Big Bang Nucleosynthesis with Long Lived Charged Massive Particles

TL;DR

This work investigates Big Bang Nucleosynthesis in the presence of long-lived CHAMPs, focusing on bound-state formation with light nuclei and the resulting modifications to nuclear reaction rates. It develops a framework for CHAMP capture and recombination, derives binding energies, and extends BBN reaction-rate calculations to CHAMP-bound scenarios, including both charged and neutral bound states and the potential late-time CHAMP decays. The analysis shows that bound-state formation can reduce $^7$Li and alter related channels, particularly for CHAMPs with Z_X>1, while neutral bound states (Z_X=1) can significantly affect D and T reactions; these effects may help alleviate the Li problem in some parameter regimes. The study links collider phenomenology of long-lived charged particles to early-universe cosmology, offering a pathway to test beyond-Standard-Model physics via CHAMP lifetimes, decays, and bound-state dynamics, and highlights the need for improved nuclear data to quantify these effects accurately.

Abstract

We consider Big Bang Nucleosynthesis (BBN) with long lived charged massive particles. Before decaying, the long lived charged particle recombines with a light element to form a bound state like a hydrogen atom. This effect modifies the nuclear reaction rates during the BBN epoch through the modifications of the Coulomb field and the kinematics of the captured light elements, which can change the light element abundances. It is possible that the heavier nuclei abundances such as $^7$Li and $^7$Be decrease sizably, while the ratios $Y_p$, D/H, and $^3$He/H remain unchanged. This may solve the current discrepancy between the BBN prediction and the observed abundance of $^7$Li. If future collider experiments found signals of a long-lived charged particle inside the detector, the information of its lifetime and decay properties could provide insights to understand not only the particle physics models but also the phenomena in the early universe in turn.

Figures (6)

• Figure 1: Theoretical predictions of $Y_p$, D/H, $^3$He/H, $^7$Li/H $^6$Li/H, $^3$He/D and $^6$Li/$^7$Li as a function of the baryon-to-photon ratio $\eta$ in standard BBN with their theoretical errors at 95 $\%$ C.L. The WMAP value of $\eta$ at 95 $\%$ C.L.is also indicated as a vertical band. In the comparison between the BBN prediction and the central value of the observed abundances, it has been pointed out that the SBBN prediction with the WMAP value of the $\eta$ shows too high by a factor of a few in $^7$Li abundance and too low by several orders of magnitude in $^6$Li abundance if there is no late time $^6$Li production other than BBN. Cyburt:2003fe
• Figure 2: $\eta_{(C,X)}/\eta^0_X$ as a function of $T/T_c$ for $\langle \sigma_{r} v \rangle n_C/H|_{T=T_c}$=1, 3, 5, 10, and 30 from left to right, respectively. Here we have ignored the standard BBN processes. Also we have taken the initial condition as $\eta_X(T_c)\sim 0$. If $\langle \sigma_{r} v \rangle n_C/H|_{T=T_c}\gg 1$, the Saha equation will be a good approximation and the capture will immidiately occur at $T\sim T_c$. On the other hand, if $\langle \sigma_{r} v \rangle n_C/H|_{T=T_c}\sim 1$ or less than 1, the approximation by the Saha equation may be falied.
• Figure 3: Theoretical predictions of $Y_p$, D/H, $^3$He/H, $^7$Li/H $^6$Li/H, $^3$He/D and $^6$Li/$^7$Li as a function of $\eta$ in standard BBN (green) and CHAMP BBN in case A (red). Here we have assumed the instantaneous capture of CHAMPs and $n_{\text{C}}/n_{\gamma}=3.0\times 10^{-11}$.
• Figure 4: Ratio of nuclear-reaction rates of SBBN and CBBN in Case B-I and B-II as a function of the cosmic temperature for the relevant processes. Here we assumed the instantaneous capture of CHAMPs by the nuclei. Case B-I means that $E_{\text{CM}}=(\mu_{ab} /\mu_{(aC)b})E_{\text{bin}}+E_0$ in a process $(a,C)+b\to (c,C)+d$ where we take $E_0$ to be the Gamow's peak energy for collisions between two charged elements, and to be $3T/2$ for collisions between a nucleus and a neutron. The Case B-II means that we take $E_{\text{CM}}=E_{\text{bin}} +E_0$ as the CM energy of processes and 10 times larger value of the p-wave part of the cross section of $^7$Be(n,$\alpha$)$^4$He than that in the standard BBN code Wagoner:1969Serpico:2004gx.
• Figure 5: Theoretical prediction of $^7$Li/H ( upper panel) and $^6$Li/$^7$Li ( lower panel) as a function of the baryon-to-photon ratio. The SBBN predictions are marked by the green bands. The red (blue) band is for Case B-I (Case B-II) in CBBN. Here we assumed $n_{\text{C}}/n_{\gamma}=3.0\times 10^{-11}$ and the instantaneous capture of CHAMPs. The definition of Case B-I and Case B-II are same as those in Fig. \ref{['fig:rates']}.