N2HDM + CP in the Dark + Fixes for R2HDM + C2HDM

Author: vollous

Diff for: docs/index.rst

@@ -52,8 +52,10 @@ BSMPT - Beyond the Standard Model Phase Transitions documentation
    :maxdepth: 1
    :caption: Models
 
-   models/r2hdm
    models/c2hdm
+   models/cp_in_the_dark
+   models/r2hdm
+   models/n2hdm
 
 .. toctree::
    :maxdepth: 1

Diff for: docs/models/c2hdm.rst

@@ -3,11 +3,12 @@
 C2HDM
 ==============
 
-This implementation was based on [`2108.03580 <https://arxiv.org/abs/2108.03580>`_]. On the scalar sector there are two doublets 
+This implementation was based on [`2108.03580 <https://arxiv.org/abs/2108.03580>`_]. 
 
-.. math::
-   \Phi_{1}=\left(\begin{array}{c}{{\phi_{1}^{+}}}\\ {{\phi_{1}^{0}}}\end{array}\right) \text{ and } \Phi_{2}=\left(\begin{array}{c}{{\phi_{2}^{+}}}\\ {{\phi_{2}^{0}}}\end{array}\right).
+On the scalar sector there are two doublets 
 
+.. math::
+   \Phi_1=\frac{1}{\sqrt{2}}\binom{\rho_1+\mathrm{i} \eta_1}{\zeta_1+\omega_1+\mathrm{i} \psi_1}, \quad \Phi_2=\frac{1}{\sqrt{2}}\binom{\rho_2+\omega_{\mathrm{CB}}+\mathrm{i} \eta_2}{\zeta_2+\omega_2+\mathrm{i}\left(\psi_2+\omega_{\mathrm{CP}}\right)}
 where we impose a softly-broken :math:`\mathbb{Z}_2` which takes
 
 .. math::
@@ -19,10 +20,15 @@ where we impose a softly-broken :math:`\mathbb{Z}_2` which takes
 The potential is given by
 
 .. math::
-   \begin{aligned}V_{\text {tree }}= & m_{11}^2 \Phi_1^{\dagger} \Phi_1+m_{22}^2 \Phi_2^{\dagger} \Phi_2-\left[m_{12}^2 \Phi_1^{\dagger} \Phi_2+\text { h.c. }\right]+\frac{1}{2} \lambda_1\left(\Phi_1^{\dagger} \Phi_1\right)^2+\frac{1}{2} \lambda_2\left(\Phi_2^{\dagger} \Phi_2\right)^2 \\& +\lambda_3\left(\Phi_1^{\dagger} \Phi_1\right)\left(\Phi_2^{\dagger} \Phi_2\right)+\lambda_4\left(\Phi_1^{\dagger} \Phi_2\right)\left(\Phi_2^{\dagger} \Phi_1\right)+\left[\frac{1}{2} \lambda_5\left(\Phi_1^{\dagger} \Phi_2\right)^2+\text { h.c. }\right] .\end{aligned}
+   \begin{aligned}V_{\text {C2HDM}}= & m_{11}^2 \Phi_1^{\dagger} \Phi_1+m_{22}^2 \Phi_2^{\dagger} \Phi_2-\left[m_{12}^2 \Phi_1^{\dagger} \Phi_2+\text { h.c. }\right]+\frac{1}{2} \lambda_1\left(\Phi_1^{\dagger} \Phi_1\right)^2+\frac{1}{2} \lambda_2\left(\Phi_2^{\dagger} \Phi_2\right)^2 \\& +\lambda_3\left(\Phi_1^{\dagger} \Phi_1\right)\left(\Phi_2^{\dagger} \Phi_2\right)+\lambda_4\left(\Phi_1^{\dagger} \Phi_2\right)\left(\Phi_2^{\dagger} \Phi_1\right)+\left[\frac{1}{2} \lambda_5\left(\Phi_1^{\dagger} \Phi_2\right)^2+\text { h.c. }\right] .\end{aligned}
 
 where all coupling constants are real except :math:`m_{12}` and :math:`\lambda_5` which, if non-real, explicitly break CP in the model at :math:`T = 0`.
 
+The :math:`T=0` vacuum is chosen to be
+
+.. math::
+   \left.\left\langle\Phi_1\right\rangle\right|_{T=0}=\frac{1}{\sqrt{2}}\binom{0}{v_1},\left.\quad\left\langle\Phi_2\right\rangle\right|_{T=0}=\frac{1}{\sqrt{2}}\binom{0}{v_2}\,.
+
 The Yukawa types defined by
    * Type I : :math:`\Phi_d = \Phi_l = \Phi_2`
    * Type II: :math:`\Phi_d = \Phi_l = \Phi_1`

Diff for: docs/models/cp_in_the_dark.rst

@@ -0,0 +1,38 @@
+.. _cp_in_the_dark:
+
+CP in the dark
+==============
+
+This implementation was based on [`1807.10322 <https://arxiv.org/abs/1807.10322>`_] and [`2204.13425 <https://arxiv.org/abs/2204.13425>`_]. 
+
+On the scalar sector there are two doublets 
+
+.. math::
+   \Phi_1=\frac{1}{\sqrt{2}}\binom{\rho_1+\mathrm{i} \eta_1}{\zeta_1+\omega_1+\mathrm{i} \psi_1}, \quad \Phi_2=\frac{1}{\sqrt{2}}\binom{\rho_2+\omega_{\mathrm{CB}}+\mathrm{i} \eta_2}{\zeta_2+\omega_2+\mathrm{i}\left(\psi_2+\omega_{\mathrm{CP}}\right)}, \quad \Phi_S=\zeta_3+\omega_S
+
+where we impose a softly-broken :math:`\mathbb{Z}_2` symmetry which takes
+
+.. math::
+   \begin{align}
+   \Phi_{1} &\to -\Phi_{1}\,,\\
+   \Phi_{2} &\to \Phi_{2}\,,\\
+   \Phi_S &\to -\Phi_S\,,
+   \end{align}
+
+The potential is given by
+
+.. math::
+    \begin{aligned}V_\text{CP in the Dark} &= m_{11}^2\left|\Phi_1\right|^2+m_{22}^2\left|\Phi_2\right|^2+\frac{1}{2} m_S^2 \Phi_S^2+\left(A \Phi_1^{\dagger} \Phi_2 \Phi_S+\text { h.c. }\right) \\& +\frac{1}{2} \lambda_1\left|\Phi_1\right|^4+\frac{1}{2} \lambda_2\left|\Phi_2\right|^4+\lambda_3\left|\Phi_1\right|^2\left|\Phi_2\right|^2+\lambda_4\left|\Phi_1^{\dagger} \Phi_2\right|^2+\frac{1}{2} \lambda_5\left[\left(\Phi_1^{\dagger} \Phi_2\right)^2+\text { h.c. }\right] \\& +\frac{1}{4} \lambda_6 \Phi_S^4+\frac{1}{2} \lambda_7\left|\Phi_1\right|^2 \Phi_S^2+\frac{1}{2} \lambda_8\left|\Phi_2\right|^2 \Phi_S^2,\end{aligned}
+
+where all coupling constants are real except :math:`A`, whose complex phase is directly linked with CP violation.
+
+The :math:`T=0` vacuum is chosen to be
+
+.. math::
+   \left.\left\langle\Phi_1\right\rangle\right|_{T=0}=\frac{1}{\sqrt{2}}\binom{0}{v_1},\left.\quad\left\langle\Phi_2\right\rangle\right|_{T=0}=\frac{1}{\sqrt{2}}\binom{0}{v_2},\left.\quad\langle S\rangle\right|_{T=0}=v_S
+
+The Yukawa types defined by
+   * Type I : :math:`\Phi_d = \Phi_l = \Phi_2`
+   * Type II: :math:`\Phi_d = \Phi_l = \Phi_1`
+   * Type  LS(=3): :math:`\Phi_d = \Phi_2\,, \Phi_l = \Phi_1`
+   * Type FL(=4): :math:`\Phi_d = \Phi_1 \,,\Phi_l = \Phi_2`

Diff for: docs/models/n2hdm.rst

@@ -0,0 +1,47 @@
+.. _n2hdm:
+
+N2HDM
+==============
+
+This implementation was based on [`1612.01309 <https://arxiv.org/abs/1612.01309>`_] and [`1912.10477 <https://arxiv.org/abs/1912.10477>`_]. 
+
+On the scalar sector there are two doublets 
+
+.. math::
+   \Phi_1=\frac{1}{\sqrt{2}}\binom{\rho_1+\mathrm{i} \eta_1}{\zeta_1+\omega_1+\mathrm{i} \psi_1}, \quad \Phi_2=\frac{1}{\sqrt{2}}\binom{\rho_2+\omega_{\mathrm{CB}}+\mathrm{i} \eta_2}{\zeta_2+\omega_2+\mathrm{i}\left(\psi_2+\omega_{\mathrm{CP}}\right)}, \quad \Phi_S=\zeta_3+\omega_S
+
+where we impose two softly-broken :math:`\mathbb{Z}_2` symmetries. One :math:`\mathbb{Z}_2` which takes
+
+.. math::
+   \begin{align}
+   \Phi_{1} &\to -\Phi_{1}\,,\\
+   \Phi_{2} &\to \Phi_{2}\,,\\
+   \Phi_S &\to \Phi_S\,,
+   \end{align}
+
+and another :math:`\mathbb{Z}_2` which takes
+
+.. math::
+   \begin{align}
+   \Phi_{1} &\to \Phi_{1}\,,\\
+   \Phi_{2} &\to \Phi_{2}\,,\\
+   \Phi_S &\to -\Phi_S\,.
+   \end{align}
+
+The potential is given by
+
+.. math::
+   \begin{aligned}V_{\mathrm{N} 2 \mathrm{HDM}}= & m_{11}^2 \Phi_1^{\dagger} \Phi_1+m_{22}^2 \Phi_2^{\dagger} \Phi_2-m_{12}^2\left(\Phi_1^{\dagger} \Phi_2+\text { h.c. }\right)+\frac{\lambda_1}{2}\left(\Phi_1^{\dagger} \Phi_1\right)^2+\frac{\lambda_2}{2}\left(\Phi_2^{\dagger} \Phi_2\right)^2 \\& +\lambda_3 \Phi_1^{\dagger} \Phi_1 \Phi_2^{\dagger} \Phi_2+\lambda_4 \Phi_1^{\dagger} \Phi_2 \Phi_2^{\dagger} \Phi_1+\frac{\lambda_5}{2}\left(\left(\Phi_1^{\dagger} \Phi_2\right)^2+\text { h.c. }\right) \\& +\frac{1}{2} m_S^2 \Phi_S^2+\frac{\lambda_6}{8} \Phi_S^4+\lambda_7\left(\Phi_1^{\dagger} \Phi_1\right) \Phi_S^2+\lambda_8\left(\Phi_2^{\dagger} \Phi_2\right) \Phi_S^2,\end{aligned}
+
+where all coupling constants are real to preserve CP in the model at :math:`T = 0`.
+
+The :math:`T=0` vacuum is chosen to be
+
+.. math::
+   \left.\left\langle\Phi_1\right\rangle\right|_{T=0}=\frac{1}{\sqrt{2}}\binom{0}{v_1},\left.\quad\left\langle\Phi_2\right\rangle\right|_{T=0}=\frac{1}{\sqrt{2}}\binom{0}{v_2},\left.\quad\langle S\rangle\right|_{T=0}=v_S
+
+The Yukawa types defined by
+   * Type I : :math:`\Phi_d = \Phi_l = \Phi_2`
+   * Type II: :math:`\Phi_d = \Phi_l = \Phi_1`
+   * Type  LS(=3): :math:`\Phi_d = \Phi_2\,, \Phi_l = \Phi_1`
+   * Type FL(=4): :math:`\Phi_d = \Phi_1 \,,\Phi_l = \Phi_2`

Diff for: docs/models/r2hdm.rst

@@ -3,10 +3,12 @@
 R2HDM
 ==============
 
-This implementation was based on [`1612.04086 <https://arxiv.org/abs/1612.04086>`_]. On the scalar sector there are two doublets 
+This implementation was based on [`1612.04086 <https://arxiv.org/abs/1612.04086>`_]. 
+
+On the scalar sector there are two doublets 
 
 .. math::
-   \Phi_{1}=\left(\begin{array}{c}{{\phi_{1}^{+}}}\\ {{\phi_{1}^{0}}}\end{array}\right) \text{ and } \Phi_{2}=\left(\begin{array}{c}{{\phi_{2}^{+}}}\\ {{\phi_{2}^{0}}}\end{array}\right).
+   \Phi_1=\frac{1}{\sqrt{2}}\binom{\rho_1+\mathrm{i} \eta_1}{\zeta_1+\omega_1+\mathrm{i} \psi_1}, \quad \Phi_2=\frac{1}{\sqrt{2}}\binom{\rho_2+\omega_{\mathrm{CB}}+\mathrm{i} \eta_2}{\zeta_2+\omega_2+\mathrm{i}\left(\psi_2+\omega_{\mathrm{CP}}\right)}
 
 where we impose a softly-broken :math:`\mathbb{Z}_2` which takes
 
@@ -19,10 +21,15 @@ where we impose a softly-broken :math:`\mathbb{Z}_2` which takes
 The potential is given by
 
 .. math::
-   \begin{aligned}V_{\text {tree }}= & m_{11}^2 \Phi_1^{\dagger} \Phi_1+m_{22}^2 \Phi_2^{\dagger} \Phi_2-\left[m_{12}^2 \Phi_1^{\dagger} \Phi_2+\text { h.c. }\right]+\frac{1}{2} \lambda_1\left(\Phi_1^{\dagger} \Phi_1\right)^2+\frac{1}{2} \lambda_2\left(\Phi_2^{\dagger} \Phi_2\right)^2 \\& +\lambda_3\left(\Phi_1^{\dagger} \Phi_1\right)\left(\Phi_2^{\dagger} \Phi_2\right)+\lambda_4\left(\Phi_1^{\dagger} \Phi_2\right)\left(\Phi_2^{\dagger} \Phi_1\right)+\left[\frac{1}{2} \lambda_5\left(\Phi_1^{\dagger} \Phi_2\right)^2+\text { h.c. }\right] .\end{aligned}
+   \begin{aligned}V_{\text {R2HDM}}= & m_{11}^2 \Phi_1^{\dagger} \Phi_1+m_{22}^2 \Phi_2^{\dagger} \Phi_2-\left[m_{12}^2 \Phi_1^{\dagger} \Phi_2+\text { h.c. }\right]+\frac{1}{2} \lambda_1\left(\Phi_1^{\dagger} \Phi_1\right)^2+\frac{1}{2} \lambda_2\left(\Phi_2^{\dagger} \Phi_2\right)^2 \\& +\lambda_3\left(\Phi_1^{\dagger} \Phi_1\right)\left(\Phi_2^{\dagger} \Phi_2\right)+\lambda_4\left(\Phi_1^{\dagger} \Phi_2\right)\left(\Phi_2^{\dagger} \Phi_1\right)+\left[\frac{1}{2} \lambda_5\left(\Phi_1^{\dagger} \Phi_2\right)^2+\text { h.c. }\right] .\end{aligned}
 
 where all coupling constants are real. :math:`m_{12}` and :math:`\lambda_5` could, in principle, be complex but are set to real to that there is no explicit CP violation in the model at :math:`T = 0`.
 
+The :math:`T=0` vacuum is chosen to be
+
+.. math::
+   \left.\left\langle\Phi_1\right\rangle\right|_{T=0}=\frac{1}{\sqrt{2}}\binom{0}{v_1},\left.\quad\left\langle\Phi_2\right\rangle\right|_{T=0}=\frac{1}{\sqrt{2}}\binom{0}{v_2}\,.
+
 The Yukawa types defined by
    * Type I : :math:`\Phi_d = \Phi_l = \Phi_2`
    * Type II: :math:`\Phi_d = \Phi_l = \Phi_1`