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Stau-catalyzed $^6$Li Production in Big-Bang Nucleosynthesis

K. Hamaguchi, T. Hatsuda, M. Kamimura, Y. Kino, T. T. Yanagida

TL;DR

This work tackles Li-6 production during Big-Bang Nucleosynthesis in scenarios with a long-lived charged relic X^- by solving the exact quantum three-body problem for $^4$He, deuteron, and X^-. Using a state-of-the-art coupled-channel approach within a $^4$He–d cluster model, it computes the $^4$He X^- + d → $^6$Li + X^- reaction rate and the corresponding astrophysical $S$-factor. The key result is $S(E_G)=0.038$ MeV barn at the Gamow peak for $T=10$ keV, yielding $^6$Li|_{CBBN} ≈ $4.3×10^{-11}$ (D/2.78×10^{-5})(n_{X^-}/s/10^{-16})$ in the long-$\tau_X$ limit, which implies $n_{X^-}/s < 1.4×10^{-16}$ from Li^6 observations. This tightens constraints on late-time entropy production and stau/gravitino scenarios, with implications for the reheating temperature and thermal leptogenesis, and provides a robust link between particle physics parameters and BBN abundances.

Abstract

If the gravitino mass is in the region from a few GeV to a few 10's GeV, the scalar lepton X such as stau is most likely the next lightest supersymmetry particle. The negatively charged and long-lived X^- may form a Coulomb bound state (A X) with a nucleus A and may affect the big-bang nucleosynthesis through catalyzed fusion process. We calculate a production cross section of Li6 from the catalyzed fusion (He4 X^-) + d \to Li6 + X^- by solving the Schrödinger equation exactly for three-body system of He4, d, and X. We utilize the state-of-the-art coupled-channel method, which is known to be very accurate to describe other three-body systems in nuclear and atomic reactions. The importance of the use of appropriate nuclear potential and the exact treatment of the quantum tunneling in the fusion process are emphasized. We find that the astrophysical S-factor at the Gamow peak corresponding to T=10 keV is 0.038 MeV barn. This leads to the Li6 abundance from the catalyzed process as Li6|_{CBBN}\simeq 4.3\times 10^{-11} (D/2.8\times 10^{-5}) ([n_{X^-}/s]/10^{-16}) in the limit of long lifetime of X. Particle physics implication of this result is also discussed.

Stau-catalyzed $^6$Li Production in Big-Bang Nucleosynthesis

TL;DR

This work tackles Li-6 production during Big-Bang Nucleosynthesis in scenarios with a long-lived charged relic X^- by solving the exact quantum three-body problem for He, deuteron, and X^-. Using a state-of-the-art coupled-channel approach within a He–d cluster model, it computes the He X^- + d → Li + X^- reaction rate and the corresponding astrophysical -factor. The key result is MeV barn at the Gamow peak for keV, yielding Li|_{CBBN} ≈ (D/2.78×10^{-5})(n_{X^-}/s/10^{-16})\tau_Xn_{X^-}/s < 1.4×10^{-16}$ from Li^6 observations. This tightens constraints on late-time entropy production and stau/gravitino scenarios, with implications for the reheating temperature and thermal leptogenesis, and provides a robust link between particle physics parameters and BBN abundances.

Abstract

If the gravitino mass is in the region from a few GeV to a few 10's GeV, the scalar lepton X such as stau is most likely the next lightest supersymmetry particle. The negatively charged and long-lived X^- may form a Coulomb bound state (A X) with a nucleus A and may affect the big-bang nucleosynthesis through catalyzed fusion process. We calculate a production cross section of Li6 from the catalyzed fusion (He4 X^-) + d \to Li6 + X^- by solving the Schrödinger equation exactly for three-body system of He4, d, and X. We utilize the state-of-the-art coupled-channel method, which is known to be very accurate to describe other three-body systems in nuclear and atomic reactions. The importance of the use of appropriate nuclear potential and the exact treatment of the quantum tunneling in the fusion process are emphasized. We find that the astrophysical S-factor at the Gamow peak corresponding to T=10 keV is 0.038 MeV barn. This leads to the Li6 abundance from the catalyzed process as Li6|_{CBBN}\simeq 4.3\times 10^{-11} (D/2.8\times 10^{-5}) ([n_{X^-}/s]/10^{-16}) in the limit of long lifetime of X. Particle physics implication of this result is also discussed.

Paper Structure

This paper contains 5 sections, 21 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The $X^-$ catalyzed process
  3. Coupled channel method
  4. Nuclear potentials
  5. Three-body basis functions

Figures (3)

  • Figure 1: Three sets of Jacobi coordinates of the $^4{\rm He}+d+X^-$ system. The entrance (exit) channel is described by the coordinate system of $c=1$ ($c=2$).
  • Figure 2: Left panel: Charge form factor of the electron scattering from $^6$Li. The calculated values (experimental data Suelzle1967) are shown by the solid line (filled circles). Right panel: The s-wave phase shift $\delta_0$ of the $^4{\rm He}+d$ scattering at c.m. energy $\varepsilon_{\rm c.m.}^{(1)} < 10$ MeV. The calculated values are shown by the solid line, while the data from the phase-shift analysis are shown by filled circles Jenny1983 and by open circles Gruebler1975.
  • Figure 3: The potential $V_{^4{\rm He}{\hbox{-}}d}(r)$ between $^4{\rm He}$ and deuteron (the solid line). To show its Coulomb barrier tail, the same potential scaled by 100 is shown by the dotted line together with the typical incident kinetic energy $E_{\rm G}\times 100$ denoted by the arrow. The dashed line shows the $^4{\rm He}-d$ relative wave function in the $^6{\rm Li}$ ground state in an arbitrary unit, $\phi_{\rm g.s.}^{(2)}(r)$.