Big Bang Nucleosynthesis Constraints on Hadronically and Electromagnetically Decaying Relic Neutral Particles

TL;DR

This work analyzes Big Bang Nucleosynthesis in the presence of decaying relic neutral particles across decay times from $10^{-2}$ s to $10^{12}$ s, detailing how hadronic and electromagnetic decays non-thermally alter light-element yields. It couples a cascade nucleosynthesis framework, including tens of non-thermal processes, with a thermonuclear network, using Monte Carlo methods and PYTHIA for hadronization to track energy deposition and secondary production. The study derives conservative bounds on relic abundances as a function of lifetime $\tau_X$, mass $M_X$, and hadronic branching ratio $B_h$, showing that $^4$He constrains early decays, $^2$H and $^6$Li constrain intermediate times, and $^3$He/$^2$H constrain late times; results are provided for $M_X = 1$ TeV and $100$ GeV across a wide range of $B_h$. These constraints—expressed in terms of $\Omega_X h^2$ (or equivalent $n_X M_X/n_\gamma$/$s$) for different $\tau_X$ and $B_h$—offer a valuable tool for testing early-Universe scenarios and particle-physics models that predict decaying relics, such as gravitinos or other superpartners. The analysis carefully preserves data-driven links to observations of $^4$He, D, $^3$He/$^2$H, $^6$Li, and $^7$Li, providing a robust catalog of limits across a broad parameter space.

Abstract

Big Bang nucleosynthesis in the presence of decaying relic neutral particles is examined in detail. All non-thermal processes important for the determination of light-element abundance yields of 2H, 3H, 3He, 4He, 6Li, and 7Li are coupled to the thermonuclear fusion reactions to obtain comparatively accurate results. Predicted light-element yields are compared to observationally inferred limits on primordial light-element abundances to infer constraints on the abundances and properties of relic decaying particles with decay times in the interval 0.01 sec < tau < 10^(12) sec. Decaying particles are typically constrained at early times by 4He or 2H, at intermediate times by 6Li, and at large times by the 3He/2H ratio. Constraints are shown for a large number of hadronic branching ratios and decaying particle masses and may be applied to constrain the evolution of the early Universe.

Figures (11)

• Figure 1: The quantity $E (l_N |{\rm d}E/{\rm d}x|_c)^{-1}$ as a function of nucleon energy $E$, where $l_N$ is the nucleon mean free path and $|{\rm d}E/{\rm d}x|_c$ is the nucleon energy loss per unit path length due to 'continuous' energy losses such as multiple Coulomb scattering. When $E (l_N |{\rm d}E/{\rm d}x|_c)^{-1}\gtrsim 1$ nucleons predominantly loose energy due to nucleon-nucleon scattering and spallation processes, whereas in the opposite case nucleons loose their energy predominantly continuously via multiple electromagnetic scatterings on $e^{\pm}$ and photons (cf. Eq. B.1). Only in the former limit nuclear cascades occur. The quantity is shown for neutrons (green - dashed) at temperatures $T=90$ and $30\,$keV and protons (red - solid) at temperatures $T = 30,10,1$ and $0.01\,$keV as labeled in the figure.
• Figure 2: Probability $P_{^6{\rm Li}}$ of energetic $^{3}$H nuclei (red - solid) and energetic $^{3}$He (blue - dotted) of initial energy $E$ to fuse on ambient $^{4}$He nuclei to form $^{6}$Li via the reactions ${\rm ^{3}H}(\alpha ,n){\rm ^{6}Li}$ and ${\rm ^{3}He}(\alpha ,p){\rm ^{6}Li}$, respectively. The figure shows this probability for $^{3}$H-nuclei at temperatures $T = 5,10,5,1$ and $0.1\,$keV and for $^{3}$He-nuclei at temperature $T = 0.1\,$keV, respectively. Survival of the freshly formed $^{6}$Li nuclei against thermal nuclear reactions is also taken into account as evident by the comparatively low $P_{^6{\rm Li}}$ at $T = 15\,$keV. The figure illustrates that $P_{^6{\rm Li}}$ dramatically increases at $T\sim 5-10\,$keV due to a decrease of the efficiency of Coulomb stopping in this narrow temperature interval (see text).
• Figure 3: Yields of (from top to bottom) neutrons (red), deuterium nuclei (green), tritium nuclei (blue), and $^{3}$He-nuclei (magenta) as a function of cosmic temperature $T$ per hadronically decaying particle $X\to q\bar{q}$ of mass $M_x = 1\,$TeV, where $q$ denotes a quark. Note that initially after hadronization of the $q$-$\bar{q}$ state on average only $1.56$ neutrons result. The remainder of the created neutrons at lower temperatures $T\lesssim 90\,$keV are resulting from the thermalization of the injected neutrons (and protons) due to inelastic nucleon-nucleon scattering processes and $^{4}$He spallation processes. Similarly, all the $^{2}$H,$^{3}$H, and $^{3}$He nuclei are due to $^{4}$He spallation processes and $np$ nonthermal fusion reactions (for $^{2}$H) induced by the thermalization of the injected energetic nucleons. The figure does note include the electromagnetic yields (cf. Fig. \ref{['yieldsEM']}) due to photodisintegration which is inevitable even for a hadronic decay since approximately $45\%$ of the rest mass energy of the decaying particle is converted into energetic $\gamma$-rays and energetic $e^{\pm}$ after hadronization and pion decays.
• Figure 4: Yields of (from top to bottom) $^{3}$He (blue), $^{3}$H (green), $^{2}$H (red), and $^{6}$Li (magenta) nuclei per TeV of electromagnetically interacting energy injected (in form of energetic $\gamma$-rays and energetic $e^{\pm}$) due to photodisintegration reactions ($^{2}$H, $^{3}$H, $^{3}$He, and $^{6}$Li) and fusion reactions ($^{6}$Li) as a function of cosmic temperature.
• Figure 5: Number of destroyed (from top to bottom) $^{4}$He (blue), $^{2}$H (red), $^{3}$He (green), and $^{7}$Li (magenta) ($^{7}$Be - light blue) nuclei per TeV of electromagnetically interacting energy injected into the primordial plasma at temperature $T$. For the purpose of illustration we have taken the $^{7}$Li and $^{7}$Be abundances equal at $^{7}$Li/H = $^{7}$Be/H $\approx 4.34\times 10^{-10}$. In reality it is the sum of both isotopes which is synthesized at ($^{7}$Li + $^{7}$Be)/H $\approx 4.34\times 10^{-10}$ in a SBBN scenario at $\Omega_bh^2\approx 0.02233$ with $^{7}$Be being converted to $^{7}$Li by electron capture at cosmic temperatures $T\approx 0.1 - 1\,$keV.