Hadronic heavy neutral lepton decays to the limit

Impact Assessment

Core Contribution. This is a phenomenology paper that refines the theoretical description of hadronic Heavy Neutral Lepton (HNL) decays in the GeV mass regime — a range where the hadronic (resonance-based) and partonic (quark-level) descriptions must be matched. The paper's three concrete advances are: (1) the first explicit *quantitative* inclusion of three-pion HNL decays mediated by the a₁(1260) resonance, borrowing the well-developed hadronic current machinery from τ-decay physics; (2) full kinematic (mass-split) treatment of three-body Kπ and KK final states; and (3) a proposed matching scheme in which the hadronic-to-partonic transition is set not by the HNL mass but by the invariant mass of the hadronic system q_H, exploiting the near-HNL-mass-independence of the differential width ratio in this projection. These are folded into the public ALPINIST toy-MC framework and used to produce updated total widths, branching ratios, and SHiP sensitivity projections.

Methodological Rigor. The work is careful and well-cross-checked. The authors reproduce known two- and three-body decay formulas, explicitly resolve prefactor-of-2 and κ_h discrepancies among prior references ([5,7,8]), validate their form-factor parametrizations against BaBar, Belle, ALEPH, and CLEO τ-decay data (Figs. 4, 14, 15, 18), and benchmark their τ→3π partial widths against TAUOLA/TAUDECAY and PDG values (Table 6). The q_H-spectral-projection argument is physically motivated (q_H sets the QCD-vacuum scale; N–ℓ/ν interactions are higher electroweak order). Limitations are stated honestly: the partonic widths are LO only, the PYTHIA hadronization is untuned and "does not lead to satisfactory results," and differential phase-space distributions for hadronized final states are missing. This transparency is a strength but also flags that the high-multiplicity (q_H > 2 GeV) regime remains unresolved.

Potential Impact. HNLs are among the most-motivated feebly-interacting particle candidates, and multiple active experiments (SHiP, NA62, LHCb, ATLAS, CMS) are cited as targeting exactly this parameter space. Improved lifetime/width predictions matter directly for displaced-vertex selection efficiencies and for sensitivity forecasting. However, the quantitative payoff is modest: total width changes at the ~10% level for 1–10 GeV, and the sensitivity gain from the new 3π channels is explicitly found to be "marginal" for zero-background experiments. The most actionable conclusion is arguably negative — that high-multiplicity partonic final states "deplete" observable hadronic signatures, undermining exclusive-final-state search strategies above ~2 GeV and favoring jet-like searches. This is a useful cautionary insight for experimental design.

Timeliness & Relevance. Very timely. The paper is aligned with the 2026 European Strategy update, the SHiP approval at ECN3, and a wave of recent HNL searches (2024–2026 references). It engages directly with the very recent Kretz–Nierste N4LO inclusive calculation. The prescription is offered as a practical standard for the community's simulation tools.

Strengths & Limitations.

Other observations. The paper is dense and notation-heavy, with the substantive derivations largely relegated to extensive appendices (D.1–D.4), which aids completeness but hurts readability. The refutation content is real but mild: it argues the widely-used k-factor prescription of Bondarenko et al. overestimates the semileptonic width (especially applying CC-derived R_τ to NC channels), qualifying a load-bearing prior approach rather than overturning it. The replication content (independent confirmation of τ partial widths and prior formula agreements) is a genuine but secondary side-benefit.

Overall, this is a solid, careful, incrementally valuable contribution that will serve as a useful reference and tooling upgrade for the HNL experimental community, but is unlikely to reshape the field or enable qualitatively new capabilities. Its main enduring value may be the q_H-matching framework and the sober message about the limits of exclusive-final-state searches at higher masses.