Role of heavy neutral lepton in lepton number violating $B$ meson decays

Dhiren Panda; Manas Kumar Mohapatra; Rukmani Mohanta

arxiv: 2604.24305 · v2 · pith:45HPHSDEnew · submitted 2026-04-27 · ✦ hep-ph

Role of heavy neutral lepton in lepton number violating B meson decays

Dhiren Panda , Manas Kumar Mohapatra , Rukmani Mohanta This is my paper

Pith reviewed 2026-05-08 03:13 UTC · model grok-4.3

classification ✦ hep-ph

keywords heavy neutral leptonslepton number violationB meson decaysbranching ratiosbeyond standard modelon-shell mediation

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The pith

Heavy neutral leptons mediate lepton-number violating B and B_c decays with branching ratios up to 10^{-8}.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how heavy neutral leptons beyond the Standard Model can appear in B meson decays that violate lepton number. It constrains the mass and mixing parameters of these leptons from data on B to mu N and B to tau N decays. It then computes the rates for several Delta L=2 processes such as B_c^- to pi^+ mu^- mu^- and B_c^- to J/psi pi^+ mu^- mu^-, with the heavy neutral leptons produced on-shell. For benchmark values |U_mu N|^2 = 10^{-6} and M_N = 2-3 GeV allowed by data, the branching ratios range from O(10^{-13}) to O(10^{-8}), with the largest values in B_c to pi mu mu and strong suppression in the J/psi channel.

Core claim

Using constraints from B to lepton N decays, the branching ratios for lepton-number violating B and B_c decays mediated by on-shell heavy neutral leptons reach up to O(10^{-8}) for |U_mu N|^2 = 10^{-6} and M_N = 2-3 GeV, with B_c^- to pi^+ mu^- mu^- having the largest enhancement and B_c^- to J/psi pi^+ mu^- mu^- being strongly suppressed.

What carries the argument

On-shell heavy neutral leptons (HNLs) acting as mediators in Delta L=2 B meson decay channels, with production and decay rates set by their mass and mixing parameters with active neutrinos.

If this is right

The predicted branching ratios lie in ranges that future B-physics experiments can probe.
B_c decay modes offer greater sensitivity to these HNL effects than ordinary B modes.
The strong channel dependence allows experiments to target specific final states for enhanced signals.
Absence of signals in these channels would tighten the allowed regions for HNL mass and mixing.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Searches at LHCb or Belle II for same-sign muon pairs in B_c decays could directly test these rates.
Confirmation would strengthen the case for HNLs as a source of lepton number violation.
The same on-shell mediation approach could be applied to other meson systems or lepton flavors.

Load-bearing premise

Heavy neutral leptons exist in the GeV mass range, are produced on-shell in B decays, and mediate the lepton number violating processes with mixing values taken from regions allowed by B to mu N and B to tau N data.

What would settle it

A precise measurement of the branching ratio for B_c^- to pi^+ mu^- mu^- that lies well outside the predicted O(10^{-13}) to O(10^{-8}) range for the benchmark |U_mu N|^2 = 10^{-6} and M_N = 2-3 GeV would falsify the central prediction.

Figures

Figures reproduced from arXiv: 2604.24305 by Dhiren Panda, Manas Kumar Mohapatra, Rukmani Mohanta.

**Figure 1.** Figure 1: FIG. 1. Feynman diagrams for LNV meson decays with pos view at source ↗

**Figure 2.** Figure 2: FIG. 2. Confidence regions for the HNL mixing parameter view at source ↗

**Figure 3.** Figure 3: FIG. 3. Confidence regions for view at source ↗

**Figure 4.** Figure 4: FIG. 4. Comparison of limits and predictions for the considered decay modes. For view at source ↗

read the original abstract

We study the phenomenology of heavy neutral leptons (HNLs) in $B$-meson decays as probes of physics beyond the Standard Model. Focusing on the leptonic channels $B \to \mu N$ and $B \to \tau N$, we constrain the allowed regions in the $M_N$--$|U_{\ell N}|^2$ plane using current experimental data. Using these constraints, we investigate lepton-number violating ($\Delta L=2$) processes mediated by on-shell HNLs, including $B_{(c)}^- \to \pi^+ \mu^- \mu^-$ and $B_c^- \to J/\psi\, \pi^+ \mu^- \mu^-$. For benchmark values $|U_{\mu N}|^2 = 10^{-6}$ and $M_N = 2$-- $3\,\mathrm{GeV}$, the predicted branching ratios lie in the range $\mathcal{O}(10^{-13})$--$\mathcal{O}(10^{-8})$. Among the channels, $B_c^- \to \pi^+ \mu^- \mu^-$ shows the largest enhancement, while $B_c^- \to J/\psi\, \pi^+ \mu^- \mu^-$ is strongly suppressed. These results indicate a clear channel dependence, with $B_c$ modes providing enhanced sensitivity to HNL effects and offering promising avenues for future searches of lepton number violation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper applies standard on-shell HNL mediation and existing two-body constraints to give benchmark branching ratios for a few LNV B and B_c channels, with B_c to pi mu mu largest at O(10^{-8}).

read the letter

The paper takes mixing angles allowed by B to l N data and plugs them into calculations for Delta L=2 modes like B_c^- to pi^+ mu^- mu^- and the J/psi version. For |U_muN|^2 = 10^{-6} and M_N = 2-3 GeV the branching ratios fall between 10^{-13} and 10^{-8}, with the plain pi mode enhanced and the J/psi one suppressed by kinematics and matrix elements. They also include the non-B_c channels for comparison. This produces a clear channel hierarchy that follows directly from phase space and standard form factors under the narrow-width approximation. The approach stays within established HNL phenomenology without new assumptions or exotic inputs. The results are transparent enough that the scaling with |U|^2 is obvious and the numerical outputs can be reproduced from the cited form-factor parametrizations. The main limitation is that everything remains benchmark-dependent; the three-body rates scale linearly with the chosen mixing and mass, so they function as illustrative targets rather than independent predictions or new constraints. Off-shell HNL contributions and uncertainty bands on the form factors are not explored in detail. The work is aimed at experimental groups scanning for lepton-number violation in B_c decays at LHCb or Belle II, where the concrete numbers could help prioritize channels. Theorists already familiar with HNL literature will find the extension useful for quick reference but not conceptually new. I would send it for peer review because the calculations are standard, the outputs are checkable, and the channel comparison adds practical value even if the framework is not novel.

Referee Report

0 major / 3 minor

Summary. The manuscript examines heavy neutral leptons (HNLs) as mediators of lepton-number violating (ΔL=2) B and B_c meson decays. It first derives constraints on the mixing parameters |U_ℓN|^2 (ℓ=μ,τ) and M_N from existing data on the two-body decays B→ℓN. These constraints are then used to compute branching ratios for the three-body LNV channels B^-→π^+μ^-μ^-, B_c^-→π^+μ^-μ^- and B_c^-→J/ψ π^+ μ^- μ^- assuming on-shell HNL exchange. For the benchmark point |U_μN|^2=10^{-6} and M_N=2–3 GeV the predicted branching ratios fall in the range O(10^{-13})–O(10^{-8}), with the largest values in the B_c→πμμ channel and strong suppression in the J/ψ mode.

Significance. If the numerical results hold, the work supplies concrete, channel-dependent benchmarks that can directly inform experimental searches for LNV at LHCb and Belle II. The observation that B_c modes are more sensitive than ordinary B modes is a useful phenomenological insight. The calculations rely on standard narrow-width and form-factor techniques already employed in the HNL literature, so the main value lies in the updated constraints and the explicit comparison across channels rather than in novel methodology.

minor comments (3)

The abstract and main text quote an overall branching-ratio range O(10^{-13})–O(10^{-8}) but do not tabulate the individual values for each channel at the benchmark points; a compact table would improve readability and allow direct comparison with experimental sensitivities.
The text states that constraints are taken from 'current experimental data' on B→μN and B→τN; explicit citation of the specific limits (e.g., LHCb or Belle upper bounds) and a brief description of how they are translated into the |U_ℓN|^2–M_N plane would strengthen the presentation.
The suppression of the B_c^-→J/ψ π^+ μ^- μ^- channel is attributed to kinematics and hadronic matrix elements; a short quantitative remark on the relative size of the form-factor suppression versus phase-space effects would clarify the origin of the channel dependence.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment, including the recommendation for minor revision. The referee summary accurately describes the scope, methods, and main findings of our work on HNL-mediated lepton-number violating B and B_c decays. We appreciate the recognition that the channel-dependent branching ratio benchmarks and the enhanced sensitivity of B_c modes constitute useful phenomenological input for LHCb and Belle II searches.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivation constrains |U_ℓN|^2 from experimental limits on B → ℓN two-body decays, then evaluates LNV branching ratios at benchmark points inside the allowed region using standard narrow-width approximation, phase-space integration, and conventional hadronic form factors. These steps are independent calculations; the BRs scale with the chosen |U|^2 by the model's Feynman rules but are not fitted to or defined by the LNV observables themselves. No self-citation load-bearing step, ansatz smuggling, or renaming of known results occurs. The paper is self-contained against external data benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central results rest on benchmark choices for HNL parameters and the assumption that on-shell HNLs mediate the listed ΔL=2 decays; no new independent evidence for the HNL itself is supplied.

free parameters (2)

M_N = 2-3 GeV
Benchmark mass value (2-3 GeV) chosen for numerical predictions of branching ratios.
|U_μN|^2 = 10^{-6}
Benchmark mixing parameter squared (10^{-6}) chosen for numerical predictions of branching ratios.

axioms (1)

domain assumption Heavy neutral leptons can be produced on-shell in B-meson decays and mediate lepton-number violating (ΔL=2) processes.
Standard assumption in HNL phenomenology invoked to connect the constrained mixing region to the predicted branching ratios.

invented entities (1)

Heavy neutral lepton (HNL) no independent evidence
purpose: Mediator particle enabling lepton-number violating B-meson decays
Postulated beyond-Standard-Model state whose existence is assumed rather than demonstrated by new evidence in the paper.

pith-pipeline@v0.9.0 · 5565 in / 1516 out tokens · 46534 ms · 2026-05-08T03:13:05.131477+00:00 · methodology