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Big-Bang Nucleosynthesis and Hadronic Decay of Long-Lived Massive Particles

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Masahiro Kawasaki, Kazunori Kohri, Takeo Moroi

Astrophysics · Submitted 24 Aug 2004 · 105 references

Pith's verdict: A careful, well-documented update of the hadronic-decay BBN bounds that has become a standard reference; the 95% C.L. labels on Figs. 38-42 are more precise-sounding than the underlying systematics warrant, but the bounds themselves are conservative and the qualitative conclusion holds.

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CitationKazunori Kohri, Masahiro Kawasaki, Takeo Moroi. "Big-Bang Nucleosynthesis and Hadronic Decay of Long-Lived Massive Particles." arXiv:astro-ph/0408426 (2004). https://pith.science/paper/M5IBN47U
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The paper

The paper claims

The paper argues that hadronic decays of a long-lived massive particle during or after big-bang nucleosynthesis would overproduce deuterium, helium-3, helium-4 and lithium-6, and uses that to place upper bounds on the particle's primordial

The reading

The paper asks how much of a long-lived massive particle $X$ could have existed in the early universe without spoiling the measured abundances of the light elements. If $X$ lives longer than about $0.1$ s, its hadronic decays inject mesons and nucleons into the plasma; at early times these interconvert protons and neutrons, and at later times they break up background helium-4 and produce deuterium, helium-3 and lithium-6. The authors compute those non-thermal reactions with a hadronic-shower model, updated nuclear cross sections and current observational abundances, then derive 95% upper limits on $E_{vis}Y_X$ as a function of the lifetime. The payoff is a model-independent constraint that becomes especially strong when the hadronic branching ratio is sizable, and an application to unstable gravitinos yields upper bounds on the reheating temperature after inflation.

What carries the argument

The load-bearing machinery is a coupled treatment of hadronic showers and big-bang nucleosynthesis. JETSET 7.4 supplies the primary spectra of pions, kaons and nucleons from the decay of $X$; electromagnetic energy-loss rates determine how far an energetic nucleus travels before it scatters off a background proton or helium-4; the condition $R_{H_i}(E^{(in)}_{H_i},tilde{E}^{(R=1)}_{H_i};T)=1$ defines the energy at which that first hadronic scattering occurs. The resulting transfer matrices are iterated through successive generations of the shower to produce the coefficients $xi_D$, $xi_{^3He}$, $xi_T$, $xi_alpha$ and $xi_{^6Li}$, which enter the BBN network as source or sink terms. This is what turns a particle-physics decay model into a quantitative prediction for the light-element abundances.

Extended reading notes

Core claim

The central claim is that non-thermal production of D, $^3$He, $^4$He and $^6$Li by the hadronic decays of a late-decaying particle gives stringent upper bounds on that particle's primordial abundance, particularly when its hadronic branching ratio $B_h$ is close to one. The authors map the excluded region in the plane of lifetime versus $E_{vis}Y_X$ for $m_X=100$ GeV, $1$ TeV and $10$ TeV, and identify three regimes: for $10^{-2}$ s $<~tau_X<~10^2$ s, proton-neutron interconversion raises the helium-4 abundance; for $10^2$ s $<~tau_X<~10^7$ s, hadrodissociation of background helium-4 drives deuterium and lithium-6 production; and for $10^7$ s $<~tau_X<~10^{12}$ s, photodissociation makes helium-3 the limiting element. Applied to an unstable gravitino, the same bounds translate into a reheating temperature below roughly $10^5$-$10^7$ GeV for $m_{3/2}sim mathcal{O}(100)$ GeV with $B_hsim 1$, or below roughly $10^6$-$10^8$ GeV for $B_hsim 10^{-3}$.

Load-bearing premise

The bounds depend on a hadronic-shower model whose energy-transfer parameters, notably the nucleon inelasticity $kappa_p=0.5$, the transverse slope $K_T=140$ MeV and the elastic slope $B_{sl}=28$ GeV$^{-2}$ for $palpha$ scattering, are fixed by hand rather than measured at the relevant energies, so the factor-level precision of the quoted limits rests on those choices.

Editorial extensions

If this is right

  • Any late-decaying particle with a sizable hadronic branching ratio is constrained more strongly than photodissociation-only analyses would suggest, especially for lifetimes between about $0.01$ s and $10^7$ s.
  • For a gravitino of mass around $100$ GeV, hadronic decay modes push the post-inflation reheating temperature below roughly $10^5$-$10^7$ GeV when $B_hsim 1$, and below roughly $10^6$-$10^8$ GeV when $B_hsim 10^{-3}$.
  • Lithium-6 becomes a sensitive probe of hadronic energy injection because energetic tritium and helium-3 produced in the shower can fuse with background helium-4 to make $^6$Li.
  • For lifetimes shorter than about $10^7$ s the upper bound on $E_{vis}Y_X$ scales approximately inversely with $B_h$, while for longer lifetimes photodissociation of helium-4 makes the bound nearly independent of $B_h$.
  • The constraints are stated in terms of $E_{vis}Y_X$ rather than $m_X$ and $Y_X$ separately, so they can be rescaled to moduli, NLSPs or other late-decaying species once the visible energy release and branching ratio are specified.

Reading between the lines

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

  • The quoted factor-level precision of the bounds is limited less by the light-element observations than by the hand-set shower parameters, so a dedicated measurement of nucleon-alpha inelasticity at the relevant energies would sharpen the constraint more than another order-of-magnitude improvement in D/H.
  • The gravitino application creates an implicit tension with high-scale thermal leptogenesis: the same reheating temperature that leptogenesis needs is often excluded unless the gravitino is heavy, stable, or its visible decay is suppressed.
  • Because the excluded region is expressed through $E_{vis}Y_X$, the results can be used as a template for any decaying relic that injects hadronic energy, including candidates not discussed in the paper.
Original abstract

We study the big-bang nucleosynthesis (BBN) with the long-lived exotic particle, called X. If the lifetime of X is longer than \sim 0.1 sec, its decay may cause non-thermal nuclear reactions during or after the BBN, altering the predictions of the standard BBN scenario. We pay particular attention to its hadronic decay modes and calculate the primordial abundances of the light elements. Using the result, we derive constraints on the primordial abundance of X. Compared to the previous studies, we have improved the following points in our analysis: The JETSET 7.4 Monte Carlo event generator is used to calculate the spectrum of hadrons produced by the decay of X; The evolution of the hadronic shower is studied taking account of the details of the energy-loss processes of the nuclei in the thermal bath; We have used the most recent observational constraints on the primordial abundances of the light elements; In order to estimate the uncertainties, we have performed the Monte Carlo simulation which includes the experimental errors of the cross sections and transfered energies. We will see that the non-thermal productions of D, He3, He4 and Li6 provide stringent upper bounds on the primordial abundance of late-decaying particle, in particular when the hadronic branching ratio of X is sizable. We apply our results to the gravitino problem, and obtain upper bound on the reheating temperature after inflation.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,740 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.23 · randomized assignment 0.01 · states quantitative result 0.51 · compares with prior results 0.86 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We study the big-bang nucleosynthesis (BBN) with the long-lived exotic particle, called X. If the lifetime of X is longer than \sim 0.1 sec, its decay may cause non-thermal nuclear reactions during or after the BBN, altering the predictions of the standard BBN scenario. We pay particular attention to its hadronic decay modes and calculate the primordial abundances of the light elements. Using the result, we derive constraints on the primordial abundance of X. Compared to the previous studies, we have improved the following points in our analysis: The JETSET 7.4 Monte Carlo event generator is used to calculate the spectrum of hadrons produced by the decay of X; The evolution of the hadronic shower is studied taking account of the details of the energy-loss processes of the nuclei in the thermal bath; We have used the most recent observational constraints on the primordial abundances of the light elements; In order to estimate the uncertainties, we have performed the Monte Carlo simulation which includes the experimental errors of the cross sections and transfered energies. We will see that the non-thermal productions of D, He3, He4 and Li6 provide stringent upper bounds on the primordial abundance of late-decaying particle, in particular when the hadronic branching ratio of X is sizable. We apply our results to the gravitino problem, and obtain upper bound on the reheating temperature after inflation.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the big-bang nucleosynthesis (BBN) with the long-lived exotic particle, called X. contribution 0.97 0.92 0.02 asserted 0.90
s1 If the lifetime of X is longer than \sim 0.1 sec, its decay may cause non-thermal nuclear reactions during or after the BBN, altering the predictions of the standard BBN scenario. background 0.99 0.12 0.06 hedged possibility 1.00
s2 We pay particular attention to its hadronic decay modes and calculate the primordial abundances of the light elements. contribution 0.71 0.94 0.04 asserted 0.95
s3 Using the result, we derive constraints on the primordial abundance of X. result 0.70 0.96 0.21 asserted 0.98
s4 Compared to the previous studies, we have improved the following points in our analysis: The JETSET 7.4 Monte Carlo event generator is used to calculate the spectrum of hadrons produced by the decay of X; The evolution of the hadronic shower is studied taking account of the details of the energy-loss processes of the nuclei in the thermal bath; We have used the most recent observational constraints on the primordial abundances of the light elements; In order to estimate the uncertainties, we have performed the Monte Carlo simulation which includes the experimental errors of the cross sections and transfered energies. contribution 0.68 0.95 0.03 asserted 0.99
s5 We will see that the non-thermal productions of D, He3, He4 and Li6 provide stringent upper bounds on the primordial abundance of late-decaying particle, in particular when the hadronic branching ratio of X is sizable. result 0.89 0.91 0.60 asserted 0.94
s6 We apply our results to the gravitino problem, and obtain upper bound on the reheating temperature after inflation. result 0.66 0.95 0.19 asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.84 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Abundances of the light elements as functions of
Figure 2. χ 2 variable as a function of η for SBBN with three degrees of freedom. For the constraint on Y , we used Fields and Olive’s result (solid) and Izotov and Thuan’s (dashed), which are given in Eqs. (2.3) and (2.4), respectively. The shaded band (vertical solid lines) shows the baryon-to-photon ratio suggested by the WMAP at the 1σ (2σ) level. For a more precise determination of η, we calculate the χ 2 -variable as a function of η, and the result is shown in
Figure 3. Flow-chart of the hadronic decay of massive particles.
Figure 4. Feynman diagrams for the decay processes
Figure 5. Same as Fig. 4, but for the radiative decay modes. (Here,
Figure 6. Charged-particle multiplicity hNchi per two hadronic jets as a function of the center of mass energy √ s [71]. The solid line is the case with e +e − annihilation, while the dashed one is for the case with p + p(¯p) collisions. For the p + p(¯p) case, we use PYTHIA Monte Carlo event generator and do not include the single diffraction. are hadronized and how the hadrons propagate in the thermal bath. Thus, let us discuss these subjects in this section. 5.1 Hadronization We first consider the hadronization processes. Since we mostly consider the cases where the mass of X is larger th
Figure 7. Spectra of the mesons (π + + π −, K+ + K−, and K0 L ) produced by the e +e − annihilation process as functions of their kinetic energy Ekin. The center-of-mass energy is taken to be √ s = 91.2 GeV. processes are small enough to be neglected. To demonstrate the agreements of the results from the JETSET package with exper￾iments, in
Figure 8. Spectra of the baryons ((a) n+¯n and (b) p+ ¯p) produced by the e +e − annihilation process as functions of their kinetic energy Ekin. The center-of-mass energy is taken to be √ s = 91.2 GeV. 21
Figure 9. Number of the hadrons produced by the e +e − annihilation process as functions of the center-of-mass energy √ s. The dotted, the short dashed, the thin solid, the dot￾dashed, and the long dashed lines are π + +π −, K+ +K−, K0 L , p+ ¯p, and n+ ¯n, respectively. We also plot the charged-particle multiplicity Nch by the thick solid line
Figure 10. Number of the hadrons produced by the p + p(¯p) scattering process. Meanings of the lines are the same as
Figure 11. Cross sections of the pp scattering processes as functions of the kinetic energy of the beam (projectile) proton in the laboratory system. The solid line is the total cross section while the dashed (dotted) line is the elastic (inelastic) cross section
Figure 12. Cross sections of the np scattering processes as functions of the kinetic energy of the beam (projectile) proton in the laboratory system. The solid line is the total cross section while the dashed (dotted) line is the elastic (inelastic) cross section. 28
Figure 13. Cross sections of the pα scattering processes as functions of the kinetic energy of the beam (projectile) proton in the laboratory system. The solid line is the total cross section while the dashed (dotted) line is the elastic (inelastic) cross section
Figure 14. Cross sections of the inelastic pα scattering processes. 29
Figure 15. Contours of the constant E˜(R=1) p , the energy of the proton just before it scatters off the background nuclei (p or 4He). The horizontal axis is the temperature while the vertical one is the initial energy of the proton E(in) p . The numbers in the figure are the values of E˜(R=1) p , and the solid line with “< Eth,pα” shows the contour for E˜(R=1) p being equal to the threshold energy for the destruction process of 4He, E(th) pα = 25 MeV. The horizontal thin-solid line denotes E(in) p = E(th) pα . Here we use η = 6.1×10−10 and Y = 0.25. breaking in this case is estimated to
Figure 16. Same as Fig. 15, but for neutron. (The horizontal thin-
Figure 17. Same as Fig. 15, but for D. The solid line with “
Figure 18. Same as Fig. 15, but for T. The solid line with “
Figure 19. Same as Fig. 15, but for
Figure 20. Same as Fig. 15, but for
Figure 21. Cross sections of the pD scattering processes. 35
Figure 22. Cross sections of the p 3He scattering processes. when they are produced, they are quickly thermalized. In this case, the typical kinetic energy of these hadrons becomes ∼ T. Thus, for the inter-conversion processes, only the exothermic reactions are relevant since the kinetic energy of the thermalized hadrons are expected to be too small to induce endothermic reactions. In addition, the inter-conversion processes occur mostly with very small velocity. Concerning the exothermic reactions, it is well-known that the cross section σ is ap￾proximately inversely proportional to the…
Figure 23. Schematic picture of hadron shower induced by a high ene
Figure 24. Number of produced or destructed hadrons per one ha
Figure 25. Same as Fig. 24, except for
Figure 26. Same as Fig. 24, except for
Figure 27. ξn as a function of the temperature. Here, we take Yp = 0.25 and η = 6.1×10−10 , the total energy of the two hadronic jets is 2Ejet = 100 GeV, 1 TeV and 10 TeV. 48
Figure 28. The cross sections of the 6Li production processes. The solid (dashed) line is for T + 4He → 6Li + n ( 3He + 4He → 6Li + p). 8 Non-thermal Production of Lithium and Beryllium In this section, we discuss the non-thermal production processes of Li and Be. As we have discussed in the previous sections, energetic T, 3He and 4He can be produced by the hadronic or photodissociation processes with the background αBG. Such energetic nuclei may scatter off the background αBG again and produce other nuclei, in particular, 6Li, 7Li, and 7Be. Although these collisions are not so frequent, they…
Figure 29. ξ (T, 3He) 6Li as a function of the temperature for 2Ejet = 100 GeV, 1 TeV and 10 TeV. Here, we take Yp = 0.25 and η = 6.1 × 10−10 . shown in
Figure 30. The cross sections of the 6Li, 7Li and 7Be production process. The solid (dashed) line is for 4He + 4He → 7Li + p ( 3He + 4He → 7Be + n), while thick solid line is the total cross section for the process 4He + 4He → 6Li + · · ·. Although the expressions (8.5) and (8.7) have the same structure, estimation of ξ ( 4He) Ak is rather difficult. This is because we only have insufficient data for the transfered energies to 4He in the non-elastic scattering processes to produce energetic 4He. In particular, for the process p/n + 4He → p/n + 4He + π + · · ·, energy distribution of 4He in…
Figure 31. ξ ( 4He) 6Li , ξ ( 4He) 7Li , and ξ ( 4He) 7Be as functions of the temperature for 2Ejet = 100 GeV, 1 TeV and 10 TeV. Here, we take Yp = 0.25 and η = 6.1 × 10−10 . So far, we have discussed the case where the parent nucleus inducing the non-thermal production of Li and Be is produced by the hadronic scattering processes. Energetic nuclei are, in fact, also produced by the photodissociation processes of αBG. Using energetic photons produced in the electromagnetic shower processes, energetic T and 3He can be produced by the processes γ + αBG → ( T + p 3He + n . Then, using T and 3He…
Figure 32. Contours of constant D/H on the τX vs. EvisYX plane for mX = 1 TeV. Here we take Bh = 1, Evis = mX , and X is assume to decay into two hadronic jets with 2Ejet = mX . Here, we take η = 6.1 × 10−10. In the SBBN, the theoreical predication is (D/H)SBBN = 2.78 × 10−5 . For 6Li, we include the non-thermal secondary production process discussed in the previous section and hence we obtain dn6Li dt = " dn6Li dt # SBBN + " dn6Li dt # photodis + " dn6Li dt # γ+αBG→T/ 3He+··· + BhnX ΓXξ (T, 3He) 6Li . (9.5) Here, the terms with the subscript “SBBN” represent the SBBN contri
Figure 33. Contours of constant 3He/D. Cosmological and model parameters are the same as
Figure 34. Contours of constant Yp. Cosmological and model parameters are the same as
Figure 35. Contours of constant 6Li/H. Cosmological and model parameters are the same as
Figure 36. Contours of constant 7Li/H. Cosmological and model parameters are the same as
Figure 37. Estimated theoretical errors of the ξ-parameters for mX = 1 TeV, Yp = 0.25 and η = 6.1 × 10−10 . In
Figure 38. Upper bounds on mX YX at 95% C.L. for Bh = 1 and mX = 100 GeV. The horizontal axis is the lifetime of X. Here, the lines with “D/H (low)” and “D/H (high)” are for the constraints (2.1) and (2.2), respectively. The straight dashed line is the upper bound by the deviation from the Planck distribution of the CMB. where ¯x th i and ¯x obs i are the center values of xi determined from the theoretical calculation and observations, while σ th i and σ obs i are their errors, respectively. In our analysis, (σ th i ) 2 is calculated by the Monte Carlo analysis. Notice that the χ 2
Figure 39. Same as Fig. 38, but for
Figure 40. Same as Fig. 38, but for
Figure 41. Same as Fig. 38, but for
Figure 42. Same as Fig. 38, but for
Figure 43. Same as Fig. 38, but for
Figure 44. Upper bounds on the reheating temperature as a funct
Figure 45. Upper bounds on the reheating temperature as a funct
Figure 46. The photon spectrum for the background temperatur
Figure 47. Bsl as a function of the center-of-mass energy √ s. The solid (dashed) line denotes the slope parameter for the pp → pp (pp¯ → pp¯) process. Here, the fitting formula given in [91] is used. calculate the slope parameter. #19 We also adopt the same formula for the elastic processes in which the projectile is neutron (i.e., npBG → np). Notice that the Coulomb correction factor for the cross section is within 6% for Kn = 100 MeV (15% for Kn = 10 MeV). Therefore, the error of the transfered energy K′ p for np → np should be within 20%. With Eq. (C.5), we can estimate the averaged transf
Figure 48. Cross section for the process 6Li(p, 3He)4He as a function of the initial energy of 6Li. For the original data, see Refs. [87, 77]. In the calculation of the surviving probability of 6Li, the dominant dissociation process is 6Li(p, 3He)4He. #26 Cross section for this process is given in Refs. [87, 77]. For the readers’ convenience, we show the plot of the cross section for this process in
Figure 49. Contours of constant P6Li→6Li. The horizontal axis is the background temper￾ature while the vertical axis is the initial kinetic energy of 6Li. number of non-thermally produced 6Li. Same is true for 7Li and 7Be when non-thermal production of these light elements are discussed. F Primordial Abundance of Gravitino In this appendix, we evaluate the primordial abundance of the gravitino in the inflationary universe. In particular, we calculate the gravitino abundance as a function of the well￾defined reheating temperature TR. Compared to the old result given in Ref. [9], there are two…

Figures reproduced from arXiv:astro-ph/0408426 by the authors.

References
How later papers used it

225 later papers cite it

Evidence: substantial. 209 of the citing papers share no author with it, and 43 of those carry a confident label from Pith's citation classifier.

Pith read 22 of the 379 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 3 of 9 papers with this label · 2 by the same authors

By the same authors

Uses its data or values 6 of 24 papers with this label
How the literature uses it

206 arXiv papers cite this in 355 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 259 sentences without a confident label

Contests it 1 paper
Builds on it 4 papers
Uses its method or tool 9 papers
Uses its data or values 23 papers
Compares with it 8 papers
Cites it as support 8 papers
  • We will see instances where other constraints, such as overproduction of gravitinos [ref] , insure that the discrete symmetry is broken at a scale well above the reheating temperature; then domain walls have been inflated away provided the scale of inflation is not much below the GUT scale.

    Discrete R Symmetries and Domain Walls · Domain Walls and Discrete $R$ Symmetries · 0.98

  • Actually in the case of sufficiently low abundances compared to the present dark matter relic density, the impact on $^6$Li due to the decays will not be significant [ref] .

    Extremely Long-Lived Charged Massive Particles as A Probe for Reheating of the Universe · CHAMP Big Bang Nucleosynthesis (CBBN) · 0.98

  • Note that for the cosmological times at which photodissociation is effective, $t≳10^4 s$, the muons and pions injected by sub-GeV vectors decay before they are slowed significantly by interactions with the cosmological background [ref] .

    Cosmological Bounds on sub-GeV Dark Vector Bosons from Electromagnetic Energy Injection · Methods for Calculating the Impact on BBN · 0.96

Cites it as background 26 papers

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