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REVIEW 3 major objections 4 minor 71 references

A light scalar from rare B decays would decay promptly into long-lived heavy neutrinos that SHiP and FPF@FCC-hh could catch, probing scalar-Higgs mixing near 10^-6 and neutrino mixing near 3×10^-10.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-01 07:07 UTC pith:L25BEIE2

load-bearing objection A useful and mostly sound sensitivity study for a genuinely new decay chain at FPF/SHiP, but a real double-counting error in the signal yield inflates the low-mass reach by up to an order of magnitude; the qualitative conclusions survive after correction. the 3 major comments →

arxiv 2607.21537 v1 pith:L25BEIE2 submitted 2026-07-23 hep-ph

Heavy neutral leptons from light scalar in fixed target and forward search experiments

ShivaSankar K.A. , Souvik Das , Arindam Das , Sanjoy Mandal This is my paper
classification hep-ph PACS 14.60.St14.80.Cp13.20.He12.60.Cn
keywords heavy neutral leptonsright-handed neutrinosU(1)_B−Lseesaw mechanismscalar-Higgs mixinglong-lived particlesSHiPForward Physics Facility
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Neutrino masses motivate a minimal extension of the Standard Model in which a new U(1)_{B−L} symmetry, once broken, gives mass to heavy right-handed partners of the neutrinos and, through the seesaw, explains why the ordinary neutrinos are light. This paper works out an observable consequence of that extension: an extra light scalar that mixes with the Higgs boson, gets produced in rare B-meson decays, and decays almost entirely into pairs of heavy neutrinos once that is kinematically allowed. Because that decay channel dominates, the scalar is short-lived even at very small mixing angles, so the particles that survive to travel into a distant detector are the heavy neutrinos themselves. Modeling the flux, decay geometry, and visible branching fractions at SHiP and the proposed Forward Physics Facility at a 100 TeV FCC-hh, the paper finds projected sensitivities reaching scalar-Higgs mixing near 10^-6 (SHiP, for scalar masses near 1 GeV) and light-heavy neutrino mixing near 3×10^-10 (FPF2 and SHiP, for heavy-neutrino masses of 0.07–0.25 GeV), beyond present bounds. If correct, one detector could simultaneously test the scalar and neutrino sectors of the minimal neutrino-mass mechanism.

Core claim

The paper's central claim is that a single decay chain — B → K(γ) + h2, h2 → NN, N → visible leptons or hadrons — turns future beam-dump and far-forward detectors into joint probes of the scalar and neutrino sectors of the minimal U(1)_{B−L} model. The structural point is that the partial width Γ(h2 → NN) is set by the neutrino Yukawa coupling and is essentially independent of the tiny scalar-Higgs mixing angle, whereas every Standard Model decay of h2 scales with sin²θ; once the channel is open it dominates, the scalar becomes prompt, and the long-lived particle that must be caught inside the detector vessel is the heavy neutrino. Setting M_N = m_h2/4, and restricting to scalar masses below

What carries the argument

The mechanism is the lifetime inversion carried by the scalar decay h2 → NN. The scalar h2 is the U(1)_{B−L} symmetry-breaking singlet mixed with the Standard Model Higgs through angle θ; rare B-meson decays produce it with a rate proportional to sin²θ. Its partial width into heavy-neutrino pairs, Γ ∝ Y_N² m_h2 cos²θ, carries no sinθ suppression, so once m_h2 > 2M_N it dominates the total width and the scalar decays promptly even at mixing angles as small as 10^-6 — the opposite of the usual Higgs-portal scenario, in which the scalar itself is the long-lived particle. The heavy neutrinos then decay through the small light-heavy mixing V_{ℓN}, and the detection probability reduces to P ≈ (L2/

Load-bearing premise

The load-bearing premise is that the scalar h2 decays promptly and predominantly into heavy-neutrino pairs whenever kinematically allowed — the paper assumes a sufficiently large B−L Yukawa coupling and fixes M_N = m_h2/4 — so if the Yukawa is smaller, or the mass ratio differs, the scalar decays to Standard Model particles or becomes long-lived instead, and the quoted sensitivity contours no longer represent the model.

What would settle it

Experimentally: a full-statistics SHiP run (6×10^20 protons on target) with zero events inside the 50 m decay vessel would rule out the claimed reach contours at the stated sinθ and |V_{ℓN}|² values, assuming the background-free estimate holds. Model-side: a Belle II or LHCb search for B → K + h2 with h2 → μμ or ππ that resolves the scalar's Standard Model decays at the same mixing angle would contradict the premise that h2 → NN dominates whenever open; and, using Eqs. (15)–(16) with the parameters behind each benchmark, one can check whether the implied Yukawa coupling is large enough that Γ(

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • SHiP, with its projected 6×10^20 protons on target, would be the strongest single probe of scalar-Higgs mixing in the 0.5–1 GeV scalar-mass window, reaching sinθ near 10^-6 and improving on FPF2 by roughly two orders of magnitude.
  • At sinθ = 10^-3, FPF2 and SHiP would surpass every current bound on |V_{eN}|² for heavy-neutrino masses of 0.125–0.25 GeV and on |V_{μN}|² for 0.07–0.25 GeV, with sensitivities starting around |V_{ℓN}|² ≈ 3×10^-10.
  • The reach is double-edged in the light-heavy mixing: if |V_{ℓN}|² is too small the heavy neutrinos decay past the detector, and if it is too large they decay before reaching it, so each sensitivity contour is bounded on both sides.
  • Existing scalar bounds do not transfer directly to this scenario: the limits from CHARM, LHCb, NA62, KTeV, and others assume the scalar decays only to Standard Model particles, whereas here a kinematically open h2 → NN channel dominates and makes the scalar short-lived.
  • Above the pion threshold the heavy neutrino's branching fraction into visible final states exceeds 90%, so nearly every decay caught in the vessel is reconstructable, supporting the background-free three-event sensitivity estimate.

Where Pith is reading between the lines

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

  • A single SHiP or FPF dataset would constrain sinθ and |V_{ℓN}|² together through the same decay chain, yielding a correlated two-dimensional exclusion that could overconstrain the minimal seesaw parameters in a way the paper's separate one-dimensional contours do not display.
  • The M_N = m_h2/4 identification is a plotting convention rather than a model prediction; scanning over other mass ratios would shift and reshape the reach windows in both figures, and the quoted peak sensitivities should be read as the favorable case at each scalar mass.
  • The projected reach near |V_{ℓN}|² ≈ 3×10^-10 lands almost exactly on the seesaw consistency floor (|V|² ≈ m_ν/M_N) shown in Fig. 6, so a positive signal would probe the minimal model down to its own theoretical basement, while a null result would tighten the seesaw rather than merely exclude an exotic corner.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies a minimal U(1)_{B-L} extension of the SM with a light singlet scalar h2 that mixes with the SM Higgs boson. The scalar is produced in rare B-meson decays and, in the scenario of interest, decays promptly into a pair of heavy neutral leptons (HNLs) with masses M_N = m_h2/4. The HNLs then propagate to SHiP or FPF@FCC and decay inside the detector into visible states. The authors compute expected signal yields, adopt a 3-event background-free sensitivity criterion, and present projected exclusion contours for the scalar-Higgs mixing angle sinθ vs. m_h2 (Fig. 5) and for the light-heavy neutrino mixing |V_eN|^2 and |V_μN|^2 vs. M_N (Fig. 6). The central quantitative claims are that SHiP and FPF2 can reach sinθ ~ 10^-6 for scalar masses near 1 GeV and can probe |V_N|^2 down to ~3×10^-10 in the 0.07–0.25 GeV HNL mass range. The signal calculation in Eqs. (24)–(25) double-counts the visible branching ratio, so all numerical sensitivity contours must be recomputed.

Significance. This is a first dedicated phenomenological study of the 'prompt scalar -> long-lived HNL' topology at far-forward experiments, and the model is well motivated by neutrino-mass generation. The paper provides a useful compilation of existing constraints and clearly states its benchmark assumptions, including the fixed ratio M_N = m_h2/4 and the choice M_Z' = 100 GeV, g_X = 0.01. The h2->NN dominance condition is satisfied for the adopted parameters, and the comparison limits in Fig. 5 are explicitly flagged by the authors as not directly applicable, which is honest. However, the algebraic double-counting of BR(N->visible) in the signal yield affects every curve in Figs. 5 and 6 and the numerical ranges quoted in Sec. IV. The qualitative conclusion that this channel can be competitive is plausible and likely survives, but the corrected contours must be checked, especially the low-mass upper edge of the |V_μN|^2 band, which may shift into regions already constrained by pion/meson peak searches.

major comments (3)
  1. [Sec. IV, Eqs. (24)–(25)] The signal yield double-counts BR(N->visible). Eq. (24) multiplies by BR(N->visible) after Acc has already been defined in Eq. (25) as P(...) × BR(N->visible). Thus N_signal is suppressed by an extra factor of BR_vis relative to the correct expression dσ × 2 BR(h2->NN) × P × BR_vis. The effect is not uniform: on the long-lived (small-mixing) boundary, where P ∝ |V|^2, the 3-event threshold is reached at a |V|^2 value that is a factor ~1/BR_vis larger than the true one, so the quoted lower edge is too conservative; on the short-lived (large-mixing) boundary the quoted upper edge is too small by a comparable factor. With BR_vis ≈ 0.1–0.3 below the pion threshold (Fig. 3), this shifts the low-mass ends of the Figs. 5–6 bands by factors of 3–10. The contours and all quoted ranges in Sec. IV must be recomputed with the correct single factor of BR(N->visible); the claim that the muon-channel r
  2. [Sec. IV, 'we fix M_N = m_h2/4'] The entire sensitivity landscape is mapped along the one-dimensional line M_N = m_h2/4. This is a strong benchmark choice: it simultaneously fixes the scalar mass, the HNL mass, and (through Y_N = √2 M_N/v_{B-L}) the scalar decay width. While the authors state this explicitly, the presented reach in |V_N|^2 as a function of M_N is conditional on this relation. Because the h2 production rate and the h2->NN branching fraction depend on m_h2, a scan over M_N/m_h2, or at least a check at two other ratios, is needed to establish that the quoted regions are representative. The prompt-decay condition h2->NN dominance appears robust for the adopted v_{B-L}, so this is a limitation rather than an internal inconsistency.
  3. [Sec. IV, paragraph before Eq. (24)] Eq. (24) is written as a differential cross-section dσ_h2/(dp_h2 dcosθ_h2) but is then used directly as a total signal rate. The integration over the scalar momentum and angle, and over the HNL momentum and angle entering Acc, is implicit but not shown. This makes it difficult for the reader to reproduce the normalization. Please display the full factorized expression, including the integral over the production phase space and the acceptance function, so that the double-counting issue in Eqs. (24)–(25) can be checked unambiguously.
minor comments (4)
  1. [Sec. IV, first paragraph] Typo: 'the the decay of mesons' should be 'the decay of mesons'.
  2. [Table I] The column 'L/(NPOT/σtotal)' is unclear; please define explicitly how the effective luminosity for SHiP (553 ab^-1) is obtained and how it is used in the signal-rate normalization.
  3. [Fig. 4 caption] The label 'B-L' in the bottom-right panel and in the legends is not self-explanatory; state which shaded regions belong to which reference and how the B−L curve is derived.
  4. [References] Reference [91] is a closely related self-citation to an arXiv preprint (2606.25951); please ensure it is publicly available and consider providing a journal reference if accepted. Minor typographical issues: 'F ASER' appears in Refs. [89,90] and should be 'FASER'; in the caption of Fig. 1, 'mass and scalar mixing' could be 'mass and scalar-mixing angle'.

Circularity Check

0 steps flagged

No significant circularity: the sensitivity curves are independent model calculations with transparent benchmark inputs; self-citations are minor and not load-bearing.

full rationale

The paper's central claims are projected sensitivity curves computed from a U(1)_{B-L} seesaw Lagrangian. Production rates (B → h2, h2 → NN), decay widths, detector acceptances, and visible branching ratios are either standard formulas or explicitly stated model inputs; no sensitivity target is used to fix a parameter, and no plotted quantity reduces to an input by construction. The benchmark choices (sinθ = 10^{-4}, 10^{-3}; |V|^2 = 10^{-6}, 10^{-8}; M_N = m_h2/4; M_Z' = 100 GeV, g_X = 0.01) are transparent scan points rather than fitted parameters. Self-citations appear ([20] for the LEP bound on v_{B-L}, [32,91] for RHN decay widths and the decay-in-volume probability), but these supply standard physics inputs or formulas that are also derivable from external literature cited alongside them ([23-31], [72,89,90]); the load-bearing argument does not terminate in those self-citations. The paper itself notes that the comparison limits in Fig. 5 are not directly applicable because they assume h2 → SM only, which is a scope caveat rather than circularity. A possible internal normalization issue—Eqs. (24)-(25) appear to multiply BR(N→visible) twice—would be an error affecting some contours, not a case of a prediction being equivalent to its inputs by construction, so it does not raise the circularity score.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 0 invented entities

The central calculation rests on standard formulas plus two hand-set relations (M_N=m_h2/4, M_Z'=100 GeV with g_X=0.01) and a set of external inputs (B-meson fluxes, RHN widths). No new particles are introduced by this paper beyond the existing B-L scalar and heavy neutrinos.

free parameters (6)
  • m_h2 (light scalar mass) = scanned 0.01-1 GeV
    Free model parameter of the B-L scalar sector; all sensitivity curves are presented as functions of m_h2.
  • sinθ (scalar-Higgs mixing) = benchmarks 1e-3, 1e-4, 1e-5, 1e-8, 1e-10 in figures
    Central coupling varied to produce sensitivity curves; not fitted to data.
  • |V_eN|^2 and |V_μN|^2 = benchmarks 1e-6 and 1e-8 for projections
    Light-heavy neutrino mixing; benchmark choices define the sinθ projections and the mixing projections are drawn against these couplings.
  • M_N / m_h2 ratio = 1/4
    Chosen by hand before Eq. (24) to map scalar masses to HNL masses; controls kinematics and lifetimes throughout the analysis.
  • M_Z' = 100 GeV
    Fixed in branching-ratio and lifetime figures; Z' is irrelevant once h2->Z'Z' is kinematically forbidden.
  • g_X = 0.01
    B-L gauge coupling fixed in figures; enters the RHN Yukawa through Y_N = 2√2 M_N g_X / M_Z'.
axioms (5)
  • domain assumption Type-I seesaw provides light neutrino masses and defines the mixing V_ℓN = m_D/M_N
    Used throughout to motivate the model and to draw the 'Seesaw' lower bound in Fig. 6; not derived in this paper.
  • ad hoc to paper The scalar h2->NN partial width dominates the total width for the parameter region studied
    Assumed to make h2 decay promptly into heavy neutrinos; stated in Sec. II and Fig. 2; load-bearing for the signature.
  • domain assumption B-meson production spectra at SHiP and FPF are taken from the cited FPF/FASER analyses
    Eqs. (20)-(21) combine detector-dependent meson spectra with scalar branching ratios; the spectra themselves are not in the paper.
  • domain assumption Zero-background approximation with ≥3 signal events gives 95% CL sensitivity
    Used to draw all projected limits; ignores detector backgrounds and systematic uncertainties.
  • domain assumption RHN decay widths and branching ratios are correctly computed in cited refs [23-32]
    Visible branching fractions and lifetimes enter N_signal through Eqs. (24)-(26).

pith-pipeline@v1.3.0-alltime-deepseek · 20651 in / 14668 out tokens · 147828 ms · 2026-08-01T07:07:57.685498+00:00 · methodology

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read the original abstract

The observation of neutrino masses strongly motivates $U(1)_{B-L}$ extensions of the Standard Model, in which heavy neutral leptons acquire Majorana masses through spontaneous $U(1)_{B-L}$ symmetry breaking and generate light neutrino masses via the seesaw mechanism. In this framework, the singlet scalar responsible for symmetry breaking mixes with the SM Higgs boson, allowing it to be produced in rare meson decays. We investigate a scenario in which this light scalar promptly decays into a pair of long-lived heavy neutrinos that subsequently decay into visible charged leptons and hadrons through light-heavy neutrino mixing inside the proposed Forward Physics Facility (FPF) at the FCC-hh and the SHiP beam-dump experiment. Taking into account realistic detector geometries, decay probabilities, and visible branching fractions, we estimate the projected sensitivities to the scalar-Higgs mixing angle as a function of the scalar mass and to the light-heavy neutrino mixing as a function of the heavy neutrino mass. We find that FPF and SHiP can significantly extend the discovery reach for both light scalars and long-lived heavy neutrinos beyond existing experimental limits, providing powerful and complementary probes of neutrino-mass generation and hidden-sector physics.

Figures

Figures reproduced from arXiv: 2607.21537 by Arindam Das, Sanjoy Mandal, ShivaSankar K.A., Souvik Das.

Figure 1
Figure 1. Figure 1: Left panel: branching ratios of scalar h2 into ee, µµ, γγ, ππ (π +π − + π 0π 0 ) and pair of RHNs (NN) as a function of scalar mass, where the solid and dashed line stands for sin2 θ = 10−8 and 10−10, respectively. Right panel: h2 decay length in rest frame as functions of mixing sin θ and scalar mass mh2 . The red (white) contour stands for the decay length Lh2 = 1.5 km (100 m) relevant for FPF (SHiP) det… view at source ↗
Figure 2
Figure 2. Figure 2: Decay length of h2 as a function of its mass without (left panel) and with (right panel) RHN decay channels, for three representative values of the scalar mixing angle, sin θ = 10−3 (red), 10−4 (blue), and 10−5 (green). In the right panel, the three curves coincide. new charged current (CC) and neutral current (NC) in￾teractions as follows L N CC ⊃ − g √ 2 Wµ ¯ℓγµPLVℓN Nm + H.c., (17) LNC ⊃ − g 2 cos θW Zµ… view at source ↗
Figure 3
Figure 3. Figure 3: Branching ratio of RHNs in different modes. The dashed black line in each of the panel stands for the branching [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Existing bounds from various experiments on model parameters: (i) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Prospective limits on sin θ in the left (right) panel as a function of mh2 for long-lived heavy neutrinos produced via the decay of a short-lived scalar and decay dominantly into electrons (muons), assuming |Ve(µ)N | 2 = 10−6 (dot-dashed) and 10−8 (dashed) for the B−L. The red, green and blue curves correspond to FPF1, FPF2 and SHiP experiments considering MN = mh2 /4. Dark gray shaded region is excluded b… view at source ↗
Figure 6
Figure 6. Figure 6: Prospective limits on |Ve(µ)N | 2 in the upper (lower) panel as a function of MN for long-lived heavy neutrinos produced via the decay of a short-lived scalar, assuming sin θ = 10−3 (dot-dashed) and sin θ = 10−4 (dashed). The red, dark-green and dark-cyan curves correspond to FPF1, FPF2 and SHiP experiments considering MN = mh2 /4 for the B−L scenario. The shaded regions are excluded by existing experiment… view at source ↗

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