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 special 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. PREPRINT, 2018. arXiv:1808.03466.
[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.