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Updated BBN Bounds on Hadronic Injection in the Early Universe: The Gravitino Problem

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Pith's one-line read Updated abundances of deuterium, helium-3, helium-4, and lithium-7 tighten Big Bang Nucleosynthesis bounds on hadronic injection and, for a gluon-gluino gravitino, cap the reheating temperature at about 5×10^5 GeV.

desk verdict Useful refresh of hadronic BBN bounds with updated central abundances, but the gravitino headline is oversimplified and the analysis lacks uncertainty propagation. read the letter →

arxiv 2501.09120 v2 pith:6TFR4LYD submitted 2025-01-15 hep-ph astro-ph.CO

Lucia Angel , Giorgio Arcadi , Matheus M. A. Paixão , Farinaldo S. Queiroz This is my paper · ORCID
classification hep-phastro-ph.CO PACS 98.80.Cq14.80.Ly
keywords bigbangnucleosynthesishadronicinjectiongravitinoproblemreheatingtemperaturelong-livedparticleslight-elementabundancesphotodissociationhadrodissociation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the newest measured abundances of the light elements—deuterium, helium-4, helium-3, and lithium-7—put stronger Big Bang Nucleosynthesis limits on long-lived particles that inject hadronic energy into the primordial plasma. Using those updated abundances, it maps model-independent exclusion contours in the plane of particle lifetime and energy injection, and converts them into an upper bound on the reheating temperature for the gravitino, a classic long-lived supersymmetric particle. For a gravitino decaying into a gluon and a gluino, the updated bounds require a reheating temperature below about $5\times10^5$ GeV for gravitino masses below the weak scale, with the tightest constraint coming from helium-3 overproduction. Since the reheating temperature controls the thermal production of dark matter relics, these bounds constrain the early thermal history of the universe.

What carries the argument

The analysis is carried out in the $(\tau_\chi,\, E_{\rm vis}Y_\chi)$ plane, where $E_{\rm vis}Y_\chi = m_\chi Y_\chi$ is the visible energy injected by a particle of mass $m_\chi$ and yield $Y_\chi \equiv n_\chi/s$ at times $t \ll \tau_\chi$; the paper fixes $m_\chi = 1$ TeV and hadronic branching ratio $B_h = 1$. The physics engine is the hadronic shower: at $t \lesssim 100$ s injected nucleons and mesons interconvert protons and neutrons, raising the $n/p$ ratio and hence ${}^4\mathrm{He}$ and D production, while at $t \gtrsim 100$ s high-energy nucleons destroy ${}^4\mathrm{He}$ and produce D, ${}^3\mathrm{He}$, ${}^6\mathrm{Li}$, and ${}^7\mathrm{Li}$. For the gravitino application, the key identity is the thermal yield-to-reheating relation $Y_{3/2} \simeq 1.9\times10^{-12}\,(T_R/10^{10}\,\mathrm{GeV})\,(1+0.045\ln(T_R/10^{10}\,\mathrm{GeV}))\,(1-0.28\ln(T_R/10^{10}\,\mathrm{GeV}))$ imported from Ref. [20], combined with the lifetime scalings $\tau_{3/2} \propto (m_{3/2}/100\,\mathrm{GeV})^{-3}$ for the gluon-gluino and photon-photino channels, which converts the BBN exclusion curves into upper limits on $T_R$ as a function of $m_{3/2}$.

What would settle it

Measure the primordial ${}^3\mathrm{He}$ abundance independently of the central value adopted here, since it drives the low-mass bound; a value a factor of two lower would weaken the $T_R \lesssim 5\times10^5$ GeV constraint, while a value a factor of two higher would strengthen it. Alternatively, determine from colliders whether the gluino is heavier than the gravitino, which rescales the gravitino yield by a known factor and would shift all the quoted $T_R$ curves.

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Extended reading notes

Core claim

The paper's central claim is that present-day measurements of D/H, $Y_p$, ${}^3\mathrm{He}/\mathrm{D}$, and ${}^7\mathrm{Li}/\mathrm{H}$, combined with a hadronic-decay treatment of long-lived particles, yield updated BBN constraints on the hadronic injection parameter $E_{\rm vis}Y_\chi$ across lifetimes $10^{-2}$ to $10^{12}$ s, and that these constraints translate directly into an upper bound on the reheating temperature in the gravitino scenario. The dominant constraints come from overproduction of ${}^3\mathrm{He}$ and D, with ${}^4\mathrm{He}$ ($Y_p$) and ${}^7\mathrm{Li}$ playing secondary roles. Adopting the standard thermal yield $Y_{3/2}(T_R)$ and the gluon-gluino decay channel ($B_h=1$), the paper finds $T_R < 5\times10^5$ GeV for gravitino masses below the weak scale, relaxing to about $10^{10}$ GeV for masses up to $\sim100$ TeV; the photon-photino channel ($B_h \approx 10^{-3}$) yields weaker bounds, with $T_R$ ranging from $5\times10^5$ GeV to $7\times10^8$ GeV below $\sim2$ TeV. The authors state that BBN can thereby be used as a probe of the reheating temperature.

Load-bearing premise

The entire reheating-temperature bound rests on the assumed thermal gravitino yield formula, which presumes gravitinos are produced thermally during reheating with all supersymmetric gauginos lighter than the gravitino; if gravitino production is non-thermal or the sparticle spectrum differs, every quoted $T_R$ limit shifts.

Editorial extensions

If this is right

  • A gravitino with hadronic decays and mass below the weak scale forces $T_R \lesssim 5\times10^5$ GeV in the gluon-gluino channel, which is below the typical temperature needed for thermal weakly interacting dark matter production, thereby constraining dark matter models.
  • The reheating temperature bounds are order-of-magnitude stronger for the gluon-gluino channel than for the photon-photino channel, so the gravitino's decay mode matters as much as its mass for cosmological viability.
  • Hadronic injection from long-lived particles can destroy ${}^7\mathrm{Be}$ and reduce ${}^7\mathrm{Li}$, and the paper's ${}^7\mathrm{Li}/\mathrm{H}$ constraints bracket the parameter region that could alleviate the cosmological lithium problem.
  • For gravitino masses between the weak scale and about 7 TeV, deuterium overproduction gives the strongest limits, with $T_R$ varying from $5\times10^5$ GeV to $2\times10^7$ GeV; above that, proton-neutron interconversion dominates and the bound relaxes toward $10^{10}$ GeV.
  • The bounds are presented as model-independent in the ($\tau_\chi$, $E_{\rm vis}Y_\chi$) plane, so the same updated contours constrain any long-lived particle that decays hadronically, not only the gravitino.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The constraint map is model-independent in ($\tau_\chi$, $E_{\rm vis}Y_\chi$), so the same updated contours would apply to other long-lived hadronically decaying species such as moduli, saxions, or dark-sector particles; the gravitino is the application the authors choose, and this extrapolation goes beyond their explicit scope.
  • If the gravitino yield were instead dominated by nonthermal production, for example from inflaton decay, the $T_R$ bounds derived here would not directly apply; the same BBN contours would instead bound the product of branching ratio and yield, so the quoted $T_R$ limit is contingent on the assumed thermal freeze-in efficiency.
  • A positive measurement of the gluino mass heavier than the gravitino would rescale the gravitino yield by a factor of order $3m_{3/2}^2/m_{\tilde g}^2$, shifting all quoted $T_R$ limits and giving a collider-tested handle on these cosmological bounds.
  • The ${}^3\mathrm{He}$ channel provides the strongest constraints at low gravitino mass, so a future measurement of primordial helium-3 (currently the least well-determined abundance used here) would most directly tighten or loosen the headline $T_R < 5\times10^5$ GeV result.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. This paper revisits Big Bang Nucleosynthesis (BBN) constraints on hadronic energy injection from long-lived particles. Using central observed values of D/H, Yp, 3He/D, and 7Li/H, the authors draw exclusion contours in the (τχ, EvisYχ) plane for mχ = 1 TeV and Bh = 1, and then apply these contours to the gravitino by combining mass-lifetime relations, Eqs. (8)-(9), with the thermal gravitino yield formula, Eq. (7), imported from Ref. [20]. The central result is a reheating-temperature bound for the gluon-gluino channel, quoted in the conclusions as TR < 5×10^5 GeV, with a weaker bound for the photon-photino channel. The model-independent BBN analysis and the updated observational inputs are potentially useful, but the headline gravitino bound depends on a 2005 yield fit that is not re-derived or cross-checked against the modern calculations cited by the authors, and the BBN exclusion contours are based on single central values without uncertainty propagation.

Significance. If the results hold, the paper provides a useful update of hadronic-injection BBN constraints and sharpens the well-known gravitino bound on the reheating temperature. The explicit presentation of constraints in the (τχ, EvisYχ) plane is a strength, and the inclusion of 3He/D and 7Li/H alongside D/H and Yp adds completeness. The authors also state their assumptions clearly, e.g., mχ = 1 TeV and Bh = 1. The main limitation is that the final quantitative claim is only as robust as Eq. (7), which is adopted without re-derivation or comparison with the more recent production calculations cited in Refs. [48,49]; in addition, the absence of observational and nuclear uncertainty envelopes means that the contours and the derived TR limits are not statistical exclusion regions in the usual sense.

major comments (5)
  1. [Sec. IV, Eq. (7), Figs. 4-5] The central quantitative claim, TR < 5×10^5 GeV, is obtained by converting the BBN limits on Y3/2 into limits on TR using the fitting formula Eq. (7), taken verbatim from Ref. [20]. That 2005 formula assumes all supersymmetric particles are lighter than the gravitino and a particular thermal-history setup; the more recent thermal-production calculations cited by the authors, Refs. [48,49], are not used, and no estimate is given for the systematic error in Y3/2 from hadronic versus gauge contributions, heavier gauginos, or nonthermal production. At fixed lifetime the inferred TR scales inversely with the yield normalization, so even a 30% change in Y3/2 shifts the headline bound by roughly 30%. The authors should re-derive or at least cross-check Eq. (7) with modern inputs and quantify the sensitivity of the TR limits to the yield normalization.
  2. [Sec. III and Figs. 2-5] The exclusion contours are computed from single central values of the observed abundances and central values of nuclear cross sections; the text states that the abundances were 'estimated using the central values of cross sections and model parameters.' No 1σ or 95% intervals are propagated, and the quoted observational values are treated as hard cutoffs. Since the contours in Figs. 2 and 3 and the TR limits in Figs. 4 and 5 are derived from these lines, the sharp statement TR < 5×10^5 GeV is not robust against even small shifts in the adopted central values. Please propagate observational and nuclear uncertainties or, failing that, show how the contours move when the abundances are varied within their current uncertainties.
  3. [Secs. III-IV, Figs. 3-5] The BBN constraints are computed only for mχ = 1 TeV and Bh = 1, but they are then applied to gravitino masses spanning roughly 10^2-10^5 GeV through the identification Evis = mχ. The paper does not justify that the hadronic cascade and photodissociation efficiencies are independent of the primary jet energy over this range. If the efficiencies change with Ejet, the (τχ, mχYχ) constraints are not directly transferable to all gravitino masses considered. Please quantify the mχ dependence, for example by repeating the BBN calculation at a low and a high mass, or state the mass interval over which the 1 TeV approximation is valid.
  4. [Sec. IV vs. Sec. V] The conclusion states 'we find TR < 5×10^5 GeV' for the gluon-gluino channel, but Sec. IV gives a more nuanced result: for sub-TeV gravitinos the 3He bound gives TR <~ 5×10^6 GeV, while for masses between the weak scale and 7 TeV the D/H bound gives limits varying from 5×10^5 GeV to 2×10^7 GeV. As written, the headline number is ambiguous and appears to be a global bound when it is actually a mass-dependent limit. The conclusions should specify the mass interval on which the 5×10^5 GeV value applies.
  5. [Sec. II, Refs. [33]] The 'updated' light-element abundances are attributed to Ref. [33], which is the authors' own earlier publication rather than an independent observational compilation. The numerical values used in Figs. 2-5, such as 3He/D = 0.4352, are not traced to primary measurements or to standard compilations such as Refs. [4,5,7,34]. Since the updated observational inputs are the main driver of the claimed improvement, the paper should cite the primary abundance determinations and state any corrections or re-analyses taken from Ref. [33].
minor comments (5)
  1. [References] Ref. [35] duplicates Ref. [20] (the same paper by Kawasaki, Kohri, and Moroi is cited with different formatting); please merge them.
  2. [Sec. II, Eq. (1) and Eq. (4)] The text defines Yi = ni/nb for light elements but Yχ = nχ/s for the decaying particle; the two normalizations should be reconciled or their relationship clarified, since the conversion between nb and s enters the comparison of BBN abundances with Yχ.
  3. [Fig. 3] The legend shows '3He/D' twice and it is not clear what the dashed versus solid purple lines represent; please clarify whether the two curves correspond to different abundance values or different epochs.
  4. [Sec. III] The subsection heading 'Hadronic Injection' appears without a number, interrupting the numbering of Sections III.A and the following material; please fix the section numbering.
  5. [Sec. I and Sec. V] There are several small typos, including the duplicated comma after 'The gravitino is the supersymmetric partner of the graviton [23],,' and 'dark mater relics' in the conclusions; a careful proofreading pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the BBN constraints come from observed abundances and the gravitino yield is an external fitting formula, so the reheating-temperature bounds are derived rather than assumed.

full rationale

The paper's central derivation chain is: observed light-element abundances (Section II) plus a BBN calculation with hadronic energy injection (Section III) produce exclusion contours in the (tau_chi, m_chi Y_chi) plane; the gravitino section then converts Y_chi into a reheating-temperature bound using the externally imported thermal-production fitting formula Eq. (7) from Ref. [20] and the lifetime formulas Eqs. (8)-(9). Nothing in this chain fits a parameter to the final TR bound. Eq. (7) is a parameter-free fitting formula with stated assumptions, and the paper explicitly notes the rescaling needed when gauginos are heavier than the gravitino. The BBN limits are not constructed from the gravitino model, and the observed abundances are external data, not outputs fitted to the gravitino. The only overlapping-author citation is Ref. [33], used for the statement 'The updated abundances of the light elements were taken from [33]'; this is an observational input rather than a model output, and the same observational data are independently represented by the PDG compilation cited as Ref. [34]. A legitimate accuracy concern is that Eq. (7) dates from 2005 while newer gravitino production calculations are cited but not used in the numerical analysis; however, this is a sensitivity or correctness issue, not circularity, because Eq. (7) is an external input and is not fitted to the paper's own exclusions. No equation in the paper reduces to another by construction, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No new parameters are fitted in this paper; the constraints depend on imported formulas from Kawasaki et al. [20] and on the authors' prior abundance compilation [33]. The fixed choices mχ = 1 TeV and Bh = 1 are not scanned, so the 'model-independent' claim is stronger than the actual computation. No new particles or forces are introduced.

free parameters (2)
  • Decaying particle mass mχ = 1 TeV (chosen input)
    All exclusion contours in Figures 2 and 3 are computed for mχ = 1 TeV and Bh = 1, with Evis = mχ; the text calls the results model-independent, but jet energies and spectra depend on this choice.
  • Hadronic branching ratio Bh = 1 (gluon-gluino), 10^-3 (photon-photino)
    The BBN contours are computed for Bh = 1; the gravitino photon-photino case uses Bh = 10^-3 from Ref. [20]. These discrete choices set the energy injected into hadrons and are not scanned or varied.
assumptions (5)
  • domain assumption The standard BBN Boltzmann network (Eq. 1), with η = 6.1e-10 from CMB, correctly predicts light element abundances in the absence of new physics.
    Invoked in Section II; the paper does not implement or audit the nuclear network, deferring technical details to Ref. [29].
  • domain assumption Partons from χ decay hadronize instantaneously on cosmological timescales, and hadronization uncertainties are negligible.
    Section III: 'the partons emitted from the decay of χ are instantaneously hadronized and fragmented into mesons and nuclei'; this underlies the entire jet-shower calculation.
  • domain assumption Equation (7) gives the thermally produced gravitino abundance as a function of reheating temperature, assuming gauginos lighter than the gravitino.
    Section IV; the paper imports this fitting formula from Ref. [20] and uses it to convert BBN yield limits into TR limits.
  • domain assumption The gravitino lifetimes are τ3/2 = 6e7 s (m3/2/100 GeV)^-3 for g + gluino and 4e8 s for γ + photino.
    Section IV, Eqs. (8) and (9), from Ref. [20]; the lifetime sets which BBN exclusion contour applies.
  • domain assumption The adopted light element abundances (D/H = 2.527e-5, Yp = 0.2453, 3He/D = 0.4352, 7Li/H = 1.58e-10) are the correct primordial values, including 7Li despite the lithium problem.
    Section II and Figure 3; the paper explicitly warns that 7Li constraints should be taken with a grain of salt.

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Pith. "Pith review of Updated BBN Bounds on Hadronic Injection in the Early Universe: The Gravitino Problem." pith.science (2026). https://pith.science/paper/6TFR4LYD

@misc{pith2026250109120,
  author       = {Pith},
  title        = {Pith review of: Updated BBN Bounds on Hadronic Injection in the Early Universe: The Gravitino Problem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6TFR4LYD}},
  note         = {Machine review of arXiv:2501.09120}
}
abstract

Late-decaying particles naturally arise in many extensions of the Standard Model, directly impacting key cosmological processes in the early universe, such as Big Bang Nucleosynthesis (BBN). BBN studies often consider electromagnetic energy injection episodes only, but in practice long-lived particles are also amenable to hadronic decays. The latter can greatly alter the predicted abundances of light elements such as $\mathrm{D}/\mathrm{H}$, $Y_p$, ${}^3\mathrm{He}/\mathrm{D}$, and ${}^7\mathrm{Li}/\mathrm{H}$. Incorporating up-to-date measurements, we place constraints on the primordial abundance of long-lived particles as a function of their lifetime. Lastly, we apply our results to the gravitino problem and set bounds on the reheating temperature, which controls the gravitino primordial abundance.

Figures

Figures reproduced from arXiv: 2501.09120 by the authors.

Figure 1
Figure 1. Diagram representing the chain reactions involved of production of light elements during BBN. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Exclusion regions based on the Yp ( [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. BBN bounds on hadronic injection based in the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Upper limits of the reheating temperature, [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Curves for the photon-photino channel. As in the gluon [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

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Reviewed August 10, 2026 · model on record in the stance chip above.