# Two-Higgs-Doublet Model¶

The Two-Higgs-Doublet Model (THDM) extends the SM by one additional Higgs doublet field with hypercharge $$Y_S=1$$. The most general CP-conserving softly-broken $$Z_2$$-symmetric renormalizable scalar potential reads

$\begin{split}V_{\mathrm{HSESM}} &= m_1^2 \Phi_1^\dagger \Phi_1 + m_2^2 \Phi_2^\dagger \Phi_2 + \frac{m_{12}^2}{2} \left(\Phi_1^\dagger \Phi_2 + \Phi_2^\dagger \Phi_1\right)\\ &+\frac{\lambda_1}{2} \left(\Phi_1^\dagger \Phi_1\right)^2 +\frac{\lambda_2}{2} \left(\Phi_2^\dagger \Phi_2\right)^2 +\lambda_3 \left(\Phi_1^\dagger \Phi_1\right)\left(\Phi_2^\dagger \Phi_2\right)\\ &+\lambda_4 \left(\Phi_1^\dagger \Phi_2\right)\left(\Phi_2^\dagger \Phi_1\right) +\frac{\lambda_2}{2} \left[\left(\Phi_1^\dagger \Phi_2\right)^2 + \left(\Phi_2^\dagger \Phi_1\right)^2\right],\end{split}$

with $$\Phi_i$$ being the Higgs doublets, and all parameters are real. Our implementation is consistent with the original literature [GH03], [BFL+12]. We choose the following set of physical parameters:

Basis THDM potential Gauge part
before SSB $$m_1$$, $$m_2$$, $$m_{12}$$, $$\lambda_1$$, $$\lambda_2$$, $$\lambda_3$$, $$\lambda_4$$, $$\lambda_5$$ $$g$$, $$g^\prime$$
Recola2 input $$M_{\mathrm{H}_l}$$, $$M_{\mathrm{H}_h}$$, $$M_{\mathrm{H}_a}$$, $$M_{\mathrm{H}_c}$$, $$c_{\alpha\beta}$$, $$t_\beta$$, $$\lambda_5$$, $$M_\mathrm{W}$$ $$\alpha_\mathrm{em}$$, $$M_\mathrm{Z}$$

The fields extend the ones in the SM by

Fields Recola identifier
$$H_\mathrm{l}$$ 'Hl'
$$H_\mathrm{h}$$ 'Hh'
$$H^+$$, $$H^-$$ 'H+', 'H-'
$$H_a$$ 'Ha'

where $$H_\mathrm{l}$$ is the lighter Higgs-boson which typically takes the role of the SM one.

## THDM interface¶

The THDM comes with special functions which can be accessed Recola2:

 set_tb_cab_rcl(tb,cab) Sets the value for $$\tan(\beta)$$ and $$c_{\alpha\beta}$$ to tb and cab, respectively. set_l5_rcl(l5) Sets the value for $$\lambda_5$$ to l5. set_Z2_thdm_yukawa_type_rcl(ytype) Sets the yukawa type in the softly-broken Z2 symmetric THDM to ytype. set_pole_mass_hl_hh_rcl(ml,gl,mh,gh) Sets the pole masses, widths of the light and heavy Higgs bosons to ml, gl and mh, gh, respectively. set_pole_mass_ha_rcl(m,g) Sets the pole mass and width of the pseudo-scalar Higgs boson ha. set_pole_mass_hc_rcl(m,g) Sets the pole mass and width of the charged Higgs boson hc.

The standard renormalization schemes are accessed by the following functions:

 use_mixing_alpha_msbar_scheme_rcl(s) Sets the renormalization scheme for the mixing angle $$\alpha$$ to an $$\overline{\mathrm{MS}}$$ scheme. use_mixing_beta_msbar_scheme_rcl(s) Sets the renormalization scheme for the mixing angle $$\beta$$ to an $$\overline{\mathrm{MS}}$$ scheme. use_mixing_alpha_onshell_scheme_rcl(s) Sets the renormalization scheme for the mixing angle $$\alpha$$ to an on-shell or BFM scheme. use_mixing_beta_onshell_scheme_rcl(s) Sets the renormalization scheme for the mixing angle $$\beta$$ to an on-shell or BFM scheme.

For details on the schems we refer to [DDL18]. On request we can provide other renormalization schemes.

## Releases¶

References

 [BFL+12] G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, Marc Sher, and Joao P. Silva. Theory and phenomenology of Two-Higgs-Doublet Models. Phys. Rept., 516:1–102, 2012. arXiv:1106.0034, doi:10.1016/j.physrep.2012.02.002.
 [DDL18] Ansgar Denner, Stefan Dittmaier, and Jean-Nicolas Lang. Renormalization of mixing angles. JHEP, 11:104, 2018. arXiv:1808.03466, doi:10.1007/JHEP11(2018)104.
 [GH03] John F. Gunion and Howard E. Haber. The CP conserving Two-Higgs-Doublet Model: the approach to the decoupling limit. Phys. Rev., D67:075019, 2003. arXiv:hep-ph/0207010, doi:10.1103/PhysRevD.67.075019.