Discovery Prospects for a Minimal Dark Matter Model at Cosmic and Intensity Frontier Experiments

TL;DR

The paper tackles the question of detecting a minimal secluded dark matter model where a Dirac fermion $\chi$ interacts with the Standard Model through a kinetically mixed dark photon $Z_D$ with $m_{Z_D}<m_\chi$. It solves coupled Boltzmann equations to map the relic-abundance curve in the $(\alpha_D, \epsilon)$ plane across freeze-in, out-of-equilibrium freeze-out, and secluded freeze-out regimes, then confronts the model with CMB, direct-detection, and beam-dump constraints. A key result is that the WIMP-next-door region above the thermalization floor is excluded, while viable regions persist below the floor, including freeze-in and out-of-equilibrium freeze-out; future intensity-frontier experiments (beam dumps) can discover visibly decaying $Z_D$ even if direct detection remains silent, with complementary reach from direct detection and collider searches. The work highlights the complementarity of direct, indirect, and accelerator-based probes in testing feebly interacting dark sectors and provides guidance for prioritizing searches for a vector-portal dark photon in light of a minimal DM framework.

Abstract

We explore the detection prospects for a minimal secluded dark matter model, where a fermionic dark matter particle interacts with the Standard Model (SM) via a kinetically mixed dark photon. We focus on scenarios where the dark photon decays visibly, making it a prime target for beam-dump experiments. In this model, the dark matter relic abundance can be achieved by a variety of mechanisms: freeze-in, out-of-equilibrium freeze-out, and secluded freeze-out. We demonstrate that the secluded freeze-out regime in the considered mass range is now entirely excluded by a combination of direct and indirect detection constraints. Moreover, we show that future direct detection and intensity frontier experiments offer complementary sensitivity to this minimal model in the parameter space where the hidden sector never enters equilibrium with the SM. In out-of-equilibrium freeze-out scenarios, nuclear-recoil direct detection experiments can still access signals above the neutrino fog that are mediated by dark photons that are too weakly coupled to be detected in future beam dump experiments. Meanwhile, future beam dump experiments provide a powerful probe of the freeze-in parameter space in this model, which is largely inaccessible to direct detection experiments. Notably, even in the absence of a future observation in direct detection experiments, a dark photon discovery remains possible at SHiP, DUNE, LHCb, and DarkQuest within this minimal dark matter model.

Figures (7)

• Figure 1: The relevant processes for achieving the measured relic abundance. SM fermion annihilations to DM pairs transfer both energy and DM abundance into the the hidden sector via $f\bar{f} \rightarrow \chi \bar{\chi}$ (left), while DM annihilations to dark photons within the hidden sector $\chi\bar{\chi} \rightarrow Z_D Z_D$ (right) deplete the DM abundance.
• Figure 2: Contours in the $\epsilon, \alpha_D$ plane that realize the measured relic abundance for a given value of $m_\chi$. In this plot we see four distinct regions, which we have labeled: freeze-in, reannihilation, leak-in, and freeze-out. We refer to the the reannihilation and leak-in phases collectively as out-of-equilibrium freeze-out. The regions are broadly indicated, with the boundaries between them occurring at significant changes in the slope of the relic abundance contours for each value of the DM mass. Note that at the final transition from leak-in to (secluded) freeze-out, the relic abundance condition becomes independent of the kinetic mixing parameter, $\epsilon$.
• Figure 3: The thermalization floor (red) and minimum mixing $\epsilon_\text{min}$ separating freeze-in and freeze-out regimes (blue) mapped into the $m_{Z_D}$-$\epsilon$ plane, for fixed $m_{\chi}/m_{Z_D} = 10$ (darker) and $m_{\chi}/m_{Z_D} = 100$ (lighter). Additional curves showing excluded regions (shaded gray) and projected reach (colored dotted lines) from accelerator-based experiments are taken from Refs. Batell:2022dpxSHiP:2021nfo, while exclusions from Supernova 1987a are taken from from Ref. Chang:2016ntp.
• Figure 4: Indirect detection constraints from CMB on the ($m_{Z_D}, \epsilon$) plane for several values of $m_\chi$ plotted with current and projected beam dump limits and other accelerator based experiments as LHCb and Belle II. The CMB constraints are not monotonic in behavior as a function of the DM mass because of the Sommerfeld enhancements at larger masses. Additional curves showing excluded regions (shaded gray) and projected reach (colored dotted lines) from accelerator-based experiments are taken from Refs. Batell:2022dpxSHiP:2021nfo, while exclusions from Supernova 1987a are taken from from Ref. Chang:2016ntp.
• Figure 5: The ratio $\sigma_{\chi n}^\mathrm{eff}/\sigma^{0}_{\chi n}$ as a function of $m_\chi$ and $m_{Z_D}/m_\chi$, showing the transition from regions where the DM-nucleon scattering can be reasonably approximated as constant (yellow) to regions where the recoil energy dependence is sizable (blue). We show contours at 90%, 70%, and 50%. Jumps at various values of $m_\chi$ reflect transitions between different experiments as discussed in the text.