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arxiv: 2604.15015 · v2 · submitted 2026-04-16 · ✦ hep-ph

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Production of doubly heavy quarkonium associated with two heavy quarks via top quark decays

Juan-Juan Niu , Xu-Chang Zheng , Hong-Hao Ma
Authors on Pith no claims yet

Pith reviewed 2026-05-10 10:39 UTC · model grok-4.3

classification ✦ hep-ph
keywords top quark decaydoubly heavy quarkoniumB_c mesoncharmoniumNRQCDLHC productionfour-body decaysdecay widths
0
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The pith

Top quark decays into four particles produce B_c mesons and charmonia at observable LHC rates.

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

The paper calculates rates for two specific four-body top-quark decays that produce a doubly heavy quarkonium state together with two additional heavy quarks. It applies nonrelativistic QCD to the color-singlet S-wave channels and obtains explicit decay widths that translate into thousands to millions of events per year at the LHC. These numbers indicate that the new channels dominate charmonium production from top quarks and supply a direct test of the narrow-width approximation for the top quark.

Core claim

Within NRQCD, the decay widths for anti-B_c, anti-B_c*, eta_c and J/psi in the channels t to (b c-bar) + c + c + s-bar and t to (c c-bar) + b + c + s-bar equal 0.2251, 0.3099, 0.0537 and 0.0555 MeV. These widths imply O(10^4--10^6) B_c(*) events and O(10^3--10^5) charmonium events per year at the LHC, establishing the proposed four-body modes as the dominant source of eta_c and J/psi production via top-quark decays.

What carries the argument

NRQCD color-singlet factorization for S-wave quarkonium states applied to the 1 to 4 body top decays that produce a heavy quarkonium plus two heavy quarks.

If this is right

  • This channel supplies a new, sizable production mechanism for B_c mesons at hadron colliders.
  • It accounts for the leading contribution to eta_c and J/psi production in top-quark decays.
  • The four-body final state provides a direct experimental test of the narrow-width approximation for the top quark.
  • Differential distributions from the calculation can guide experimental searches and background estimates.

Where Pith is reading between the lines

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

  • Confirmation of the rates would allow LHC data to constrain the long-distance matrix elements used in the calculation.
  • Top-quark decay simulations used in other analyses may need to include these modes to avoid underestimating rare signals.
  • The same framework could be extended to additional quarkonium states or to next-to-leading-order corrections in future studies.

Load-bearing premise

The color-singlet NRQCD model with wave functions taken from external fits accurately gives the production rates without large higher-order or color-octet corrections.

What would settle it

An LHC measurement of B_c or charmonium yields from top decays that lies well outside the predicted ranges of 10^3 to 10^6 events per year would show the calculated widths are incorrect.

Figures

Figures reproduced from arXiv: 2604.15015 by Hong-Hao Ma, Juan-Juan Niu, Xu-Chang Zheng.

Figure 1
Figure 1. Figure 1: (e–h) t(p0) (bc¯)(p1) c(p2) c(p3) s¯(p4) W+ (a) t(p0) (bc¯)(p1) c(p2) c(p3) s¯(p4) W+ (b) t(p0) (bc¯)(p1) c(p2) c(p3) s¯(p4) W+ (c) t(p0) (bc¯)(p1) c(p2) s¯(p4) c(p3) W+ (d) t(p0) b(p2) (cc¯)(p1) c(p3) s¯(p4) W+ (e) t(p0) b(p2) (cc¯)(p1) c(p3) s¯(p4) W+ (f) t(p0) b(p2) (cc¯)(p1) c(p3) s¯(p4) W+ (g) t(p0) b(p2) (cc¯)(p1) c(p3) s¯(p4) W+ (h) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Invariant-mass differential distributions for th [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Angular and z differential distributions for the four-body top-quark decay channels. From left to right, the panels show dΓ/d cos θ12, dΓ/d cos θ13, dΓ/d cos θ23, and dΓ/dz, where θij denotes the angle between ~pi and ~pj in the top-quark rest frame, and z is the normalized longitudinal momentum fraction of the produced doubly heavy quarkonium. G. Chen, Eur. Phys. J. C 71, 1563 (2011). [32] G. Y. Wang, X. … view at source ↗
read the original abstract

In this paper, we analyze the $1 \rightarrow 4$ decay channel for the production of doubly heavy quarkonium, $(b\bar{c})$ or $(c\bar{c})$, via top-quark decays, $t \to (b\bar{c}) + c + c + \bar{s}$ and $t \to (c\bar{c}) + b + c + \bar{s}$, within the framework of nonrelativistic QCD (NRQCD). The dominant contributions are considered in color-singlet S-wave states, i.e., $(b\bar{c})[^1S_0]$, $(b\bar{c})[^3S_1]$, $(c\bar{c})[^1S_0]$, and $(c\bar{c})[^3S_1]$. Our calculations show that the decay widths for $\bar{B_{c}}$, $\bar{B_{c}^{*}}$, $\eta_{c}$ and $J/\psi$ production are 0.2251, 0.3099, 0.0537 and 0.0555 MeV, respectively, resulting in ${\cal O}(10^{4}\text{--}10^{6})$ level of $\bar{B}_c^{(*)}$ events and ${\cal O}(10^{3}\text{--}10^{5})$ level of charmonium produced at LHC per year. In particular, we find that the dominant contribution to $\eta_{c}$ and $J/\psi$ production via top-quark decays arises from this decay channel proposed in this work. Moreover, this multi-body top-quark decay process can serve as a sensitive probe for validating the narrow-width approximation (NWA). Finally, we provide a detailed analysis of theoretical uncertainties and differential distributions to facilitate the corresponding experimental searches. The production of a hadron associated with three quarks contains rich physical information, providing new insights for the LHC to study $B_c$ mesons and charmonia.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes the 1→4 decay channels t → (b¯c) + c + c + ¯s and t → (c¯c) + b + c + ¯s for producing doubly heavy quarkonia in color-singlet S-wave states within NRQCD. It reports decay widths of 0.2251 MeV for anti-B_c, 0.3099 MeV for anti-B_c*, 0.0537 MeV for η_c, and 0.0555 MeV for J/ψ, leading to estimated LHC event rates of O(10^4–10^6) for B_c(*) and O(10^3–10^5) for charmonium per year. The paper asserts that this channel dominates charmonium production via top decays, discusses its use as a probe for the narrow-width approximation, and provides uncertainty analysis and differential distributions.

Significance. If the results hold and the dominance claim is substantiated, this work identifies a new multi-body production mechanism for B_c mesons and charmonia at the LHC with potentially observable yields, while also offering a test of the narrow-width approximation in top decays. The inclusion of differential distributions and uncertainty estimates strengthens its utility for phenomenology, though the overall impact depends on addressing the lack of comparisons to other charmonium production channels in top decays.

major comments (2)
  1. Abstract: The claim that 'the dominant contribution to η_c and J/ψ production via top-quark decays arises from this decay channel' is unsupported, as the manuscript computes only the proposed 1→4 process in color-singlet NRQCD and provides no quantitative estimates or citations for competing channels (e.g., t → bW with b-fragmentation into charmonium or t → b + gg with gg → charmonium). This renders the dominance assertion unverifiable.
  2. Results (numerical widths): The quoted decay widths (0.2251 MeV, 0.3099 MeV, 0.0537 MeV, 0.0555 MeV) rely on long-distance matrix elements as external inputs; the manuscript must propagate their fitting uncertainties explicitly into the event-rate estimates and dominance claim, as these are load-bearing for the O(10^3–10^6) LHC yields.
minor comments (2)
  1. The abstract and introduction should state the specific values chosen for heavy quark masses m_b, m_c and the renormalization scale for α_s to allow direct reproducibility of the short-distance coefficients.
  2. Ensure that the discussion of the narrow-width approximation includes a clear quantitative test or comparison metric against the full 1→4 calculation to substantiate its utility as a probe.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: Abstract: The claim that 'the dominant contribution to η_c and J/ψ production via top-quark decays arises from this decay channel' is unsupported, as the manuscript computes only the proposed 1→4 process in color-singlet NRQCD and provides no quantitative estimates or citations for competing channels (e.g., t → bW with b-fragmentation into charmonium or t → b + gg with gg → charmonium). This renders the dominance assertion unverifiable.

    Authors: We agree that the dominance claim is not supported by explicit comparisons to other charmonium production mechanisms in top decays. Our calculation is restricted to the color-singlet 1→4 channels under consideration, without quantitative estimates or citations for alternatives such as b-fragmentation or gluon-initiated processes. We will revise the abstract to remove the dominance assertion entirely. The revised text will instead emphasize that this multi-body channel provides a new production mechanism with potentially observable yields, while noting that a comprehensive comparison to competing channels lies beyond the present scope and would require separate calculations. revision: yes

  2. Referee: Results (numerical widths): The quoted decay widths (0.2251 MeV, 0.3099 MeV, 0.0537 MeV, 0.0555 MeV) rely on long-distance matrix elements as external inputs; the manuscript must propagate their fitting uncertainties explicitly into the event-rate estimates and dominance claim, as these are load-bearing for the O(10^3–10^6) LHC yields.

    Authors: We acknowledge that the LDMEs are external inputs whose fitting uncertainties must be propagated to the predicted widths and event rates. Although the manuscript already contains a general uncertainty analysis, it does not explicitly vary the LDMEs within their reported fit errors. In the revision we will add this propagation: we will present the decay widths and corresponding LHC event yields as ranges reflecting the LDME uncertainties, and we will update the discussion of numerical results to reflect these variations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses external LDMEs

full rationale

The paper computes perturbative short-distance coefficients for the 1→4 top-decay channels in color-singlet NRQCD and multiplies by long-distance matrix elements (wave functions at the origin) taken from external fits or lattice QCD. These LDMEs are independent inputs, not fitted or derived within the present work. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation. The dominance assertion for η_c/J/ψ is an evidentiary claim without internal comparison to alternatives, but this is a gap in support rather than a circular reduction of the calculated widths to their own inputs. The framework remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central results rest on standard NRQCD inputs whose values are taken from external literature or fits rather than derived here.

free parameters (3)
  • long-distance matrix elements for color-singlet S-wave states
    Wave functions at the origin or equivalent NRQCD matrix elements for B_c, B_c*, eta_c and J/psi are required inputs and are fitted from other decays or lattice calculations.
  • heavy quark masses m_b and m_c
    Quark masses enter the kinematics and phase space; typical values are chosen from PDG or other fits.
  • strong coupling alpha_s at relevant scales
    Running coupling evaluated at the hard scale of the decay; choice of scale introduces uncertainty.
axioms (2)
  • domain assumption NRQCD factorization theorem separates short-distance coefficients from long-distance matrix elements
    Invoked to justify the perturbative calculation of the hard process times the nonperturbative binding factors.
  • domain assumption Color-singlet S-wave dominance; color-octet and higher orbital contributions negligible
    Stated as the dominant contributions considered in the abstract.

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Reference graph

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