Possible solution to the $^7$Li problem by the long lived stau

TL;DR

This work investigates whether the $^7$Li discrepancy between standard BBN predictions and observations can be resolved within the MSSM by introducing a long-lived charged NLSP, the stau, that forms bound states with $^7$Be/$^7$Li during BBN. The mechanism relies on a tiny mass difference $ ext{Δ}m$ between the stau and the neutralino LSP, allowing staus to survive until BBN and drive new destruction channels through hadronic currents, stau-catalyzed fusion, and especially internal conversion in bound states. A numerical exploration shows a viable parameter region around $ ext{Δ}m oughly (100-200)$ MeV and $Y_{ ilde{ au}} oughly 10^{-20}$ where $^7$Li/H is brought into agreement with observations while meeting other light-element constraints, with internal conversion dominating the Li depletion. The findings suggest a potentially testable link between MSSM cosmology and primordial element abundances, though they acknowledge limitations (e.g., Saha-based bound-state estimates) and outline directions for refining the modeling and expanding the parameter scan.

Abstract

Modification of standard big-bang nucleosynthesis is considered in the minimal supersymmetric standard model to resolve the excessive theoretical prediction of the abundance of primordial lithium 7. We focus on the stau as a next-lightest superparticle, which is long lived due to its small mass difference with the lightest superparticle. It provides a number of additional decay processes of $\mathrm{^{7}Li}$ and $\mathrm{^{7}Be}$. A particularly important process is the internal conversion in the stau-nucleus bound state, which destroys the $\mathrm{^{7}Li}$ and $\mathrm{^{7}Be}$ effectively. We show that the modification can lead to a prediction consistent with the observed abundance of $\mathrm{^{7}Li}$.

Figures (5)

• Figure 1: Feynmann diagrams of the decay of staus. (a) $\tilde{\tau} \to \tau \tilde{\chi}^0$, (b) $\tilde{\tau} \to \pi \nu_\tau \tilde{\chi}^0$, and (c) $\tilde{\tau} \to l \nu_l \nu_{\tau} \tilde{\chi}^0$.
• Figure 2: (color online). The lifetime of free stau as the functions of $\delta m$. Here we take $m_{\tilde{\chi}^{0}} = 300 \, \mathrm{GeV}$, $\theta_{\tau} = \pi/3$, and $\gamma_{\tau} = 0$. The hadronic decay is dominant for $\delta m > m_{\pi}$ while the leptonic decay is exclusively allowed for $\delta m < m_{\pi}$.
• Figure 3: The Feynmann diagrams of internal conversion of $^7$Be ($^7$Li).
• Figure 4: (color online). The lifetimes of internal conversion processes as the function of $\delta m$. Top panel: $(\tilde{\tau} {\rm ^7Be}) \to \tilde{\chi}^0 + \nu_{\tau} + {\rm ^7 Li}$, bottom panel: $(\tilde{\tau} {\rm ^7Li}) \to \tilde{\chi}^0 + \nu_{\tau} + {\rm ^7 He}$. We take $m_{\tilde{\chi}^0}$ = 300GeV, $\theta_{\tau}=\pi/3$, and $\gamma_{\tau}=0$ in both figures.
• Figure 5: (color online). The constraints from the light-element abundance shown in the $\delta m$--$Y_{\tilde{\tau}}$ plane. The white region is the parameter space which is consistent with all the observational abundance including $^{7}$Li/H=$(1.23^{+0.32}_{-0.25})\times 10^{-10}$Ryan:1999vr. The regions enclosed by dotted (green), dashed (light blue), and dash-dotted (purple) lines are excluded by the observations on $^4$He, D and $^{6}$Li, respectively. The thick-dotted line represents a yield value of stau whose daughter particle, neutralino, accounts for all the dark matter component. Here we took $\eta = 6.1\times 10^{-10}$, $m_{\tilde{\chi}^0}$ = 300 GeV, $\theta_{\tau}=\pi/3$ and $\gamma_{\tau}=0$.