Impact of new invisible particles on $B\to K^{(*)} E_{\rm miss}$ observables

TL;DR

The paper tackles the Belle II hint of an excess in $B^+\to K^+ E_{\text{miss}}$ by exploring NP with light invisible states coupling to $b\to s$ transitions within a low-energy EFT framework. It systematically analyzes both two-body and three-body final states involving new scalars, fermions, and vectors, using a chiral-basis EFT to connect to $B\to K$ and $B\to K^*$ hadronic form factors. A global fit to Belle II, BaBar, and ALEPH data identifies viable scenarios with best-fit masses around a few hundred MeV to a few GeV, notably two-body $m_{\phi/V}=2.1$ GeV and several three-body configurations; some couplings are constrained by existing $B\to K^* E_{\text{miss}}$ and $B_s \to E_{\text{miss}}$ limits. The paper emphasizes that the momentum-transfer spectra, especially the $q^2$ distribution and the $K^*$ polarization fraction $F_L$, provide strong discriminants among NP explanations, and it offers concrete predictions for upcoming Belle II measurements that can confirm or refute these light hidden-sector scenarios, highlighting the broader potential to uncover GeV-scale new physics in rare $b$-hadron decays.

Abstract

Motivated by a recent Belle~II measurement that suggests an excess in the rare decay $B \to K\, E_{\rm miss}$, and building upon our recent differential decay rate likelihood analysis of the existing experimental information, we investigate possible new physics (NP) scenarios in which light invisible states participate in flavour-changing $b \to s$ transitions. In particular, we consider the total and differential $B\to K^* E_{\rm miss}$ decay rates and $K^*$ polarisation effects in each NP scenario preferred by the $B\to K E_{\rm miss}$ measurement. We show that future measurements of these $B \to K^* E_{\rm miss}$ observables will offer decisive discrimination among the different NP explanations. Our results highlight the strong complementarity of the rare semi-invisible $b$-hadron decay observables, and underline the importance of analysing their momentum transfer spectra when probing extensions of the Standard Model that feature new light degrees of freedom.

Figures (10)

• Figure 1: Invisible light new states contributing to the process $B^+ \to K^{+}E_{\text{miss}}$ which can provide a better fit to the Belle II (ITA) data compared to the $\mu \times \text{SM}$. The same states contribute to the associated process $B \to K^* E_{\text{miss}}$, with upcoming measurements expected from Belle II.
• Figure 2: Minimised log-likelihood ratio of the $\mu \times \text{SM}$ and SM plus $\sum X$ scenarios with respect to the SM only hypothesis, for different values of the mass $m_{X}$.
• Figure 3: The predicted number of SM + $\sum X$ signal events for $B\to K E_{\text{miss}}$ in bins of $q_{\text{rec}}^{2}$ for the best-fit masses and couplings in Table \ref{['tab:best-fit']}, accounting for the Belle II, BaBar and LEP data. We compare to the number of observed events (black dots) at Belle II with the backgrounds subtracted.
• Figure 4: SM and SM + $\psi\bar{\psi}$ (Dirac) or $\psi\psi$ (Majorana) predictions for the differential decay rate of $B\to K^{(*)}E_{\text{miss}}$ divided by the total SM decay rate, given the best-fit mass and couplings from the combined likelihood fit.
• Figure 5: SM and SM + $\phi\bar{\phi}$ predictions for the differential decay rate of $B\to K^{(*)}E_{\text{miss}}$ divided by the total SM decay rate, given the best-fit masses and couplings (scalar and vector couplings above and below, respectively) from the combined likelihood fit.