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Probing sterile neutrino in $B$ ($D$) meson decays at Belle II (BESIII)

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Pith's one-line read A missing-mass search in semileptonic B decays at Belle II could constrain or discover GeV-scale sterile neutrinos, with sensitivity comparable to or better than upgraded LHCb for masses below 2 GeV.

arxiv 1908.00376 v2 pith:NLQXE6QE submitted 2019-08-01 hep-ph

C. S. Kim , Youngjoon Kwon , Donghun Lee , Sechul Oh , Dibyakrupa Sahoo This is my paper · ORCID
classification hep-ph
keywords belleneutrinobesiiiconstraintdatadecaysmajoranasterile
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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The reading

Sterile neutrinos are hypothetical heavy cousins of the ordinary neutrinos that do not interact directly with matter, but can mix with electron, muon, and tau neutrinos. The strength of this mixing is usually written as |U_ℓN|^2. This paper proposes using B meson decays at the Belle II experiment in Japan to look for these particles. In a decay like B→DμN, the heavy neutrino N would be invisible, so the detector would only see the D meson and a muon. The unseen mass, computed from the missing energy and momentum, would be exactly the mass of N. In ordinary B decays the missing mass is nearly zero, so a bump in the missing mass distribution would be a clean signal.

Belle II produces billions of B mesons, but only a small fraction can be fully reconstructed with the hadronic tagging method used here. The paper estimates that even with only 4.8×10^8 fully reconstructed B decays, the search could match the sensitivity of a much larger LHCb dataset for sterile neutrinos below about 2 GeV in mass. This is because the proposed mode does not require the heavy neutrino to decay inside the detector, avoiding several suppression factors. The paper also studies the more challenging case where N does decay inside the detector, which could reveal whether the neutrino is its own antiparticle, a Majorana fermion. Here a helicity flip suppression reduces the expected events, especially for light neutrinos.

Overall, the paper provides a concrete, quantitative case for adding this search to the Belle II program. The main caveats are the optimistic assumptions of perfect reconstruction efficiency in the signal and a simplified treatment of backgrounds.

Extended reading notes

Core claim

The central claim is that a missing-mass search in B→DμN decays at Belle II, using hadronically tagged events, can constrain |U_μN|^2 to a level comparable to upgraded LHCb and better below m_N < 2 GeV, and that the sequential decay of N, including helicity flip, can be used to distinguish Dirac from Majorana neutrinos. As stated in the abstract: "Our constraint on |U_μN|^2 that can be achieved from the full Belle II data is comparable with what can be obtained from the much larger data set of the upgraded LHCb." If correct, the paper demonstrates that a comparatively small sample of 4.8×10^8 fully reconstructed B decays yields a competitive sterile-neutrino probe.

Load-bearing premise

The projected limits are directly proportional to the assumed unit reconstruction efficiencies ε_D=ε_μ=1 stated in Section 3. This is load-bearing because Eq. (3) scales the extracted |U|^2 linearly with these efficiencies; if the true efficiencies are 50%, all quoted limits worsen by a factor of two, and the claim of parity with LHCb at m_N<2 GeV could fail, especially since the 50-event threshold is also optimistic.

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Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central projections depend on the same-group theoretical inputs (canonical BR, Γ_N) and on hand-chosen efficiencies and thresholds. No new physical entities are introduced.

free parameters (5)
  • Signal-side reconstruction efficiencies ε_D, ε_μ = assumed = 1
    Set to unity in Eq. (3) to compute projected |U_ℓN|^2 limits; if <1, limits scale linearly.
  • Tau reconstruction efficiency ε_τ = 0.001
    Chosen to represent the fraction of τ decays with measurable 4-momentum; affects |U_τN|^2 constraints.
  • Observation threshold N_obs = 50 events
    Used as the limiting count in Eq. (3) and Fig. 1; arbitrary and optimistic relative to a typical 3-event 95% C.L. Poisson limit.
  • Detector fiducial length L_D = 1 m
    Assumed size of Belle II drift chamber for displaced-vertex acceptance; directly enters P_decay.
  • Soft pion/photon energy cuts = E_π < 0.2 GeV, E_γ < 0.1 GeV
    Define the SM background B→Dμνπ_soft/γ_soft for the illustrative distributions in Fig. 2.
assumptions (5)
  • domain assumption Sterile neutrino N mixes with active neutrinos via |U_ℓN|^2 and has no other interactions
    Standard seesaw extension used throughout; no alternative new-physics contributions are considered in the central constraint.
  • domain assumption Canonical branching ratio Br(B→DℓN) is taken from Ref [19]
    The sensitivity estimate in Eq. (3) uses this theory input without re-derivation; it is a same-group calculation.
  • domain assumption N total decay width Γ_N from Eqs. (30-32) of Ref [19]
    Used in P_decay for the displaced-vertex analysis.
  • domain assumption Hadronic tagging efficiency from Belle II physics book [22]
    The 4.8×10^8 fully reconstructed B events is taken as given.
  • ad hoc to paper Helicity flip factor P_flip approximates the full spin treatment of LNV N decay
    The paper states a full propagator calculation would be more accurate; P_flip is introduced as an effective factor.

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Pith. "Pith review of Probing sterile neutrino in $B$ ($D$) meson decays at Belle II (BESIII)." pith.science (2026). https://pith.science/paper/NLQXE6QE

@misc{pith2026190800376,
  author       = {Pith},
  title        = {Pith review of: Probing sterile neutrino in $B$ ($D$) meson decays at Belle II (BESIII)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NLQXE6QE}},
  note         = {Machine review of arXiv:1908.00376}
}
abstract

We present, how a systematic study of $B \to D\ell N$ ($D \to K \ell N$) decays with $\ell=\mu,\tau$, at Belle II (BESIII) can provide unambiguous signature of a heavy neutrino $N$ and/or constrain its mixing with active neutrinos $\nu_\ell$, which is parameterized by $|U_{\ell N}|^2$. Our constraint on $|U_{\mu N}|^2$ that can be achieved from the full Belle II data is comparable with what can be obtained from the much larger data set of the upgraded LHCb. Additionally, our method offers better constraint on $|U_{\mu N}|^2$ for mass of sterile neutrino $m_N < 2$ GeV. We can also probe the Dirac and Majorana nature of $N$ by observing the sequential decay of $N$, including suppression from observation of a displaced vertex as well as helicity flip, for Majorana $N$.

Figures

Figures reproduced from arXiv: 1908.00376 by the authors.

Figure 1
Figure 1. a also shows that our constraint is comparable with the 95% C.L. upper-limit on |UµN| 2 , shown as a thick solid line, predicted in Ref. [7] based on 4.8 × 1012 B decay events at up￾graded LHCb (with the decay B → Dµµπ). For mN < 2 GeV (important for light sterile neutrino searches) our constraint sig￾nificantly surpasses the above-mentioned constraint predicted for LHCb upgrade. This is primarily due to the suppres… view at source ↗
Figure 2
Figure 2. Distribution of events corresponding to SM process B → Dµνµ, SM background process B → Dµνµπsoft/γsoft, and the new physics (NP) decays B → DµN for mN = (1.0, 2.0, 3.0) ± 0.1 GeV, with respect to a few observables. Note that the number of events for SM and SM background processes are very large and, hence, those are shown with the vertical axis in log-scale, while the NP scenarios are shown in a linear scale. too fe… view at source ↗
Figure 3
Figure 3. Meson-level Feynman diagrams contributing to the decays B 0 → D −µ +µ ∓π ± . The sterile neutrino is produced at the first ver￾tex and decays at the second vertex, which is at an observable distance away from the first vertex. The circular blobs connote the contribu￾tions from the corresponding hadronic form factors and decay con￾stants. The cross in the Majorana scenario denotes the helicity flip involved in the de… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Distribution of number of events of the lepton number con￾serving B → Dµ ±µ ∓π decays. Here we have considered the displaced vertices to lie within 1 m so that the events can be observed at Belle II. In the numerical study shown in [PITH_FULL_IMAGE:figures/full_fig_p0…
Figure 5
Figure 5. Figure 5: Distribution of events for various energies of the neutrino as measured in the B rest frame and considering the events with various displaced vertices of lengths. Here the decays happen within the distance L and only those decays with L 6 1 m are currently feasible for…
Figure 6
Figure 6. Figure 6: Numerical study of feasibility of observing purely Dirac (LNC) signal B → Dµ ±µ ∓π and purely Majorana (LNV) signal B → Dµ ±µ ±π, inside Belle II detector with decay lengths less than 1 m. Here we have neglected the contributions from both |UeN| 2 and |UτN| 2 when comp…

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