Dark Matter Freeze-out Research Articles

Sommerfeld enhancement at NLO and the dark matter unitarity bound

We reexamine the consequences of perturbative unitarity on dark matter freeze-out when both Sommerfeld enhancement and bound state formation affect dark matter annihilations. At leading order the annihilation cross section is infrared dominated and the connection between the unitarity bound and the upper bound on the dark matter mass depends only on how the different partial waves are populated. We compute how this picture is modified at next-to-leading order with the goal of assigning a reliable theory uncertainty to the freeze-out predictions. We explicitly compute next-to-leading order corrections in a simple model with Abelian gauge interactions and provide an estimate of the theoretical uncertainty for the thermal masses of heavy electroweak n-plets. Along the way, we clarify the regularization and matching procedure necessary to deal with singular potentials in quantum mechanics with a calculable, relativistic UV completion. Published by the American Physical Society 2024

Relic density and temperature evolution of a light dark sector

We have developed a set of four fully coupled Boltzmann equations to precisely determine the relic density and temperature of dark matter by including three distinct sectors: dark matter, light scalar, and standard model sectors. The intricacies of heat transfer between dark matter (DM) and the standard model sector through a light scalar particle are explored, inspired by stringent experimental constraints on the scalar-Higgs mixing angle and the DM-scalar coupling. Three distinct sectors emerge prior to DM freeze-out, requiring fully coupled Boltzmann equations to accurately compute relic density. Investigation of forbidden, resonance, and secluded DM scenarios demonstrates significant deviations between established methods and the novel approach with fully coupled Boltzmann equations. Despite increased computational demands, this emphasizes the need for improved precision in relic density calculations, underlining the importance of incorporating these equations in comprehensive analyses. Published by the American Physical Society 2024

Unitarity in the non-relativistic regime and implications for dark matter

Unitarity sets upper limits on partial-wave elastic and inelastic cross-sections, which are often violated by perturbative computations. We discuss the dynamics underlying these limits in the non-relativistic regime, namely long-range interactions, and show how the resummation of the 2-particle-irreducible diagrams arising from squaring inelastic processes unitarizes both elastic and inelastic cross-sections. We provide a simple prescription to obtain the unitarized cross-sections from those that do not include resummation of the squared inelastic processes. Our results are model-independent, apply to all partial waves, and affect elastic and inelastic cross-sections, with extensive implications for new physics scenarios, such as dark-matter freeze-out, indirect detection and self-interactions.

Thermal dark matter with low-temperature reheating

We explore the production of thermal dark matter (DM) candidates (WIMPs, SIMPs, ELDERs and Cannibals) during cosmic reheating. Assuming a general parametrization for the scaling of the inflaton energy density and the standard model (SM) temperature, we study the requirements for kinetic and chemical DM freeze-out in a model-independent way. For each of the mechanisms, up to two solutions that fit the entire observed DM relic density exist, for a given reheating scenario and DM mass. As an example, we assume a simple particle physics model in which DM interacts with itself and with SM through contact interactions. We find that low-temperature reheating can accommodate a wider range of couplings and larger masses than those permitted in the usual instantaneous high-temperature reheating. This results in DM solutions for WIMPs reaching masses as high as 1014 GeV, whereas for SIMPs and ELDERs, we can reach masses of 1013 GeV. Interestingly, current experimental data already constrain the enlarged parameter space of these models with low-reheating temperatures. Next-generation experiments could further probe these scenarios.

Successful Freeze-Out of Strongly Interacting Dark Matter with Even-Numbered Interactions.

Strongly interacting massive particles π have been advocated as prominent dark matter candidates when they regulate their relic abundance through odd-numbered 3π→2π annihilation. We show that successful freeze-out may also be achieved through even-numbered interactions XX→ππ once bound states X among the particles of the low-energy spectrum exist. In addition, X-formation hosts the potential of also catalyzing odd-numbered 3π→2π annihilation processes, turning them into effective two-body processes πX→ππ. Bound states are often a natural consequence of strongly interacting theories. We calculate the dark matter freeze-out and comment on the cosmic viability and possible extensions. Candidate theories can encompass confining sectors without a mass gap, glueball dark matter, or ϕ^{3} and ϕ^{4} theories with strong Yukawa or self-interactions.

Radiation back-reaction during dark-matter freeze-out via metastable bound states

The formation and decay of metastable bound states can deplete significantly the density of multi-TeV thermal-relic dark matter. The effect depends on the interplay of bound-state formation, ionisation, transition and decay processes. Existing calculations take into account bound-state ionisation and excitations due to the radiation of the thermal bath. However, the dynamics of Hydrogen recombination suggests that the resonant radiation produced in bound-state formation or de-excitations may backreact, ionising or exciting the bound states thus impeding recombination. In this paper we examine this effect in the context of dark-matter freeze-out. To this end, we employ the generalised Saha equilibrium equation for metastable bound states, and discuss its salient features. We show that, in sharp contrast to Hydrogen recombination, the radiation produced during dark matter freeze-out is more likely to thermalise or redshift, rather than ionise or excite the metastable bound states.This holds not only for the low-energy (resonant) radiation produced in bound-state formation and transition processes, but also for the high-energy radiation produced in dark-matter annihilations and bound-state decays. While our computations are carried out in a minimal dark U(1) model, our conclusions only strengthen in more complex models.

Ultraheavy atomic dark matter freeze-out through rearrangement

Atomic dark matter is usually considered to be produced asymmetrically in the early Universe. In this work, we first propose that the symmetric atomic dark matter can be thermally produced through the freeze-out mechanism. The dominant atom antiatom annihilation channel is the atomic rearrangement. It has a geometrical cross section much larger than that of elementary fermions. After the atomic formation, this annihilation process further depletes dark matter particles and finally freezes out. To give the observed dark matter relic, the dark atoms are naturally ultraheavy, ranging from 106 to 1010 GeV. Published by the American Physical Society 2024

Light thermal self-interacting dark matter in the shadow of non-standard cosmology

In this paper, we construct a viable model for a GeV scale self-interacting dark matter (DM), where the DM was thermally produced in the early universe. Here, a new vector-like fermion with a dark charge under the U(1)_D gauge symmetry serves as a secluded WIMP DM and it can dominantly annihilate into the light dark gauge boson and singlet scalar through the dark gauge interaction. Also, the self-interaction of DM is induced by the light dark gauge boson via the same gauge interaction. In addition to these particles, we further introduce two Weyl fermions and a doublet scalar, by which the dark gauge boson produced from s-wave DM annihilations can mostly decay into active neutrinos after the dark symmetry breaking such that the CMB bound on the DM with low masses can be eluded. In order to have a common parameter region to explain the observed relic abundance and self-interaction of DM, we also study this model in a non-standard cosmological evolution, where the cosmic expansion driven by a new field species is faster than the standard radiation-dominated universe during the freeze-out of DM. Reversely, one can also use the self-interacting nature of light thermal DM to examine the non-standard cosmological history of the universe.

Dark matter interactions from an extra U(1) gauge symmetry with kinetic mixing and Higgs charge* *Supported by the National Natural Science Foundation of China (12135014)

We investigate fermionic dark matter interactions with standard model particles from an additional gauge symmetry, assuming kinetic mixing between the and gauge fields as well as a nonzero charge of the Higgs doublet. To ensure gauge-invariant Yukawa interactions and the cancellation of gauge anomalies, standard model fermions are assigned Y-sequential charges proportional to the Higgs charge. Although the Higgs charge should be small owing to collider constraints, it is useful to decrease the effective cross section of dark matter scattering off nucleons by two orders of magnitude to easily evade direct detection bounds. After performing numerical scans in the parameter space, we find that the introduction of the Higgs charge can also enhance the dark matter relic density by at least two orders of magnitude. In the case where the resonance effect is important for dark matter freeze-out, when the observed relic density and direct detection constraints are tangled, the Higgs charge can expand physical windows to some extent by relieving the tension between the relic density and direct detection.

Dilution of dark matter relic density in singlet extension models

We study the dilution of dark matter (DM) relic density caused by the electroweak first-order phase transition (FOPT) in the singlet extension models, including the singlet extension of the standard model (xSM), of the two-Higgs-doublet model (2HDM+S) and the next-to-minimal supersymmetric standard model (NMSSM). We find that in these models the entropy released by the strong electroweak FOPT can dilute the DM density to 1/3 at most. Nevertheless, in the xSM and NMSSM where the singlet field configure is relevant to the phase transition temperature, the strong FOPT always happens before the DM freeze-out, making the dilution effect negligible for the current DM density. We derive an analytical upper bound on the freeze-out temperature and a numerical lower bound on nucleation temperature in the xSM. On the other hand, in the 2HDM+S where the DM freeze-out temperature is independent of FOPT, the dilution may salvage some parameter space excluded by excessive DM relic density or by DM direct detections.

An asymmetric SIMP dark matter model

In this paper, we construct the first asymmetric strongly interacting massive particles (SIMP) dark matter (DM) model, where a new vector-like fermion and a new complex scalar both having nonzero chemical potentials can be asymmetric DM particles. After the spontaneous breaking of a U(1)D dark gauge symmetry, these two particles can have accidental ℤ4 charges making them stable. By adding one more complex scalar as a mediator between the SIMP DM, the relic density of DM is determined by 3 → 2 and two-loop induced 2 → 2 annihilations in this model. On the other hand, the SIMP DM can maintain kinetic equilibrium with the thermal bath until the DM freeze-out temperature via the new gauge interaction. Interestingly, this model can have a bouncing effect on DM, whereby the DM number density rises after the chemical freeze-out of DM. With this effect, the prediction of the DM self-interacting cross section in this model can be consistent with astrophysical observations, and the ratio of the DM energy density to the baryonic matter energy density can be explained by primordial asymmetries. We also predict the DM-electron elastic scattering cross section that can be used to test this model in future projected experiments.

New pathways to the relic abundance of vector-portal dark matter

We fully explore the thermal freezeout histories of a vector-portal dark matter model, in the region of parameter space in which the ratio of masses of the dark photon $A^{\prime}$ and dark matter $\chi$ is in the range $1 \lesssim m_{A^{\prime}}/m_{\chi} \lesssim 2$. In this region $2 \rightarrow 2$ and $3 \rightarrow 2$ annihilation processes within the dark sector, as well as processes that transfer energy between the dark sector and the Standard Model, play important roles in controlling the thermal freezeout of the dark matter. We carefully track the temperatures of all species, relaxing the assumption of previous studies that the dark and Standard Model sectors remain in thermal equilibrium throughout dark matter freezeout. Our calculations reveal a rich set of novel pathways which lead to the observed relic density of dark matter, and we develop a simple analytic understanding of these different regimes. The viable parameter space in our model provides a target for future experiments searching for light (MeV-GeV) dark matter, and includes regions where the dark matter self-interaction cross section is large enough to affect the small-scale structure of galaxies.

Toward a full description of MeV dark matter decoupling: A self-consistent determination of relic abundance and Neff

Thermal dark matter at the MeV mass scale has its abundance set during the highly nontrivial epochs of neutrino decoupling and electron annihilation. The technical obstacles attached to solving Boltzmann equations of multiple interacting sectors being both relativistic and nonrelativistic have to-date prevented the full treatment of this problem. Here, for the first time, we calculate the freeze-out of light dark matter, taking into account the energy transfer between the dark sector, neutrinos, and the electromagnetically interacting plasma from annihilation and elastic scattering processes alike. We develop a numerically feasible treatment that allows to track photon and neutrino temperatures across freeze-out and to arrive at a precision prediction of ${N}_{\mathrm{eff}}$ for arbitrary branching ratios of the dark matter annihilation channels. In addition, our treatment resolves for the first time the dark matter temperature evolution across freeze-out involving three sectors. It enters in the efficiency of velocity-dependent annihilation channels and for a flavor-blind $p$-wave annihilation into electron- and neutrino-pairs of all generations, we find the present Planck data exclude a complex scalar dark matter particle of mass of ${m}_{\ensuremath{\phi}}\ensuremath{\le}7\text{ }\text{ }\mathrm{MeV}$.

Freeze-in and freeze-out of sterile neutrino dark matter

A sterile neutrino with a keV-scale mass is a compelling dark matter candidate. We propose a new production mechanism involving the decay and annihilation of a complex scalar singlet with a Higgs portal coupling which develops a vacuum expectation value. The interactions of the resulting pseudo Nambu-Goldstone boson may thermalise the dark sector.We determine the region of parameter space where dark sector thermalisation is reached and discuss the most relevant cosmological observables.The scenario can be considered as the combination of a freeze-in of the dark sector followed by relativistic freeze-out.

Saha equilibrium for metastable bound states and dark matter freeze-out

The formation and decay of metastable bound states can significantly decrease the thermal-relic dark matter density, particularly for dark matter masses around and above the TeV scale. Incorporating bound-state effects in the dark matter thermal decoupling requires in principle a set of coupled Boltzmann equations for the bound and unbound species. However, decaying bound states attain and remain in a quasi-steady state. Here we prove in generality that this reduces the coupled system into a single Boltzmann equation of the standard form, with an effective cross-section that describes the interplay among bound-state formation, ionisation, transitions and decays. We derive a closed-form expression for the effective cross-section for an arbitrary number of bound states, and show that bound-to-bound transitions can only increase it. Excited bound levels may thus decrease the dark matter density more significantly than otherwise estimated. Our results generalise the Saha ionisation equilibrium to metastable bound states, potentially with applications beyond the dark matter thermal decoupling.

Electroweak symmetry breaking and WIMP-FIMP dark matter

Electroweak Symmetry Breaking (EWSB) is known to produce a massive universe that we live in. However, it may also provide an important boundary for freeze-in or freeze-out of dark matter (DM) connected to Standard Model via Higgs portal as processes contributing to DM relic differ across the boundary. We explore such possibilities in a two-component DM framework, where a massive U(1)X gauge boson DM freezes-in and a scalar singlet DM freezes-out, that inherits the effect of EWSB for both the cases in a correlated way. Amongst different possibilities, we study two sample cases; first when one DM component freezes in and the other freezes out from thermal bath both necessarily before EWSB and the second, when both freeze-in and freeze-out occur after EWSB. We find some prominent distinctive features in the available parameter space of the model for these two cases, after addressing relic density and the recent most direct search constraints from XENON1T, some of which can be borrowed in a model independent way.

Bound-state effects on dark matter coannihilation: Pushing the boundaries of conversion-driven freeze-out

Bound-state formation can have a large impact on the dynamics of dark matter freeze-out in the early Universe, in particular for colored coannihilators. We present a general formalism to include an arbitrary number of excited bound states in terms of an effective annihilation cross section, taking bound-state formation, decay and transitions into account, and derive analytic approximations in the limiting cases of no or efficient transitions. Furthermore, we provide explicit expressions for radiative bound-state formation rates for states with arbitrary principal and angular quantum numbers $n,\ell$ for a mediator in the fundamental representation of $SU(3)_c$, as well as electromagnetic transition rates among them in the Coulomb approximation. We then assess the impact of bound states within a model with Majorana dark matter and a colored scalar $t$-channel mediator. We consider the regime of coannihilation as well as conversion-driven freeze-out (or coscattering), where the relic abundance is set by the freeze-out of conversion processes. We find that the region in parameter space where the latter occurs is considerably enhanced into the multi-TeV regime. For conversion-driven freeze-out, dark matter is very weakly coupled, evading direct and indirect detection constraints but leading to prominent signatures of long-lived particles that provide great prospects to be probed by dedicated searches at the upcoming LHC runs.

Dark freeze-out cogenesis

We propose a new mechanism where a multi-component dark sector generates the observed dark matter abundance and baryon asymmetry and thus addresses the coincidence between the two. The thermal freeze-out of dark matter annihilating into meta-stable dark partners sets the dark matter relic abundance while providing the out-of-equilibrium condition for baryogenesis. The meta-stable state triggers baryon asymmetry production by its decay well after the freeze-out and potentially induces a period of early matter domination before its decay. The dark matter and baryon abundances are related through number conservation within the dark sector (cogenesis). The “coincidence” is a natural outcome with GeV- to TeV-scale symmetric dark matter and the dark sector’s interactions with the Standard Model quarks. We present a UV-complete model and explore its phenomenological predictions, including dark matter direct detection signals, LHC signatures of new massive particles with color charges and long-lived particles with displaced vertices, dark matter-induced nucleon conversions, (exotic) dark matter indirect detection signals, and effects on the cosmological matter power spectrum. As a side result, we provide a novel analytical treatment for dark sector freeze-out, which may prove useful in the study of related scenarios.

Scalar and fermion two-component SIMP dark matter with an accidental ℤ4 symmetry

In this paper, we construct for the first time a two-component strongly interacting massive particles (SIMP) dark matter (DM) model, where a complex scalar and a vector-like fermion play the role of the SIMP DM candidates. These two particles are stable due to an accidental ℤ4 symmetry after the breaking of a U(1)D gauge symmetry. By introducing one extra complex scalar as a mediator between the SIMP particles, this model can have 3 → 2 processes that determine the DM relic density. On the other hand, the SIMP DM particles can maintain kinetic equilibrium with the thermal bath until the DM freeze-out temperature via the U(1)D gauge couplings. Most importantly, we find an unavoidable two-loop induced 2 → 2 process tightly connecting to the 3 → 2 process that would redistribute the SIMP DM number densities after the chemical freeze-out of DM. Moreover, this redistribution would significantly modify the predictions of the self-interacting cross section of DM compared with other SIMP models. It is crucial to include the two-loop induced 2 → 2 annihilations to obtain the correct DM phenomenology.

Dark matter freeze-out during SU(2)L confinement

We explore the possibility that dark matter is a pair of vector-like fermionic SU(2)L doublets and propose a novel mechanism of dark matter production that proceeds through the confinement of the weak sector of the Standard Model. This confinement phase causes the Standard Model doublets and dark matter to confine into pions. The dark pions freeze-out before the weak sector deconfines and generate a relic abundance of dark matter. We solve the Boltzmann equations for this scenario to determine the scale of confinement and constituent dark matter mass required to produce the observed relic density. We determine which regions of this parameter space evade direct detection, collider bounds, and successfully produce the observed relic density of dark matter. For a TeV scale pair of vector-like fermionic SU(2)L doublets, we find the weak confinement scale to be ∼ 700 TeV.