Leptogenesis and the Higgs portal

Matthias Le Dall and Adam Ritz

Phys. Rev. D 90, 096002 – Published 12 November 2014

Abstract

We study the impact on leptogenesis of Higgs portal couplings to a new scalar singlet. These couplings open up additional $C P$ -violating decay channels for the higher mass singlet neutrinos $N_{2}$ and $N_{3}$ . We analyze the simplest case of two-level $N_{1} - N_{2}$ leptogenesis, including significant mass hierarchies, in which the $C P$ asymmetry is generated in part by singlet-mediated decays of $N_{2}$ . For these models, provided the lightest singlet neutrino $N_{1}$ is sufficiently weakly coupled to avoid excessive washout, its mass scale is not directly constrained by the Davidson–Ibarra bound.

12 More

Received 28 August 2014

DOI:https://doi.org/10.1103/PhysRevD.90.096002

Authors & Affiliations

Matthias Le Dall and Adam Ritz

Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, V8P 5C2 Canada

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 90, Iss. 9 — 1 November 2014

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Two hidden sector decay channels for RHN that contribute to the $C P$ asymmetry. The superscripts “v” and “w” stand for the vertex and wave function diagrams.
Reuse & Permissions
Figure 2
The left plot graphically represents the $N / S$ cut. The right figure exhibits the quadratic constraint in Eq. (11). The vertical dashed lines represent the momentum $| \vec{l} |$ upper and lower bounds, $| \vec{l} |_{\pm} = M_{i} (1 \pm \sqrt{δ}) / 2$ , which become $| \vec{l} |_{0} = M_{i} \sqrt{1 - δ} / 2$ at $y = - \sqrt{1 - δ}$ . The imaginary part of the vertex correction is nonzero contributions only from the gray area.
Reuse & Permissions
Figure 3
Two three-body decay diagrams contributing to the $C P$ -asymmetry at the same order in couplings as the loop-corrected two-body decays. As discussed in the text, their inclusion is important in ensuring that the full $C P$ asymmetry is well-defined and free of infrared divergences.
Reuse & Permissions
Figure 4
The bubble diagrams enumerating the cuts that contribute to the $C P$ asymmetry from both the vertex loop corrections (a) and three-body final states (b). The external state lines that are on shell by definition are cut with a double line, while the Cutkosky cuts are shown with a single line.
Reuse & Permissions
Figure 5
Classes of decay and scattering diagrams and subdiagrams. We subtract the $N_{i}$ real intermediate states coupling through $α$ and $λ$ order by order to avoid double counting, as discussed in the text.
Reuse & Permissions
Figure 6
Plots of the unsubtracted thermal rates (blue), along with their on-shell parts (red). The plots in (a), (b), and (c) are for $L H \underset{1}{\to} \bar{L H}$ , $L H \underset{2}{\to} \bar{L H}$ , and $N_{1} S \underset{2}{\to} L H$ respectively, generated using $λ_{1} \sim 0.002$ , $λ_{2} \sim 0.07$ , $α_{12} \sim 0.07$ , $M_{2} = 10^{10} GeV$ , and $M_{1} = 10^{8} GeV$ .
Reuse & Permissions
Figure 7
A list of the decay and scattering processes included in our Boltzmann equations. This list is not exhaustive, though it includes the dominant contributions. In the limit where the quarks, Higgs, and singlet $S$ are massless, the $t$ -channel diagrams are counted twice since it is possible to swap $Q - t$ and $H - S$ .
Reuse & Permissions
Figure 8
Plots of the efficiency factor $κ_{2}$ , as a function of $K_{2}$ , for various values of $K_{21}$ . In the limit $K_{21} ≪ K_{2}$ , the efficiency factor approaches its value in one-flavor standard leptogenesis (shown here in black, dashed, buried under the blue line). Increasing $K_{21}$ has a significant effect on the efficiency factor at low $K_{2}$ . The asymptotic behavior is also shown (dotted lines) for low $K_{2}$ , from (62) and (64).
Reuse & Permissions
Figure 9
The plot on the left (a) shows the $N_{1}$ abundance $Y_{1} (Z)$ offset compared to equilibrium at the end of the first phase due to the $N_{2} \to N_{1} S$ decay, referring to Eq. (68) along with the approximations (69). These values are also the initial conditions for the abundance at the start of the very last phase. The plot on the right (b) represents the efficiency factor $κ_{1}$ for various initial values of $Y_{1} (Z)$ at the start of the $N_{1}$ phase, as given in the left plot.
Reuse & Permissions
Figure 10
Plot (a) shows the $N_{2}$ and $N_{1}$ abundances (red and blue) and $Y_{L - \bar{L}}$ (purple) in the toy two-flavor model, compared to the $N_{2}$ abundance (in dashed red) and the lepton asymmetry (in dashed purple) in the one-flavor case. Plots (b) and (c) show further examples of the two-level toy model. The coupling $N_{2} \to N_{1} S$ allows $N_{2}$ to cope better with expansion, which causes a reduction of the generated lepton asymmetry. In turn, this results in the $N_{1}$ abundance being further out of equilibrium. The color coding is the same in all these and subsequent plots.
Reuse & Permissions
Figure 11
These plots show a viable example of the high-scale scenario. We show the evolution of the abundances and (rescaled) asymmetry (a) and the relative rates (b) as a function of temperature. In this regime, the $C P$ asymmetry is dominated by the standard Yukawa contribution, $ε_{i} \propto m_{ν} M_{i} / v^{2}$ , and the final plot (c) displays the $C P$ asymmetries $ε_{1, 2}$ as functions of $M_{2}$ , for a constant mass ratio, $M_{2} / M_{1} = 10^{4}$ . With a large mass hierarchy, there would be plenty of time for $N_{1}$ -mediated processes to wash out all of the lepton asymmetry unless the $N_{1}$ interactions are sufficiently suppressed, hence the very small Yukawa $λ_{1}$ .
Reuse & Permissions
Figure 12
These plots, in the same format as Fig. 11, show a viable example in the low-mass regime. The hidden sector-sourced $C P$ asymmetry from $N_{2}$ decays is the dominant contribution. The dominant scattering processes are also mediated by the hidden sector. This is also an explicit example of a scenario leading to a lepton asymmetry enhancement, thanks to the evolution traversing the sphaleron freeze-out temperature.
Reuse & Permissions
Figure 13
Scenarios representig low (a) and high (b) scale models which take advantage of the sphaleron cutoff temperature in order to liberate the parameters from stringent constraints.
Reuse & Permissions
Figure 14
Plots showing the impact of $Δ L = 1$ and $Δ N = 2$ processes on the dynamics for high scales ${M_{2}, M_{1}} = {10^{8}, 10^{4}} GeV$ (on the left) and low scales ${M_{2}, M_{1}} = {2, 0.2} TeV$ (on the right). The color coding, blue, red, purple, and black, is the same as in Figs. 11, 12, and 13. The dotted pattern is for decays only, dashed for decays plus $Δ L = 1$ scattering, and plain for decays plus $Δ L = 1$ and $Δ N = 2$ scattering.
Reuse & Permissions
Figure 15
The effect of ${K_{2}, K_{1}, K_{21}, β}$ on the dynamics for high ${M_{2}, M_{1}} = {10^{8}, 10^{4}} GeV$ (top two plots) and low ${M_{2}, M_{1}} = {2, 0.2} TeV$ (bottom four plots) mass regimes. The color coding, blue, red, purple, and black, is the same as Figs. 11, 12, and 13, while the dotted, dashed, and plain lines represent the variation of each parameter.
Reuse & Permissions
Figure 16
Plots of the full loop functions $F$ (solid) and the approximations (dashed) discussed in this section, as a function of the RHN mass hierarchy.
Reuse & Permissions
Figure 17
The differing contributions to the total $C P$ asymmetry $ε_{2}$ for various mass ratios $M_{2} / M_{1}$ . The high-mass ratio is dominated by the Yukawa-sourced $C P$ asymmetry, $ε_{0} \propto \sum_{α} m_{α} M_{2} / v^{2}$ (black, dotdashed line). The low-mass $C P$ asymmetry is proportional to the $β$ coupling via the vertex correction, $ε_{(β)} \sim \sqrt{M_{1} / M_{2}} | α β | / M_{2}$ (dotted lines). In the intermediate mass range, the $C P$ asymmetry is dominantly generated by the wave function correction $ε_{(α)} \sim | α |^{2} \sqrt{M_{1} / M_{2}}$ (dashed lines).
Reuse & Permissions
Figure 18
The left plot shows the thermal equilibrium parameter $K_{N_{i} \leftrightarrow L H}$ for both decays (plain) and inverse decays (dashed), for several equilibrium parameters $K_{N_{i} \leftrightarrow L H}$ . The right plot shows the solutions $z_{d}$ and $z_{i d}^{\pm}$ to the equilibrium condition for decays and inverse decays respectively. Decays and inverse decays are both in equilibrium in the gray area, which only happens if $K \geq 0.6$ .
Reuse & Permissions
Figure 19
This plot is a summary of the important scattering processes to account for, in order to properly manage the effect of $N_{1}$ on the lepton asymmetry. The corresponding Feynman diagrams are shown in the main text, in Fig. 7.
Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology