Probing Light Thermal Dark-Matter With a Higgs Portal Mediator

Abstract

We systematically study light (< few GeV) Dark Matter (DM) models that thermalize with visible matter through the Higgs portal and identify the remaining gaps in the viable parameter space. Such models require a comparably light scalar mediator that mixes with the Higgs to avoid DM overproduction and can be classified according to whether this mediator decays (in)visibly. In a representative benchmark model with Dirac fermion DM, we find that, even with conservative assumptions about the DM-mediator coupling and mass ratio, the regime in which the mediator is heavier than the DM is fully ruled out by a combination of collider, rare meson decay, and direct detection limits; future and planned experiments including NA62 can further improve sensitivity to scenarios in which the Higgs portal interaction does not determine the DM abundance. The opposite, regime in which the mediator is lighter than the DM and the latter annihilates to pairs of visibly-decaying mediators is still viable, but much of the parameter space is covered by rare meson decay, supernova cooling, beam dump, and direct detection constraints. Nearly all of these conclusions apply broadly to the simplest variations (e.g. scalar or asymmetric DM). Future experiments including SHiP, NEWS, and Super-CDMS SNOLAB can greatly improve coverage to this class of models.

Figures (4)

• Figure 1: Leading Feynman diagrams giving rise to $\chi$ annihilation in the early universe. If $m_\chi > m_\phi$ the annihilation is predominantly through the $t$-channel and the mediator decays into SM states via Higgs mixing. If $m_\chi < m_\phi$, DM annihilates directly to SM fermions through the $s$ channel which depends on the SM-mediator coupling and is the most predictive scenario; If $m_\phi > 2 m_\chi$ the $\phi$ will decay invisibly to dark matter. In the $2 m_\chi > m_\phi > m_\chi$ regime, it may also be possible to annihilate through the forbidden channel D'Agnolo:2015koa
• Figure 2: Experimental constraints on Dirac fermion DM that annihilates through a light, Higgs-mixed mediator. We normalize the vertical axis using the $e$-$\phi$ coupling, $g_e$ introduced in the text because this coupling always contributes to the annihiation over the mass range considered here-- see discussion in Section II. Top Left: Parameter space for $m_\chi < m_\phi$ compared against the relic density contour computed assuming $m_\phi = 3 m_\chi$ (solid black curve). The curve bifurcates near $m_\chi \sim m_\pi$ where there is disagreement in the literature about light Higgs couplings to hadronic states (see text). Like the relic density contour, the direct detection constraints are also invariant under different assumptions about the mass ratio and DM-mediator coupling since the SM-DM scattering cross section is proportional to the $\kappa_e$ variable plotted on the vertical axis. However, for meson decay and collider constraints, which only constrain the mediator-Higgs mixing, we adopt the conservative values $g_\chi = 1$ and $m_\chi/m_\phi = 1/3$ for building $(g_\chi g_e)^2 (m_\chi/m_\phi)^4$ for comparison with the solid black relic curve; choosing smaller values of either quantity makes these constraints stronger -- except in the resonant annihilation region. Top Right: Same as left, but in the resonant annihilation region $m_\phi \approx 2 m_\chi$, which is the only regime in which the relic density curve moves appreciably. This plot also adopts the extreme value $g_\chi = 2\pi$ near the perturbativity limit, and reveals the maximum amount of viable parameter space for this scenario. As on the top-left plot, direct detection constraints and projections remain invariant, but the meson and collider bounds shift slightly as they are now computed for $m_\chi/m_\phi = 1/2.2$ instead. Bottom Right: Same as top-left, but with $m_\phi = 10 m_\chi$. Bottom Left: Same as top-left, but with the reduced coupling $g_\chi = 0.1$.
• Figure 3: Leading short distance contribution to $B^+ \to K^+ \chi \chi$ and $K^+ \to \pi^+ \bar{\chi} \chi$ decay due to scalar mediated interactions. For $m_\phi < m_{B} - m_{K}$, this decay can also proceed via $B^+ \to K^+ \phi$ Similar diagrams yield for $\phi$ mediated contributions to fully SM final states (e.g. $B^+ \to K^+ \mu^+ \mu^-$).
• Figure 4: Existing constraints on the mediator-Higgs mixing in the visibly decaying $\phi \to {\rm SM ~SM}$ regime. Top row: The DM is a particle-antiparticle symmetric thermal relic whose abundance is set by $t$-channel $\chi \chi \to \phi \phi$ annihilation, which determines the requisite $g_\chi$ coupling for a given DM mass point. Note that most of the parameter space is covered by direct searches for the mediator decaying into SM particles, so except for direct detection, the plots do not require any assumption about the DM provided that the mediator decays visibly. For direct detection, we show two different regimes: $m_\chi \approx m_\phi$ (but with a slightly lighter mediator) which is the least constrained regime, and $m_\chi = 10 \, m_\phi$; for $m_\chi /m_\phi > 10$, the DM is no longer light in this parameter space, so this regime is beyond the scope of this work. Bottom row: Same as top row, but with $g_\chi = 1$, which corresponds to couplings larger than thermal, but still compatible with asymmetric DM, whose antiparticles have all been depleted by annihilation; these plots represent the most aggressive bounds and projections compatible with both DM-SM equilibration and perturbative unitarity. Combined, these four plots bracket the full parameter space of interest; smaller mass ratios than shown on the left column would invalidate the visibly decaying assumption; larger mass ratios than the right column would no longer correspond to the light DM regime; smaller DM-mediator couplings than the top row would overclose the universe; larger DM-mediator couplings than the bottom row would require a UV completion near the GeV scale. Note also that the plots in the left column show bounds from $N_{\rm eff.}$ (gray vertical dashed curves) Nollett:2013pwa due to light DM freeze-out after neutrino decoupling (see text); the right column does not show this bound because for $m_\chi \sim 10 m_\phi$ the left boundary of these plots, corresponding to $m_\chi \sim 10$ MeV, is safe from this constraint.