finite-naturalness considerations to bound the UV completion scale. Motivated by recent NA62 and Belle II results, we then develop a unified phenomenological framework for the missing-energy signatures of these anomalous light vectors, focusing on scenarios where the new vector decays predominantly into neutrinos so that the leading probes are rare processes with invisible final states. As applications, we survey current and projected searches across flavour and electroweak observables, including $K\toπE_{\rm miss}$, $B\to K^{(*)}E_{\rm miss}$, and $Z\toγE_{\rm miss}$, and discuss their interplay with direct searches for anomalons.

Figures (3)

• Figure 1: Upper limits (blue lines) at $90\%$ C.L. on $g_X{\cal A}_{XWW}^{\rm SM}$ from the NA62 search NA62:2025upx (left, based on the 2016--2022 dataset) and the KOTO search KOTO:2024zbl (right). The red line in the left panel is the upper limit from the recast of the full 2016--2024 dataset NA62:2025upx of NA62 from Ref. Guadagnoli:2025xnt.
• Figure 2: Left panel: Regions of constant $\Delta\chi^2\equiv\chi^2-\chi^2_{\rm min}$ in the $(g_X{\cal A}_{XWW}^{\rm SM},\,g_X{\cal A}_{XYY}^{\rm SM})$ plane. The green, yellow, and orange bands correspond to the $1\sigma$, $2\sigma$, and $3\sigma$ regions obtained from the combined fit to $B\to K^{(*)}X$ and $Z\to\gamma X$. For comparison, the solid, dashed, and dot-dashed gray contours show the corresponding $1\sigma$, $2\sigma$, and $3\sigma$ regions from $Z\to\gamma X$ alone. The red and blue curves illustrate the predictions of the $L$-only and $L=-4R$ models of Ref. DiLuzio:2025qkc, while the purple curve corresponds to the vectorial model from gauged $\tau$-flavor symmetry. The colored dots mark the best-fit points of each model. Right panel: Improvement with respect to the SM as a function of $g_X$ for the gauged $\tau$-flavor symmetry model with $m_X = 2.1$ GeV. The solid curve includes $B\to K^{(*)}X$ and $Z\to\gamma X$, while the dashed curve omits $Z\to\gamma X$. The gray dashed horizontal lines indicate the $1\sigma$, $2\sigma$, and $3\sigma$ thresholds for a $\chi^2$ distribution with one degree of freedom. The red dashed line shows, for comparison, the significance over the SM for an interpretation of the Belle II excess in terms of neutrino emission.
• Figure 3: Upper panel: Lower limits on the gauge coupling $g_X$ at $90\%$ C.L. for the gauged $\tau$-flavor symmetry benchmark, derived from missing-energy searches in $Z\to\gamma X$ at LEP (L3) L3:1997exg (pink), $K^+\to\pi^+X$ at NA62 NA62:2025upx (red), $K_L\to\pi^0X$ at KOTO KOTO:2024zbl (blue), $D\to\pi X$ at CLEO CLEO:2008ffk (orange), $B\to\pi X,\rho X$ at Belle Belle:2013tnz (purple), and $B^+\to K^+X$ at Belle II Belle-II:2023esi (green, recast in Ref. Abumusabh:2025zsr). Also shown are indicative bounds from direct LHC searches (yellow) and finite-naturalness estimates (gray bands). Lower panel: same as upper panel, considering future projections (dashed lines) for rare meson decays at flavor factories and invisible $Z$ decays at FCC-ee (see text for details).