Revisiting big-bang nucleosynthesis constraints on long-lived decaying particles

We study the effects of long-lived massive particles, which decayed during the big-bang nucleosynthesis (BBN) epoch, on the primordial abundance of light elements. Compared to previous studies, (i) the reaction rates of standard BBN reactions are updated, (ii) the most recent observational data on the light element abundance and cosmological parameters are used, (iii) the effects of the interconversion of energetic nucleons at the time of inelastic scattering with background nuclei are considered, and (iv) the effects of the hadronic shower induced by energetic high-energy antinucleons are included. We compare the theoretical predictions on the primordial abundance of light elements with the latest observational constraints, and we derive upper bounds on the relic abundance of the decaying particle as a function of its lifetime. We also apply our analysis to an unstable gravitino, the superpartner of a graviton in supersymmetric theories, and obtain constraints on the reheating temperature after inflation.

Figure 1

Flowchart of the effects of the decay of massive particles. New effects induced by “energetic” antinucleons ($\overline{n}$ and $\overline{p}$) are included in this paper.

Figure 2

Schematic picture of a hadronic shower induced by a high-energy projectile $n$ (or $p$) which scatters off the background proton or the background ${}^4\mathrm{He}$. (Here, $T$ denotes tritium.)

Figure 3

The same as Fig. 2, but for a high-energy projectile $\overline{n}$ (or $\overline{p}$).

Figure 4

Theoretical predictions of the light element abundance as functions of the baryon-to-photon ratio $\eta =n_{\mathrm{B}}/n_{\gamma }$. (The upper horizontal axis shows ${\mathrm{\Omega }}_{\mathrm{B}}{h}^2$, where ${\mathrm{\Omega }}_{\mathrm{B}}$ is the density parameter of baryon and $h$ is the Hubble constant in units of $100\mathrm{km}/\sec /\mathrm{Mpc}$.) The vertical band shows $\eta =(6.11\pm 0.08)\times {10}^{-10}$, which is the $2\sigma$ band of the baryon-to-photon ratio suggested by the CMB observations [41]. For $Y_p$, we plot results for an effective number of neutrino species $N_{\nu }=2$, 3, and 4 (from bottom to top). The boxes indicate the observational values with $2\sigma$ uncertainties. [For $Y_p$, the boxes surrounded by the solid and dashed lines correspond to Eq. (2.4) and (2.3), respectively.]

Figure 5

${\tilde{\xi }}_{n,N}$ values for $T=4\mathrm{keV}$ as functions of the kinetic energy (left panel) and those for $E_N=1\mathrm{TeV}$ as functions of the cosmic temperature (right panel). Here, $N=n$, $\overline{n}$, $p$, and $\overline{p}$, and we have $\eta =6.1\times {10}^{-10}$ and $Y_p=0.25$.

Figure 6

${\tilde{\xi }}_{\mathrm{D},N}$ values for $T=4\mathrm{keV}$ as functions of the kinetic energy (left panel) and those for $E_N=1\mathrm{TeV}$ as functions of the cosmic temperature (right panel). Here, $N=n$, $\overline{n}$, $p$, and $\overline{p}$, and we have $\eta =6.1\times {10}^{-10}$ and $Y_p=0.25$.

Figure 7

${\tilde{\xi }}_{\mathrm{T},N}$ values for $T=4\mathrm{keV}$ as functions of the kinetic energy (left panel) and those for $E_N=1\mathrm{TeV}$ as functions of the cosmic temperature (right panel). (In the subscript of ${\tilde{\xi }}_{\mathrm{T},N}$, T denotes tritium.) Here, $N=n$, $\overline{n}$, $p$, and $\overline{p}$, and we have $\eta =6.1\times {10}^{-10}$ and $Y_p=0.25$.

Figure 8

${\tilde{\xi }}_{{}^3\mathrm{He},N}$ values for $T=4\mathrm{keV}$ as functions of the kinetic energy (left panel) and those for $E_N=1\mathrm{TeV}$ as functions of the cosmic temperature (right panel). Here, $N=n$, $\overline{n}$, $p$, and $\overline{p}$, and we have $\eta =6.1\times {10}^{-10}$ and $Y_p=0.25$.

Figure 9

${\tilde{\xi }}_{\alpha ,N}$ values for $T=4\mathrm{keV}$ as functions of the kinetic energy (left panel) and those for $E_N=1\mathrm{TeV}$ as functions of the cosmic temperature (right panel). Here, $N=n$, $\overline{n}$, $p$, and $\overline{p}$, and we have $\eta =6.1\times {10}^{-10}$ and $Y_p=0.25$.

Figure 10

${\tilde{\xi }}_{\alpha ,N}$ values for $T=4\mathrm{keV}$ as functions of the kinetic energy, plotted using the current method (the red and blue lines) as well as the old method, which is without the interconversion between $n$ and $p$ at inelastic scattering (the black lines). Here, we follow the same parameters as those used in the left panel of Fig. 9.

Figure 11

Constraints on $m_X{Y}_X$ vs the ${\tau }_X$ plane, assuming that the main decay modes are $e^{+}{e}^{-}$ (left panel) or $b\overline{b}$ (right panel). The BBN constraints come from ${}^4\mathrm{He}$ (the green lines), D (the cyan lines), and ${}^3\mathrm{He}/\mathrm{D}$ (the red lines). The orange shaded region is excluded by the CMB spectral distortion.

Figure 12

Constraints on the $m_X{Y}_X$ vs ${\tau }_X$ plane assuming that the main decay modes are $u\overline{u}$ (upper left panel), $b\overline{b}$ (upper right panel), $t\overline{t}$ (lower left panel), and $gg$ (lower right panel). The black, red, green, blue, and magenta solid lines denote the BBN constraints for $m_X=0.03$, 0.1, 1, 10, 100, and 1000 TeV, respectively. The orange shaded regions are excluded by the constraint from the CMB spectral distortion.

Figure 13

Constraints on the $m_X{Y}_X$ vs ${\tau }_X$ plane assuming that the main decay modes are $e^{+}{e}^{-}$ (upper left panel), ${\tau }^{+}{\tau }^{-}$ (upper right panel), $\gamma \gamma$ (lower left panel), and $W^{+}{W}^{-}$ (lower right panel). The black, red, green, blue, and magenta solid lines denote the BBN constraints for $m_X=0.03$, 0.1, 1, 10, 100, and 1000 TeV, respectively. The orange shaded regions are excluded by the constraint from the CMB spectral distortion.

Figure 14

Constraints on $m_X{Y}_X$ vs ${\tau }_X$ plane, assuming that $m_X=1\mathrm{TeV}$ and that the main decay mode is $b\overline{b}$. The solid cyan, solid red, and dashed lines denote the BBN constraints from D, ${}^3\mathrm{He}/\mathrm{D}$, and ${}^4\mathrm{He}$, respectively. Here, we use Eq. (2.3) as the observational constraint on $Y_p$. The orange shaded region is excluded by the CMB spectral distortion.

Figure 15

Abundance of ${}^7\mathrm{Li}/\mathrm{H}$ (left panels) and ${}^6\mathrm{Li}/{}^7\mathrm{Li}$ (right panels) for decay particles with a mass of 1 TeV which decay mainly into $b\overline{b}$ (upper panels) and $e^{+}{e}^{-}$ (lower panels). The constraints from other light elements and CMB are shown in the pink shaded region (surrounded by the red solid line) and the orange shaded region, respectively.

Figure 16

Upper bound on the reheating temperature $T_{\mathrm{R}}$ as a function of $m_{3/2}$ at 95% C.L. for models of (1) point 1 (upper left panel), (2) point 2 (upper right panel), (3) point 3 (lower left panel), and (4) point 4 (lower right panel), respectively. The regions surrounded by the black-dotted line indicate a region consistent with Eq. (2.3).