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Bipartite Solution to the Lithium Problem

Sougata Ganguly, Tae Hyun Jung, Tae-Sun Park, Chang Sub Shin

Abstract

The primordial lithium problem remains a persistent motivation for new-physics modifications of Big Bang nucleosynthesis, yet the precision of the observed deuterium abundance now places strong constraints on such attempts. This indicates that the challenge is not simply to reduce $^{7}\mathrm{Li}$, but to realize the correlated shifts among light-element abundances required to do so without spoiling deuterium. We investigate this issue in a concrete two-step decay scenario involving two unstable particles undergoing sequential late decays. In the first stage, a majoron with lifetime $τ_J \sim 10\,\text{--}\,10^4\,\mathrm{sec}$ decays predominantly into neutrinos, increasing the neutron abundance and thereby reducing the primordial $^{7}\mathrm{Li}+\!{}^{7}\mathrm{Be}$ yield. This mechanism, however, simultaneously drives deuterium above the observationally allowed range. In the second stage, an axion-like particle with a longer lifetime $τ_φ\gtrsim 10^5\,\mathrm{sec}$ decays into photons, inducing late-time photodissociation that compensates the excess deuterium without erasing the earlier reduction of lithium, while further amplifying the depletion of $^{7}\mathrm{Li}+\!{}^{7}\mathrm{Be}$. Although the setup is model-dependent, it serves as an explicit proof of concept that the lithium abundance can be lowered consistently with current deuterium constraints. More broadly, our analysis highlights that a viable resolution may require a nontrivial combination of decay channels and decay epochs, and clarifies the pattern of abundance response that successful late-decay scenarios must achieve.

Bipartite Solution to the Lithium Problem

Abstract

The primordial lithium problem remains a persistent motivation for new-physics modifications of Big Bang nucleosynthesis, yet the precision of the observed deuterium abundance now places strong constraints on such attempts. This indicates that the challenge is not simply to reduce , but to realize the correlated shifts among light-element abundances required to do so without spoiling deuterium. We investigate this issue in a concrete two-step decay scenario involving two unstable particles undergoing sequential late decays. In the first stage, a majoron with lifetime decays predominantly into neutrinos, increasing the neutron abundance and thereby reducing the primordial yield. This mechanism, however, simultaneously drives deuterium above the observationally allowed range. In the second stage, an axion-like particle with a longer lifetime decays into photons, inducing late-time photodissociation that compensates the excess deuterium without erasing the earlier reduction of lithium, while further amplifying the depletion of . Although the setup is model-dependent, it serves as an explicit proof of concept that the lithium abundance can be lowered consistently with current deuterium constraints. More broadly, our analysis highlights that a viable resolution may require a nontrivial combination of decay channels and decay epochs, and clarifies the pattern of abundance response that successful late-decay scenarios must achieve.

Paper Structure

This paper contains 8 sections, 15 equations, 10 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. EFFECTS OF PARTICLE INJECTION ON BBN
  3. Part I: early-time neutrino injection
  4. Part II: late-time photon injection
  5. SOLUTION TO THE LITHIUM PROBLEM
  6. SUMMARY AND CONCLUSIONS
  7. PHOTO-DISSOCIATION CROSS SECTIONS OF ${}^7\text{Li}$ AND ${}^7\text{Be}$
  8. FITTING COEFFICIENTS

Figures (10)

  • Figure 1: Schematic picture of the bipartite solution.
  • Figure 2: Evolution of $n/\text{H}$ (blue), $\text{D}/\text{H}$ (green), ${}^7\text{Li}/\text{H}$ (magenta), ${}^7\text{Be}/\text{H}$ (black), $({}^7\text{Li}/\text{H} + {}^7\text{Be}/\text{H})$ (purple), and $Y_J$ (gray) as a function of $T$ for $m_J = 100\,\rm MeV$, $\tau_J = 10^3\,\rm sec$, and $Y_J^{(0)} = 3 \times 10^{-6}$. The dashed lines depict their evolution in SBBN.
  • Figure 3: BBN constraint on $\tau_J - Y_J^{(0)}$ plane for $m_J = 100\,\rm MeV$, taken from Chang:2024mvg. Exclusion limit at 95% confidence level (C.L.) from $\text{D}$, ${}^4\text{He}$, and ${}^3\text{He}$ are depicted by green, blue, and magenta colored regions, respectively. The dark gray region is excluded from the majoron domination during/after BBN. The observed value of lithium abundance can be explained in the parameter region outlined by purple dotted lines. $\Delta N_{\rm eff}$ constraint from Planck 2018 and future experiment CMB-S4 CMB-S4:2016ple is depicted by black solid and dashed lines, respectively. The light blue region is excluded from SN 1987A constraint.
  • Figure 4: Evolution of $\text{D}/\text{H}$ (green), ${}^7\text{Li}/\text{H}$ (magenta), ${}^7\text{Be}/\text{H}$ (black), $({}^7\text{Li}+\!{}^7\text{Be})/\text{H}$ (purple), and $Y_\phi$ (gray) are shown as a function of $T$ for $m_\phi = 20\,\rm MeV$, $\tau_\phi = 10^6\,\rm sec$, and $Y_\phi^{(0)} = 10^{-9}$. The dashed lines depict their evolution in SBBN.
  • Figure 5: BBN constraint on $\tau_\phi-Y_\phi^{(0)}$ plane for $m_\phi = 20\,\rm MeV$. The light blue region is excluded from the deuterium abundance at 95% C.L.
  • ...and 5 more figures