Higgs Triplet Extension of the Standard Model¶
This Higgs Triplet Extension of the Standard Model (HT) is a simple extended Higgs sector with one additional real vevless SU(2) Higgs triplet field \(\Sigma\) with hypercharge \(Y_\Sigma=0\). Our conventions follow mainly [FPPRMW09]. See also [CDJ08].
In the vevless case the most general renormalizable scalar potential reads
with \(\Phi\) being the SM Higgs doublet and \(F\) being defined as
Parameter conventions¶
Parameters of the model can be set with the generic function
set_parameter_rcl()
.
All parameters in the HT are defined to be real and we choose the following set of physical parameters:
Basis |
HT potential |
Gauge part |
---|---|---|
before SSB |
\(m_\Phi\), \(m_\Sigma\), \(\lambda\), \(a_2\), \(b_4\) |
\(g\), \(g^\prime\) |
Recola2 input |
\(M_{\mathrm{H}_1}\), \(M_{\mathrm{H}^\pm}\), \(a_2\), \(b_4\), \(M_\mathrm{W}\) |
\(\alpha_\mathrm{em}\), \(M_\mathrm{Z}\) |
The default values are
Parameter |
Recola identifier |
default value |
---|---|---|
\(M_{\mathrm{H}_1}\) |
|
125 |
\(M_{\mathrm{H}^\pm}\) |
|
500 |
\(a_{2}\) |
|
0.1 |
\(b_{4}\) |
|
0.2 |
The fields extend the ones in the SM by
Fields |
Recola identifier |
---|---|
\(H_\mathrm{1}\) |
|
\(H_\mathrm{2}\) |
|
\(H^+\) |
|
\(H^-\) |
|
where \(H_\mathrm{1}\) is the lighter Higgs-boson which typically takes the role of the SM one.
Power counting and renormalization¶
The model has been implemented with a power counting (see SM power
counting) that assumes the couplings \(a_2\),
\(b_2\) to scale as \(\mathrm{QED}^2\). The renormalization has been
performed in the complete on-shell scheme with the possibility to switch between
standard EW renormalization schemes. The new Higgs-potential parameters are
renormalized MSbar. Concerning the renormalization see also
[BH98]. The mass correction to the second neutral Higgs-boson can be
printed by increasing the print level set_print_level_parameters_rcl()
.
Snippet code using the HT¶
from pyrecola import *
set_output_file_rcl('*')
set_print_level_squared_amplitude_rcl(2)
# Change HT parameters
set_parameter_rcl("MH1", 125.)
set_parameter_rcl("MHP", 350.)
set_parameter_rcl("a2", 0.3)
set_parameter_rcl("b4", -0.7)
# enable to draw off-shell currents
# set_draw_level_branches_rcl(1)
define_process_rcl(1, 'e+ e- -> H+ H-', 'NLO')
generate_processes_rcl()
p1 = [500., 0., 0., 500.]
p2 = [500., 0., 0., -500.]
# generate a sample PSP using RAMBO
p = set_outgoing_momenta_rcl(1, [p1, p2])
# compute tree squared and tree one-loop interference
compute_process_rcl(1, p, 'NLO')
# get all different contributions (pow=[n,m,o] == gs^n e^m k^o)
A0 = get_squared_amplitude_rcl(1, 'LO', pow=[0, 4])
# born-virtual interference (EW corrections)
A1 = get_squared_amplitude_rcl(1, 'NLO', pow=[0, 6])
print("A0:", A0)
print("A1:", A1)
reset_recola_rcl()
program main
use recola
implicit none
integer, parameter :: dp = kind (23d0)
real(dp) :: p(0:3,1:4), A0, A1
call set_parameter_rcl("MH1", complex(125d0,0d0))
call set_parameter_rcl("MHP", complex(350,0d0))
call set_parameter_rcl("a2", complex(0.3d0,0d0))
call set_parameter_rcl("b4", complex(-0.7d0,0d0))
call set_output_file_rcl('*')
call set_print_level_squared_amplitude_rcl(2)
! enable to draw off-shell currents
! call set_draw_level_branches_rcl(1)
call define_process_rcl(1, 'e+ e- -> H+ H-', 'NLO')
call generate_processes_rcl
p(:,1) = [500d0, 0d0, 0d0, 500d0]
p(:,2) = [500d0, 0d0, 0d0, -500d0]
! generate a sample PSP using RAMBO
call set_outgoing_momenta_rcl(1, p(:,1:2), p)
! compute tree squared and tree one-loop interference
call compute_process_rcl(1, p, 'NLO')
call get_squared_amplitude_rcl(1,[0,4], 'LO' , A0)
call get_squared_amplitude_rcl(1,[0,6], 'NLO', A1)
write(*,*) "A0:", A0
write(*,*) "A1:", A1
end program main
#include "recola.hpp"
#include <iostream>
int main(int argc, char *argv[])
{
Recola::set_output_file_rcl("*");
Recola::set_print_level_squared_amplitude_rcl(2);
Recola::set_parameter_rcl("MH1", 125.);
Recola::set_parameter_rcl("MHP", 350.);
Recola::set_parameter_rcl("a2", 0.3);
Recola::set_parameter_rcl("b4", -0.7);
// enable to draw off-shell currents
// Recola::set_draw_level_branches_rcl(1);
Recola::define_process_rcl(1, "e+ e- -> H+ H-", "NLO");
// generate it
Recola::generate_processes_rcl();
// generate a sample PSP using RAMBO
double pin[2][4] =
{{500., 0., 0., 500.},
{500., 0., 0., -500.}};
double p[4][4];
Recola::set_outgoing_momenta_rcl(1, pin, p);
// compute tree squared and tree one-loop interference
double A2[2];
Recola::compute_process_rcl(1, p, "NLO", A2);
double A0,A1;
int pow[2] = {0, 4};
Recola::get_squared_amplitude_rcl(1, pow, "LO", A0);
pow[1] = 6;
Recola::get_squared_amplitude_rcl(1, pow, "NLO", A1);
std::cout << "A0: " << A0 << std::endl;
std::cout << "A1: " << A1 << std::endl;
return 0;
}
UFO model files¶
References
- BH98
T. Blank and W. Hollik. Precision observables in SU(2) x U(1) models with an additional Higgs triplet. Nucl. Phys. B, 514:113–134, 1998. arXiv:hep-ph/9703392, doi:10.1016/S0550-3213(97)00785-2.
- CDJ08
Mu-Chun Chen, Sally Dawson, and C.B. Jackson. Higgs Triplets, Decoupling, and Precision Measurements. Phys. Rev. D, 78:093001, 2008. arXiv:0809.4185, doi:10.1103/PhysRevD.78.093001.
- FPPRMW09
Pavel Fileviez Perez, Hiren H. Patel, Michael.J. Ramsey-Musolf, and Kai Wang. Triplet Scalars and Dark Matter at the LHC. Phys. Rev. D, 79:055024, 2009. arXiv:0811.3957, doi:10.1103/PhysRevD.79.055024.