Dark matter from dark photons: A taxonomy of dark matter production

We analyze how dark matter (DM) can be produced in the early Universe, working in the framework of a hidden sector charged under a $U(1{)}^{\prime }$ gauge symmetry and interacting with the Standard Model through kinetic mixing. Depending on the masses of the dark matter particle and of the dark photon, as well as on the hidden $U(1{)}^{\prime }$ gauge coupling and the kinetic mixing parameter, we classify all the distinct regimes along which the observed dark matter relic density can be accounted for. We find that nine regimes are potentially operative to produce the DM particles, and these operate along five distinct dynamical mechanisms. Among these, four regimes are new and correspond to regimes in which the DM particles are produced by on-shell dark photons. One of them proceeds along a new dynamical mechanism, which we dub sequential freeze-in. We argue that such regimes and the associated dynamical mechanisms are characteristic of DM models for which, on top of the Standard Model and the dark sector, there are other massive, but relatively light particles—akin to the dark photon—that interact with both the SM and the DM sectors.

Figure 1

The three sectors (blobs) and their three connections (lines). In the limit of a massless dark photon, (or more generally, as ${\epsilon }_{\mathrm{eff}}\to 0$; see text), the connection between the SM and dark photon blob is absent.

Figure 2

The nine possible DM production regimes in the dark photon scenario. A double-sided arrow means that the two corresponding sectors have reached chemical equilibrium; a single-sided arrow indicates slow out-of-equilibrium production of one sector by the other one; a dashed line corresponds to a subdominant interaction between the sectors. Regimes Ia and Ib, II, IIIa and IIIb, IVa and IVb, Va and Vb are associated with five distinct mechanisms to produce the DM abundance: the freeze-in (I), sequential freeze-in (II), reannihilation (III), secluded freeze-out (IV) and freeze-out (V) mechanisms, respectively. (see Secs.  3a and 3b). Notice that the diagrams are identical for the reannihilation and secluded freeze-out mechanisms. Note also that the SM-to-${\gamma }^{\prime }$ connection is parametrized by ${\epsilon }_{\mathrm{eff}}$ when we take into account the thermal corrections. Without such corrections, it is parametrized by $\epsilon$.

Figure 3

Feynman diagrams for all the connecting processes between the three populations.

Figure 4

DM relic density obtained as a function of $\kappa$ and ${\alpha }^{\prime }$ for $m_{\mathrm{DM}}=3\mathrm{GeV}$ and $m_{{\gamma }^{\prime }}=1\mathrm{GeV}$. This diagram displays the various different production regimes which can lead to the observed relic density without taking thermal effects into account. For this particular choice of masses, one obtains six different production regimes along four dynamical mechanisms: freeze-in (Ia and Ib), sequential freeze-in (II), reannihilation (IIIa), and freeze-out (Va and Vb).

Figure 5

Same as Fig. 4, but with $m_{\mathrm{DM}}=100\mathrm{GeV}$ and $m_{{\gamma }^{\prime }}=10\mathrm{GeV}$.

Figure 6

Values of $\kappa$ needed to account for the observed relic density, as a function of $m_{\mathrm{DM}}$, for the standard freeze-in (regime Ia, green line) and for the sequential freeze-in (regime II, orange line for $m_{{\gamma }^{\prime }}=1\mathrm{GeV}$ and blue line for $m_{{\gamma }^{\prime }}=10\mathrm{GeV}$) in the $\kappa -m_{\mathrm{DM}}$ plane. The shaded regions thus correspond to regime Ib—that is, freeze-in from thermalized dark photons. We consider $m_{{\gamma }^{\prime }}<m_{\mathrm{DM}}$.

Figure 7

The imaginary part of the dark photon propagator (double wiggly lines) in a medium includes both its decay rate and creation rates.

Figure 8

Comparison of the evolution of the dark photon (black lines) and DM abundances (red lines), with (solid) and without (dashed) thermal effects on dark photon production. The dotted lines give the abundance of dark photons in the massless limit. Panels (a) and (b) differ by the choice of dark matter and dark photon masses. Both panels consider values of the couplings which lead to the observed relic density when the thermal corrections are taken into account (solid red lines): $\kappa =2\times {10}^{-11}$ and $\epsilon =5.6\times {10}^{-9}$ for panel (a), and ${\kappa }_{\mathrm{II}}=3.6\times {10}^{-14}$ and $\epsilon ={10}^{-11}$ for panel (b).

Figure 9

Same as Fig. 4, with $m_{\mathrm{DM}}=3\mathrm{GeV}$ and $m_{{\gamma }^{\prime }}=1\mathrm{GeV}$, but taking into account thermal effects on dark photon production.

Figure 10

Same as Fig. 5, with $m_{\mathrm{DM}}=100\mathrm{GeV}$ and $m_{{\gamma }^{\prime }}=10\mathrm{GeV}$, but with thermal effects included.

Figure 11

Dark matter candidates as shown in Fig. 6, but with thermal corrections to dark photon production taken into account. The additional dashed lines are given for the sake of comparison. They correspond to the curves shown in Fig. 6, and thus are without thermal effects.

Figure 12

Dispersion relations for ${\omega }_T(k)$ (blue solid line) and ${\omega }_L(k)$ (orange solid line) in the relativistic regime, $T\gg m_e$. They are normalized to ${\omega }_P=1$. The dashed orange line is the dispersion relation of a standard massive particle. The dispersion relation of the transverse mode has ${\omega }_T={\omega }_P$ for small $k$ and ${\omega }_T\approx \sqrt{3/2{\omega }_P^2+k^2}$ for large $k$. That of the longitudinal mode has ${\omega }_L={\omega }_P$ for small $k$ but asymptotes to ${\omega }_L\approx k$ for large $k$. Also shown is the wave-function normalization $Z_L$ (green solid line) which goes to zero at large $k$, revealing that the longitudinal mode propagates only for small enough momenta.

Figure 13

For $\epsilon ={10}^{-9}$, all contributions to the dark photon yield as a function of the inverse temperature. One can distinguish contributions from pair annihilation and Compton processes for both transverse (red dashed line) and longitudinal modes (blue dashed line), from the coalescence process (orange dashed line) and from all contributions together (solid black line). For the coalescence, we have taken into account the thermal corrections to the mass of the SM particles that annihilate into a dark photon [30].

Figure 14

The sectors and their connections in the Higgs phase of the dark photon model.