PREPRINT

Observable ΔNeff in Dirac Scotogenic Model

Debasish Borah, Pritam Das, Dibyendu Nanda

Submitted on 23 November 2022

Figures are fetched from the INSPIRE database at: https://inspirehep.net/literature/2514147

Left panel: Neutrino mass generation at a one-loop level in Dirac scotogenic model. Here, $S_i (~ with~ i=1,2)$ is the physical mass eigenstate.\\ Right panel: one-loop contribution charged lepton flavour violating process $l_\alpha\rightarrow l_\beta\gamma$.
Figure 1: Left panel: Neutrino mass generation at a one-loop level in Dirac scotogenic model. Here, Si( with i=1,2) is the physical mass eigenstate.\ Right panel: one-loop contribution charged lepton flavour violating process lαlβγ.
Left panel: Neutrino mass generation at a one-loop level in Dirac scotogenic model. Here, $S_i (~ with~ i=1,2)$ is the physical mass eigenstate.\\ Right panel: one-loop contribution charged lepton flavour violating process $l_\alpha\rightarrow l_\beta\gamma$.
Figure 2: Left panel: Neutrino mass generation at a one-loop level in Dirac scotogenic model. Here, Si( with i=1,2) is the physical mass eigenstate.\ Right panel: one-loop contribution charged lepton flavour violating process lαlβγ.
Dominant DM annihilation processes. In the right panel Feynman diagram, $\phi$ corresponds to all the states of $\phi$ including $\phi^0, \phi^\pm$ depending upon the final state lepton.
Figure 3: Dominant DM annihilation processes. In the right panel Feynman diagram, ϕ corresponds to all the states of ϕ including ϕ0,ϕ± depending upon the final state lepton.
Scattering processes associated with thermalisation of $\chi$ with the SM bath.
Figure 4: Scattering processes associated with thermalisation of χ with the SM bath.
Comparison of elastic scattering rate of $\chi$ from the SM bath with Hubble expansion rate for different choices of mass and quartic coupling $\lambda_5$.
Figure 5: Comparison of elastic scattering rate of χ from the SM bath with Hubble expansion rate for different choices of mass and quartic coupling λ5.
Comparison of elastic scattering rate of $\chi$ from the SM bath with Hubble expansion rate for different choices of mass and quartic coupling $\lambda_5$.
Figure 6: Comparison of elastic scattering rate of from the SM bath with Hubble expansion rate for different choices of mass and quartic coupling .
Comparison of elastic scattering rate of $\chi$ from the SM bath with Hubble expansion rate for different choices of mass and quartic coupling $\lambda_5$.
Figure 7: Comparison of elastic scattering rate of from the SM bath with Hubble expansion rate for different choices of mass and quartic coupling .
Comparison of elastic scattering rate of $\chi$ from the SM bath with Hubble expansion rate for different choices of mass and quartic coupling $\lambda_5$.
Figure 8: Comparison of elastic scattering rate of from the SM bath with Hubble expansion rate for different choices of mass and quartic coupling .
Thermalisation of $\nu_R$ with the dark sector.
Figure 9: Thermalisation of with the dark sector.
Higgs portal coupling and mass variation for the temperature ratio $(\frac{T_{\nu_R}}{T_\gamma})^4$ with $x$.
Figure 10: Higgs portal coupling and mass variation for the temperature ratio with .
Higgs portal coupling and mass variation for the temperature ratio $(\frac{T_{\nu_R}}{T_\gamma})^4$ with $x$.
Figure 11: Higgs portal coupling and mass variation for the temperature ratio with .
Higgs portal coupling and mass variation for the temperature ratio $(\frac{T_{\nu_R}}{T_\gamma})^4$ with $x$.
Figure 12: Higgs portal coupling and mass variation for the temperature ratio with .
Higgs portal coupling and mass variation for the temperature ratio $(\frac{T_{\nu_R}}{T_\gamma})^4$ with $x$.
Figure 13: Higgs portal coupling and mass variation for the temperature ratio with .
Left panel: The solid and dashed lines represent dark matter and RH$\nu$ decoupling patterns for two benchmark points indicated by two colours. Right panel: Decoupling temperatures of DM and right-handed neutrinos.
Figure 14: Left panel: The solid and dashed lines represent dark matter and RH decoupling patterns for two benchmark points indicated by two colours. Right panel: Decoupling temperatures of DM and right-handed neutrinos.
Left panel: The solid and dashed lines represent dark matter and RH$\nu$ decoupling patterns for two benchmark points indicated by two colours. Right panel: Decoupling temperatures of DM and right-handed neutrinos.
Figure 15: Left panel: The solid and dashed lines represent dark matter and RH decoupling patterns for two benchmark points indicated by two colours. Right panel: Decoupling temperatures of DM and right-handed neutrinos.
Variation of dark matter mass and its co-relation with different parameters for relic abundance. All the points do satisfy the $3\sigma$ bound on DM relic abundance $\Omega h^2=0.117-0.123$. The colour band shows $\Delta N_{eff}$ values for respective parameters. The red and blue dashed line satisfies the current bound on neutrino mass $m_\nu=0.12$ eV from Eq. \eqref{enmass} for mixing angles $sin\theta=0.001$ and $sin\theta=0.01$ respectively. A larger mixing angle would not influence the DM analysis due to the tiny Yukawa ($y_\phi\sim10^{-6}$) associated with $\phi$.
Figure 16: Variation of dark matter mass and its co-relation with different parameters for relic abundance. All the points do satisfy the bound on DM relic abundance . The colour band shows values for respective parameters. The red and blue dashed line satisfies the current bound on neutrino mass eV from Eq. for mixing angles and respectively. A larger mixing angle would not influence the DM analysis due to the tiny Yukawa () associated with .
Variation of dark matter mass and its co-relation with different parameters for relic abundance. All the points do satisfy the $3\sigma$ bound on DM relic abundance $\Omega h^2=0.117-0.123$. The colour band shows $\Delta N_{eff}$ values for respective parameters. The red and blue dashed line satisfies the current bound on neutrino mass $m_\nu=0.12$ eV from Eq. \eqref{enmass} for mixing angles $sin\theta=0.001$ and $sin\theta=0.01$ respectively. A larger mixing angle would not influence the DM analysis due to the tiny Yukawa ($y_\phi\sim10^{-6}$) associated with $\phi$.
Figure 17: Variation of dark matter mass and its co-relation with different parameters for relic abundance. All the points do satisfy the bound on DM relic abundance . The colour band shows values for respective parameters. The red and blue dashed line satisfies the current bound on neutrino mass eV from Eq. for mixing angles and respectively. A larger mixing angle would not influence the DM analysis due to the tiny Yukawa () associated with .
Variation of $\Delta N_{\rm eff}$ with other the Higgs-$\chi$ quartic coupling ($\lambda_5$). In the left panel, we show singlet scalar mass ($M_\chi$)  while in the right panel we show the dark matter mass ($M_{\rm DM}$) in the colour bar. All the points do satisfy bounds such as dark matter relic, neutrino mass and LFV for Br($\mu\rightarrow e\gamma  $)
Figure 18: Variation of with other the Higgs- quartic coupling (). In the left panel, we show singlet scalar mass () while in the right panel we show the dark matter mass () in the colour bar. All the points do satisfy bounds such as dark matter relic, neutrino mass and LFV for Br()
Variation of $\Delta N_{\rm eff}$ with other the Higgs-$\chi$ quartic coupling ($\lambda_5$). In the left panel, we show singlet scalar mass ($M_\chi$)  while in the right panel we show the dark matter mass ($M_{\rm DM}$) in the colour bar. All the points do satisfy bounds such as dark matter relic, neutrino mass and LFV for Br($\mu\rightarrow e\gamma  $)
Figure 19: Variation of with other the Higgs- quartic coupling (). In the left panel, we show singlet scalar mass () while in the right panel we show the dark matter mass () in the colour bar. All the points do satisfy bounds such as dark matter relic, neutrino mass and LFV for Br()
The allowed current $3\sigma$ allowed bound for dark matter parameter spaces in $M_{\rm DM}~vs.~ M_{\phi^0}$ plane and the colour bar indicating the singlet scalar mass ($M_\chi$). The left panel represents the case when $y_\chi=y_\phi=0.2$ and the right panel is for $y_\chi=y_\phi=0.02$.
Figure 20: The allowed current allowed bound for dark matter parameter spaces in plane and the colour bar indicating the singlet scalar mass (). The left panel represents the case when and the right panel is for .
The allowed current $3\sigma$ allowed bound for dark matter parameter spaces in $M_{\rm DM}~vs.~ M_{\phi^0}$ plane and the colour bar indicating the singlet scalar mass ($M_\chi$). The left panel represents the case when $y_\chi=y_\phi=0.2$ and the right panel is for $y_\chi=y_\phi=0.02$.
Figure 21: The allowed current allowed bound for dark matter parameter spaces in plane and the colour bar indicating the singlet scalar mass (). The left panel represents the case when and the right panel is for .
The contribution to $\Delta N_{\rm eff}$ vs. dark matter mass when both the Yukawa couplings are equal. Here the colour band indicates the decoupling temperature of the dark matter candidate. All the points do satisfy the current 3$\sigma$ range of the dark matter relic abundance.
Figure 22: The contribution to vs. dark matter mass when both the Yukawa couplings are equal. Here the colour band indicates the decoupling temperature of the dark matter candidate. All the points do satisfy the current 3 range of the dark matter relic abundance.
The contribution to $\Delta N_{\rm eff}$ vs. dark matter mass when both the Yukawa couplings are equal. Here the colour band indicates the decoupling temperature of the dark matter candidate. All the points do satisfy the current 3$\sigma$ range of the dark matter relic abundance.
Figure 23: The contribution to vs. dark matter mass when both the Yukawa couplings are equal. Here the colour band indicates the decoupling temperature of the dark matter candidate. All the points do satisfy the current 3 range of the dark matter relic abundance.
Br$(\mu\rightarrow e\gamma)$ versus DM mass for two different choices of Yukawa couplings. The red and blue points correspond to the two choices of Yukawa couplings $y\phi=0.2$ and $y_\phi=0.02$ respectively. The green and purple horizontal lines are respectively the current and future sensitivity bounds from MEG-I \cite{MEG:2016leq} and MEG-II \cite{MEGII:2018kmf} experiments.
Figure 24: Br versus DM mass for two different choices of Yukawa couplings. The red and blue points correspond to the two choices of Yukawa couplings and respectively. The green and purple horizontal lines are respectively the current and future sensitivity bounds from MEG-I \cite{MEG:2016leq} and MEG-II \cite{MEGII:2018kmf} experiments.
Schematic diagram for one-loop dark matter scattering off nucleon via SM Higgs
Figure 25: Schematic diagram for one-loop dark matter scattering off nucleon via SM Higgs
Spin-independent scattering cross-section of DM for two different choices of Yukawa couplings $y_\chi$.
Figure 26: Spin-independent scattering cross-section of DM for two different choices of Yukawa couplings .