BBN Constraints on the Hadronic Annihilation of sub-GeV Dark Matter

TL;DR

Sub-GeV thermal relic dark matter with dominant $p$-wave annihilation is challenging to constrain via CMB or gamma-ray observations. This work assesses big bang nucleosynthesis (BBN) sensitivity to residual hadronic annihilations into $\pi^\ m{\pm}$ and $K^\rm{\pm}$, solving coupled Boltzmann equations to track their impact on proton-neutron conversion before the deuterium bottleneck. The authors derive $2\sigma$ limits on the annihilation parameter $b$ across $m_\chi$ in the 100 MeV to 10 GeV range and apply the results to a dark-photon-mediated scalar DM benchmark, showing BBN constraints that are competitive with, and complementary to, collider and direct-detection probes. The results establish BBN as a robust sub-GeV DM constraint and motivate higher-precision light-element abundance measurements to further tighten the bounds.

Abstract

We investigate the impact of residual annihilation from sub-GeV mass thermal relic dark matter candidates during big bang nucleosynthesis (BBN). Focusing on candidates with $p$-wave annihilation channels, we show that the hadronic injection of pions and kaons beyond freeze-out, and their subsequent interaction with protons and neutrons prior to the deuterium bottleneck, provides a sensitivity to annihilation that surpasses that of the CMB and indirect detection in the galaxy.

Figures (5)

• Figure 1: Comparison of the rates that go into the pion Boltzmann equation, showing the pion decay rate (blue), pion-nucleon interaction rate (red), and the pion injection rate due to DM annihilation (yellow) with $m_\chi = 400$ MeV, and $b=10^{-23}\ \rm cm^3/s$. The Hubble parameter (black, dashed) is also shown for reference.
• Figure 2: Evolution in the difference $\Delta X = X - X|_{\rm SBBN}$ in the fractions of neutrons (solid) and protons (dashed) away from the SBBN values when pions are injected with DM mass $m_\chi=400\ \rm MeV$ and varying DM annihilation rate $b$.
• Figure 3: The evolution of abundances with DM freeze-out governed by annihilation to pions with $m_\chi = 400$ MeV, and $b = 10^{-23}\ \rm cm^3/s$. The evolution of the pion number densities is described in the text.
• Figure 4: The $95\%$ CL sensitivity to $p$-wave DM annihilation to pions (blue) and kaons (red) during BBN. Note that we set the DM freeze-out abundance to its observed value, and then the region above the contours is nominally excluded by requiring consistency with BBN's prediction of D/H and $Y_p$ compared to observations PDG2020Cooke:2013cba*Riemer-Sorensen:2014aoa*Balashev:2015hoe*Riemer-Sorensen:2017pey*2018MNRAS*Cooke:2017cwoAver:2020fon*Valerdi:2019beb*Fernandez:2019hds*Kurichin:2021ppm*2020ApJ*2021MNRAS*2022MNRAS. Dashed colored curves indicate a branching ratio of 1, while solid curves indicate a branching ratio of 0.1 with the remainder of annihilation products neglected. Also shown are limits from EM injection to BBN Depta:2019lbe, and cosmic ray injection of positrons from Voyager 1 and AMS-02 data (with the dotted curve indicating a less conservative cosmic ray propagation model) Boudaud:2018oya. The gray-dashed horizontal line indicates the value of $b$ required for thermal freeze-out to match the measured DM abundance.
• Figure 5: The $90\%$ CL limits on DM annihilation to pseudoscalar mesons during BBN (green). As in Fig. \ref{['fig:blimit']}, we set the DM freeze-out abundance to its observed value, and then the region above the contour is nominally excluded by BBN's prediction of D/H and $Y_p$ compared to observations PDG2020Cooke:2013cba*Riemer-Sorensen:2014aoa*Balashev:2015hoe*Riemer-Sorensen:2017pey*2018MNRAS*Cooke:2017cwoAver:2020fon*Valerdi:2019beb*Fernandez:2019hds*Kurichin:2021ppm*2020ApJ*2021MNRAS*2022MNRAS. Also shown are limits from BaBar BaBar:2017tiz, NA64 NA64:2023wbi, and CRESST-II CRESST:2015txj (gray regions), and the thermal relic line (gray-dashed curve) where the choice of parameters corresponds to the observed DM relic abundance Berlin:2018bsc. A conventional slice of the dark photon model parameter space is shown with the $\alpha_D=0.5$ and $m_{A'}=3m_\chi$ fixed.