Cosmological beam dump: Constraints on dark scalars mixed with the Higgs boson

Precision cosmology provides a sensitive probe of extremely weakly coupled states due to thermal freeze-in production, with subsequent decays impacting physics during well-tested cosmological epochs. We explore the cosmological implications of the freeze-in production of a new scalar $S$ via the superrenormalizable Higgs portal. If the mass of $S$ is at or below the electroweak scale, peak freeze-in production occurs during the electroweak epoch. We improve the calculation of the freeze-in abundance by including all relevant QCD and electroweak production channels. The resulting abundance and subsequent decay of $S$ is constrained by a combination of x-ray data, cosmic microwave background anisotropies and spectral distortions, $N_{\mathrm{eff}}$, and the consistency of big bang nucleosynthesis with observations. These probes constrain technically natural couplings for such scalars from $m_S\sim 10\mathrm{keV}$ all the way to $m_S\sim 100\mathrm{GeV}$. The ensuing constraints are similar in spirit to typical beam dump limits, but extend to much smaller couplings, down to mixing angles as small as ${\theta }_{Sh}\sim {10}^{-16}$, and to masses all the way to the electroweak scale.

Figure 1

An overview of the excluded parameter space for the superrenormalizable Higgs portal scalar, including the updated constraints from this work due to the diffuse x-ray background (XRay), CMB anisotropies, spectral distortions, $N_{\mathrm{eff}}$, and BBN. Constraints from new short-range forces (Force) [18, 19, 20, 21] and stellar cooling (Stellar) [22] from other authors are also shown. We also display the projected SHiP sensitivity [2] and an estimate of supernova (SN) constraints [23]. Note that the primary uncertainties impacting the limits are for the $S$ decay rate for $m_S\sim \mathrm{GeV}$ (see Fig. 2), and the cosmological $S$ abundance for $m_S\gtrsim m_W$. See the text for further details.

Figure 2

The $S$ lifetime as a function of $m_S$ for $\theta ={10}^{-6}$ (reproduced from Ref. [27]).

Figure 3

A density plot of the thermal mixing angle ${\theta }_{\mathrm{eff}}(T)$ from (16), showing the location of the thermal resonance for $T<140\mathrm{GeV}$. The peak of the resonance defines the resonance temperature $T_{\mathrm{res}}$ as a function of $m_S$. The behavior of $m_h(T)$ follows (9) with the naive $v(T)$ model, but with an additional $T$-dependent contribution added to ensure that $m_h(T)$ tracks down to the minimum value of $m_h(T{)}_{\min }\sim 15\mathrm{GeV}$ near the crossover transition, as suggested by lattice simulations [41]. A finite Higgs damping rate of $0.05T$ was also added for illustration.

Figure 4

$S$-producing interactions in the electroweak symmetric phase. Left: Yukawa annihilations. Center: Gauge boson scatterings. Right: Compton-like scatterings.

Figure 5

Total $S$ freeze-in emissivity and the contribution from each production channel category as a function of temperature for $\theta ={10}^{-5}$.

Figure 6

The $S$ abundance yield from each production channel category with $\theta ={10}^{-5}$. Top left: QCD production. Top right: Compton-like scattering. Bottom left: Gauge boson scattering. Bottom right: Yukawa annihilation.

Figure 7

The total $S$ abundance yield from nonresonant $2\to 2$ production channels as a function of $m_S$ (with $\theta ={10}^{-10}$). The mass region where $S$ is resonant with the Higgs boson is excluded, and we note that for $m_S$ above a few tens of GeV, other production channels may also be significant. (See the text for details.)

Figure 8

The emissivity of the production channel $bW\to tS$ showing the two types of IR divergences present in the calculation. The soft $S$ emission is physical and unique to this production channel. The Coulomb-like enhancement is present in all reactions with a $t$- or $u$-channel spin-1 mediator, is unphysical, and signifies the breakdown of our calculations. (See the text for details.)

Figure 9

The total $S$ emissivity as a function of temperature, including the estimated error range from adopting the MB approximation compared to the correct emissivity with quantum distributions of particles 1, 2, and 3.

Figure 10

Effective fraction of energy deposited leading to ionization of the cosmic plasma at $z=300$ for ${\mathrm{\Gamma }}_S={10}^{14}\mathrm{s}$, for the baseline and spectator decay models.

Figure 11

Detailed cosmological constraints on $S$ in the MeV–GeV mass range, excluding BBN (see Fig. 13). The solid lines and shaded areas represent the parameters excluded in the baseline decay model. Dashed lines refer to the projected sensitivity to spectral distortions of a PIXIE-like detector [73] and the thin gray line exhibits the would-be PIXIE sensitivity in the spectator $S$ decay model.

Figure 12

Fraction of $S$ rest energy decaying into electromagnetic energy as a function of its mass for the baseline and spectator decay models.

Figure 13

BBN constraints above the di-pion threshold. Solid lines and shaded areas are ruled out if $S$ follows the baseline decay model. Thin gray lines show the region for the spectator decay model instead. For comparison, dashed lines represent the future spectral distortion sensitivity from a PIXIE-like detector [73].

Figure 14

Survival of the $ZZS$ vertex at higher order in the symmetric phase.