Freeze-in leptogenesis via dark-matter oscillations

We study the cosmology and phenomenology of freeze-in baryogenesis via dark-matter oscillations, taking the dark matter to couple to Standard Model leptons. We investigate viable models both with and without a $Z_2$ symmetry under which all new fields are charged. Lepton flavor effects are important for leptogenesis in these models, and we identify scenarios in which the baryon asymmetry is parametrically distinct from and enhanced relative to leptogenesis from sterile neutrino oscillations. The models we study predict the existence of new, electroweak-charged fields, and can be tested by a combination of collider searches, structure-formation studies, x-ray observations, and terrestrial low-energy tests.

Figure 1

Feynman diagram illustrating the production of DM (${\chi }_i$), its propagation, and subsequent annihilation. First, the scalar ${\mathrm{\Phi }}^{*}$ decays into ${\chi }_i$ and the SM particle $e_{\alpha }^c$; following propagation, the ${\chi }_i$ field annihilates with another SM field $e_{\beta }^c$ to reconstitute ${\mathrm{\Phi }}^{*}$. The net reaction is $e_{\beta }^c{\mathrm{\Phi }}^{*}\to e_{\alpha }^c{\mathrm{\Phi }}^{*}$. The process is a coherent sum over ${\chi }_i$ mass eigenstates since ${\chi }_i$ is out of equilibrium.

Figure 2

In the massless-${\chi }_1$ limit, ${\mathcal{I}}^{(4)}(x_{\mathrm{ew}},{\beta }_{\mathrm{osc}})$ versus $M_2$ for various $M_{\mathrm{\Phi }}$.

Figure 3

For the minimal model in the massless-${\chi }_1$ limit, contours of $Y_B/Y_B^{\mathrm{obs}}$ (blue, solid) and $\theta$ (gray, dashed) in the $(M_{\mathrm{\Phi }},c{\tau }_{\mathrm{\Phi }})$ plane, for (a) $M_2=15$ keV, (b) $M_2=25$ keV, (c) $M_2=50$ keV, and (d) $M_2=100$ keV, with the $F$ matrix set to the minimal model benchmark form of Eq. (a2). At each point in the plane, $\theta$ is chosen to satisfy the DM constraint.

Figure 4

For the minimal model in the massless-${\chi }_1$ limit, $Y_B$ versus $M_{\mathrm{\Phi }}$ for various $\theta$ and $M_2$, with the $F$ matrix set to the minimal model benchmark form of Eq. (a2). For each combination of parameters, $\mathrm{Tr}[F^{†}F]$ is chosen to satisfy the DM constraint.

Figure 5

For the minimal model, contours of $Y_B/Y_B^{\mathrm{obs}}$ (blue, solid) and $r$ (red, dashed) in the $(M_1,{\sin }^2\theta )$ plane, for $M_{\mathrm{\Phi }}=500\mathrm{GeV}$ and $M_2=15\mathrm{keV}$, with the $F$ matrix set to the minimal model benchmark form of Eq. (a2). At each point in the plane, $\mathrm{Tr}[F^{†}F]$ is chosen to satisfy the DM constraint.

Figure 6

For various $M_1$, the contours enclose the $(M_{\mathrm{\Phi }},M_2)$ space that is viable for DM and leptogenesis in the minimal model, with the $F$ matrix set to the minimal model benchmark form of Eq. (a2). At each point in the plane, $\mathrm{Tr}[F^{†}F]$ and $\theta$ are chosen to maximize $Y_B$ subject to both the DM abundance constraint and the upper bound on $r$ indicated; for the contours shown, that maximum $Y_B$ is equal to $Y_B^{\mathrm{obs}}$.

Figure 7

For the UVDM model, contours of $Y_B/Y_B^{\mathrm{obs}}$ in the $(M_{{\mathrm{\Phi }}_1},c{\tau }_{{\mathrm{\Phi }}_1})$ plane, for various DM masses and mixings, with the $F$ matrices set to the UVDM benchmark of Eq. (a9). At each point in the plane, the abundance of DM produced by ${\mathrm{\Phi }}_2$ decays, $Y_{\chi }^{\mathrm{UV}}$, is chosen so that the total DM energy density from ${\mathrm{\Phi }}_1$ and ${\mathrm{\Phi }}_2$ decays matches the observed value. The dashed contours are based on the $\mathcal{O}(F^4)$ asymmetry of Eq. (21), while the solid contours are based on numerical solution of the quantum kinetic equations presented in Appendix pp4-s2. The two calculations are in reasonable agreement in the perturbative regime, $c{\tau }_{{\mathrm{\Phi }}_1}\gtrsim 1\mathrm{cm}$. In (a) and (c) we take the massless ${\chi }_1$ limit, with $M_2=15keV$. In (b) and (d) we take $M_1=15keV$ and $M_2=20keV$.

Figure 8

The viable $(M_{{\mathrm{\Phi }}_1},c{\tau }_{{\mathrm{\Phi }}_1})$ space for DM and leptogenesis in the UVDM model, for various DM masses and mixings. The abundance of DM produced by ${\mathrm{\Phi }}_2$ decays, $Y_{\chi }^{\mathrm{UV}}$, is chosen so that the total DM energy density from ${\mathrm{\Phi }}_1$ and ${\mathrm{\Phi }}_2$ decays matches the observed value. These contours are based on numerical solution of the quantum kinetic equations presented in Appendix pp4-s2. In (a–c) we take maximal DM mixing for $M_1=0$, $M_1=15$ keV, and $M_1=M_2/2$, and in (d) we take ${\theta }_1={\theta }_2=1/10$ and $M_1=0$.

Figure 9

For a particular set of BSM particle masses and DM couplings, the baryon asymmetry as a function of Z2V coupling strength, with either one, two or all three independent Z2V couplings turned on. The DM couplings are set to the minimal model benchmark, Eq. (a2), with only the electron and muon coupling to DM, and with $\mathrm{Tr}{F}^{†}F$ determined by the DM abundance constraint.

Figure 10

Baryon asymmetries in the larger-$M_1$ regime of the Z2V model, with the $F$ matrix set to the Z2V benchmark form of Eq. (a13). We take $M_{\mathrm{\Phi }}=500\mathrm{GeV}$, which roughly maximizes the range of viable $M_1$ values. At each point in the plane, $\mathrm{Tr}[F^{†}F]$ and $\theta$ are chosen to maximize $Y_B$ subject to the DM abundance constraint. In (a), we show contours of $Y_B/Y_B^{\mathrm{obs}}$, using the $\mathcal{O}(F^4)$ perturbative calculation of Eq. (27), without thermal averaging. In (b) we compare $Y_B=Y_B^{\mathrm{obs}}$ contours based on the nonthermally-averaged perturbative calculation, the $\mathcal{O}(F^4)$ pertrubative calculation with thermal averaging [see the discussion leading to Eq. (e20)], and numerical solution of the QKEs (see Appendix pp4-s2).

Figure 11

In the Z2V model, contours of $Y_B/Y_B^{\mathrm{obs}}$ in the $(M_{\mathrm{\Phi }},{\sin }^2\theta )$ plane for $M_2=15\mathrm{keV}$ (a–c) and $M_2=50\mathrm{keV}$ (d–f), in the massless-${\chi }_1$ limit, with the $F$ matrix set to the Z2V benchmark form of Eq. (a13). We compare the results from numerical integration of the QKEs with the $\mathcal{O}(F^4)$ contribution of Eq. (27) (a, d), the $\mathcal{O}(F^6)$ contribution of Eq. (e48) (b, e), and the sum of both (c, f). For the perturbative contributions, we adopt the same thermal ansatz for the DM momentum distribution as used to derive the QKEs, which means using the ${\mathcal{I}}_{\mathrm{t}.\mathrm{a}.}^{(4)}$ function defined in Eq. (e20) in place of ${\mathcal{I}}^{(4)}$ in Eqs. (e9) and (e45), and we impose the DM constraint using the $\mathcal{O}(F^2)$ result for ${\rho }_{\mathrm{dm}}$ based on Eqs. (e3)–(e6).

Figure 12

Similar to Fig. 11, except without thermal averaging in the perturbative calculation. In (a), we take $M_1=15\mathrm{keV}$ and $M_2=20\mathrm{keV}$ to provide a view of the larger-$M_1$ parameter space that complements Fig. 10. Comparison of (b) and (c) with Figs. 11 and 11 shows the effect of thermal averaging.

Figure 13

Similar to Fig. 4, except for the Z2V model instead of the minimal model: in the massless-${\chi }_1$ limit, $Y_B$ versus $M_{\mathrm{\Phi }}$ for various $\theta$ and $M_2$, with the $F$ matrix set to the Z2V benchmark form of Eq. (a13). For each combination of parameters, $\mathrm{Tr}[F^{†}F]$ is chosen to satisfy the DM constraint.

Figure 14

Similar to Fig. 5, except for the Z2V model instead of the minimal model: contours of $Y_B/Y_B^{\mathrm{obs}}$ (blue, solid) and $r$ (red, dashed) in the $(M_1,{\sin }^2\theta )$ plane, for $M_{\mathrm{\Phi }}=500\mathrm{GeV}$ and $M_2=15\mathrm{keV}$, with the $F$ matrix set to the Z2V benchmark form of Eq. (a13). At each point in the plane, $\mathrm{Tr}[F^{†}F]$ is chosen to satisfy the DM constraint.

Figure 15

Similar to Fig. 6, except for the Z2V model instead of the minimal model. For various $M_1$, the contours enclose the $(M_{\mathrm{\Phi }},M_2)$ space that is viable for DM and leptogenesis in the Z2V model, with the $F$ matrix set to the Z2V benchmark form of Eq. (a13). At each point in the plane, $\mathrm{Tr}[F^{†}F]$ and $\theta$ are chosen to maximize $Y_B$ subject to both the DM abundance constraint and the upper bound on $r$ indicated; for the contours shown, that maximum $Y_B$ is equal to $Y_B^{\mathrm{obs}}$.

Figure 16

LHC constraints from searches for promptly decaying sleptons [33, 34, 35, 36], displaced leptons [37], and HSCPs [38], along with parameter space for the minimal model [from Fig. 3] and for the UVDM model, under two different DM coupling assumptions [from Figs. 7 and 7]. As discussed in the text, the green prompt and purple displaced excluded regions are for ${\mathcal{B}}_e=100\%$; the corresponding limits for ${\mathcal{B}}_{\mu }=100\%$ are roughly similar. For the prompt case, the cyan region is a tentative estimate of the limits for ${\mathcal{B}}_e={\mathcal{B}}_{\mu }=50\%$ (see the text). The lifetime cutoffs for the prompt and HSCP exclusion regions are highly approximate. We take the CMS HSCP exclusion contour from Ref. [41] and extend it from $M_{\mathrm{\Phi }}=270\mathrm{GeV}$ to $M_{\mathrm{\Phi }}=360\mathrm{GeV}$ by assuming a similar behavior.

Figure 17

Feynman diagram for DM decay induced by Z2V couplings.

Figure 18

Contours of $Y_B/Y_B^{\mathrm{obs}}$ (blue, solid) and X-ray bounds on $\lambda$ (red, dashed) in the $(M_{\mathrm{\Phi }},{\sin }^2\theta )$ plane for $M_2=15\mathrm{keV}$ (a-c), $M_2=50\mathrm{keV}$ (d-f), and $M_2=200\mathrm{keV}$ (g-i). We take the massless-${\chi }_1$ limit and adopt benchmark scenarios with a single Z2V coupling and the $F$ matrix chosen as described in Sec. pp1-s3. In the left column (plots a, d, and g), the flavor structure of the DM and Z2V couplings is such that the charged fermion in the diagram of Fig. 17 is a $\tau$ lepton; the $\lambda$ bounds for the cases of $\mu$-mediated and $e$-mediated decays are shown in the middle column (plots b, e, and h) and right column (plots c, f, and i), respectively.

Figure 19

Contours of $\mathcal{R}=0.1$ (blue) and $\mathcal{R}=1$ (red), where $\mathcal{R}$ is the ratio of decay widths defined in Eq. (35). The solid and dashed contours are for the tau-mediated and electron-mediated scenarios, respectively.

Figure 20

The temperature-dependent function $c_{\mathrm{\Phi }}$, defined in Eq. (b11).

Figure 21

For various $M_{\mathrm{\Phi }}$, (a) ${\mathcal{I}}^{(4)}$, (b) ${\mathcal{I}}^{(6)}$, (c) ${\tilde{\mathcal{I}}}^{(4)}$, and (d) ${\tilde{\mathcal{I}}}^{(6)}$, plotted against $\beta$.