BBN for the LHC: Constraints on lifetimes of the Higgs portal scalars

LHC experiments can provide a remarkable sensitivity to exotic metastable massive particles, decaying with significant displacement from the interaction point. The best sensitivity is achieved with models where the production and decay occur due to different coupling constants, and the lifetime of exotic particles determines the probability of decay within a detector. The lifetimes of such particles can be independently limited from standard cosmology, in particular, the big bang nucleosynthesis (BBN). In this paper, we analyze the constraints on the simplest scalar model coupled through the Higgs portal, where the production occurs via $h\to SS$, and the decay is induced by the small mixing angle of the Higgs field $h$ and scalar $S$. We find that throughout most of the parameter space, $2m_{\mu }<m_S<m_h/2$, the lifetime of an exotic particle has to be less than 0.1 s, while below $2m_{\mu }$ it could grow to about a second. The strong constraints on lifetimes are induced by the nucleonic and mesonic decays of scalars that tend to raise the $n/p$ ratio. Strong constraints on lifetimes of the minimal singlet extensions of the Higgs potential are welcome news for the MATHUSLA proposal that seeks to detect displaced decays of exotic particles produced in the LHC collisions. We also point out how more complicated exotic sectors could evade the BBN lifetime constraints.

Figure 1

Left: Branching ratios of the scalar $S$ in our baseline decay model. See text for details. Right: Scalar $S$ lifetime of our baseline model and the spectator model for the mixing angle $\theta ={10}^{-6}$.

Figure 2

Left: Temperature evolution ($x=m/T$) of the $Y_S$ intermediate abundance for $m_S=5\mathrm{MeV}$ and 500 MeV for the three benchmark Higgs branching ratios. Right: Metastable abundance of $S$ prior to its decay normalized over the baryon density. Values shown for $\mathrm{Br}(h\to SS)={10}^{-1}$, ${10}^{-2}$, and ${10}^{-3}$. The dashed lines correspond to the perturbative spectator model.

Figure 3

Left: $X_n$ evolution for the SBBN and the injection of pions, kaons, baryons, and muons (neutrinos) as described in the text (see Appendix pp1-s1 for the muon case) for lifetimes of 0.05 s with the initial $Y_S$ abundance tuned to yield $\mathrm{\Delta }{Y}_p=0.01$ (maximum allowed shift of $Y_p$). The baryonic injection is taken at $\kappa =0.5$ (full line); the lines for $\kappa =1$ (dashed) and $\kappa =0.2$ (dotted) are also displayed. Right: Limit of injected pairs for each channel as a function of the $S$ lifetime. The upper-right dotted line for $\kappa =0.2$ is at $Y_p=0.26$, and the upper-left dotted island yields $Y_p=0.24$.

Figure 4

Constraints on $Y_S^2⟨\sigma v{⟩}_{{\pi }^{+}{\pi }^{-}}$ from $SS$ annihilations into charged pions from the BBN ${}^4\mathrm{He}$ abundance at $Y_p=0.26$.

Figure 5

Left: Departure from the SM $N_{\mathrm{eff}}$ as the Universe cools down for electron injections (blue lines) and muon injections (orange lines; see Appendix pp1-s2 for details). The extrema of the neutrino decoupling temperature ranges are shown in full lines and dashed lines as labeled in the figure. Right: Bound of maximal stored energy decaying into electrons or muons as a function of particle lifetimes. The full lines and dashed lines represent the neutrino decoupling temperatures as on the left. We also show for comparison some benchmark bounds in this parameter space from the BBN $Y_p$ results. The thin olive curves are the neutron enrichment constraint from annihilation into pions for $m_S=140\mathrm{MeV}$ (solid lines) and $m_S=275\mathrm{MeV}$ (dotted lines). The thin purple line is the $Y_p$ constraint for a $m_S=250\mathrm{MeV}$ particle decaying into muons.

Figure 6

Left: Lifetime constraint as a function of the $S$ mass for three $h\to SS$ branching ratios. The lettered regions represent different assumptions or physics and are described in the text. The dotted lines correspond to the perturbative spectator model. Right: Same as left, except transposed in the decay length of $S$, assuming it is boosted to $E_S=200\mathrm{GeV}$.