Boltzmann Suppressed Ultraviolet Freeze-in

Abstract

If the dark matter mass $m$ exceeds the maximum temperature of the Universe ($T_{\rm max} < m$), then its production rate will be Boltzmann suppressed. The important implications of this Boltzmann suppression have been explored for dark matter freeze-in via renormalizable operators. Here we extend these considerations to the case of ultraviolet (UV) freeze-in for which freeze-in proceeds via non-renormalizable operators. The UV freeze-in variant has a number of appealing features, not least that a given effective field theory can describe a multitude of UV completions, and thus such analyses are model agnostic for a given high dimension freeze-in operator. We undertake model independent analyses of UV freeze-in for portal operators of general mass dimensions. Subsequently, we explore a number of specific examples, namely, Higgs portals, bino dark matter, and gravitino dark matter. Finally, we discuss how significant differences arise if one departs from the standard assumptions regarding inflationary reheating (i.e. transitions from an early matter dominated era to radiation domination). As a motivated example we examine the implications of early kination domination. Boltzmann suppressed UV freeze-in is well motivated and permits a number of compelling scenarios. In particular, we highlight that for $T_{\rm max} \sim$ 1 TeV it is feasible that the freeze-in mechanism is entirely realized within a couple of orders of magnitude of the TeV scale, making it experimentally accessible in contrast to traditional freeze-in scenarios.

Figures (9)

• Figure 1: Instantaneous reheating. The thick black solid lines show the parameter values that reproduce the observed dark matter abundance (that is Eq. \ref{['eq:Yafter']}). The thin black dashed correspond to the relativistic and non-relativistic approximations (cf. Eq. \ref{['eq:Yafter-app']}), for $n=2$ (mass dimension six freeze-in operator). The transition between the two regimes is depicted by the dotted red lines $m = T_\text{rh}$. The red bands correspond to the regions where the EFT approach breaks ($m > \Lambda$ and $T_\text{rh} > \Lambda$), and the thermalization limit (i.e. in this region the dark matter enters thermal equilibrium with the Standard Model bath).
• Figure 2: Instantaneous reheating. As Figure \ref{['fig:plots']} but for different values of $n$. With $n=0$, 2, 4, 6 corresponding to freeze-in operators of dimension 5, 6, 7, 8, respectively. We check that along each curve the dark matter does not enter equilibrium with the visible sector.
• Figure 3: Non-instantaneous reheating. The thick black line shows the parameter values for which the observed dark matter abundance is reproduced. The thin dashed correspond to the relativistic and non-relativistic approximations: black after reheating (that is, the same as in Figure \ref{['fig:plots']}) and blue during reheating. The transition between the three regimes is depicted by the dotted red lines $m = T_\text{rh}$ and $m = T_\text{max}$. The red bands indicate $m > \Lambda$ or $T_\text{max} > \Lambda$. We assume $n=2$ and $L=0$, and that prior to reheating the Universe was in an early matter dominated phase.
• Figure 4: Non-instantaneous reheating. As Figure \ref{['fig:plots3']} but for different values of $n$ with $L=0$. With $n=0$, 2, 4, 6 corresponding to freeze-in operators of mass dimension 5, 6, 7, 8, respectively. We check that along each curve the dark matter does not enter equilibrium with the visible sector.
• Figure 5: Dimension-five Higgs portal. Left. We consider fermion dark matter undergoing Boltzmann suppressed UV freeze-in via the Higgs portal, i.e. $\frac{1}{\Lambda}|H|^2\bar{q}q$ leading to $\frac{m_q}{\Lambda m_h^2}\bar{\chi}\chi\bar{q}q$. Taking the instantaneous reheating approximation, and including the $p$-wave ($L=1$) suppression (cf. Appendix \ref{['sec:app']}), we show contours of $T_\text{rh}$ that give correct relic density of dark matter as $m$ and $\Lambda$ are varied. Experimental bounds from direct detection "DD" and invisible Higgs decay "BR$_{\rm inv}$" are overlaid. The shaded region indicates where EFT breaks down. We confirm that the dark matter does not equilibrate with the Standard Model over the relevant parameter space. Right. We recast the LH panel in the familiar direct detection parameter space, showing the exclusion on the spin-independent scattering cross section from XENONnT XENON:2025vwd, PandaX-4T PandaX:2024qfu, and LUX-ZEPLIN LZ:2022lsv. We also indicate the "neutrino fog" (green), where direct detection becomes challenging.