.. _ht:

.. currentmodule:: pyrecola

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 :m:`\Sigma` with hypercharge
:math:`Y_\Sigma=0`. Our conventions follow mainly :cite:`FileviezPerez:2008bj`. See
also :cite:`Chen:2008jg`.

In the vevless case the most general renormalizable scalar potential reads

.. math:: V_{\mathrm{HT}} = -m_\Phi^2 \Phi^\dagger \Phi
                            -m_\Sigma^2 F
  +\frac{\lambda}{4} \left(\Phi^\dagger \Phi\right)^2
  +\frac{b_4}{4} F^2
  +\frac{a_2}{2} \Phi^\dagger \Phi F,
  :label: eq:htpot

with :math:`\Phi` being the *SM* Higgs doublet and :math:`F` being defined as

.. math:: F = 2 \mathrm{Tr} \left[ \Sigma\cdot\Sigma\right].

Parameter conventions
*********************

Parameters of the model can be set with the generic function
:py:meth:`set_parameter_rcl`.
All parameters in the HT are defined to be real and we choose the following set of physical parameters:

.. list-table::
   :widths: 6 10 4
   :header-rows: 1
   :align: center

   * - Basis
     - HT potential
     - Gauge part

   * - before SSB
     - :m:`m_\Phi`, :m:`m_\Sigma`, :m:`\lambda`, :m:`a_2`, :m:`b_4`
     - :m:`g`, :m:`g^\prime`

   * - Recola2 input
     - :m:`M_{\mathrm{H}_1}`, :m:`M_{\mathrm{H}^\pm}`, :m:`a_2`, :m:`b_4`, :m:`M_\mathrm{W}`
     - :m:`\alpha_\mathrm{em}`, :m:`M_\mathrm{Z}`


The default values are

.. list-table::
   :widths: 6 12 8
   :header-rows: 1
   :align: center

   * - Parameter
     - |recola| identifier
     - default value
   * - :m:`M_{\mathrm{H}_1}`
     - ``'MH1'``
     - 125
   * - :m:`M_{\mathrm{H}^\pm}`
     - ``'MHP'``
     - 500
   * - :m:`a_{2}`
     - ``'a2'``
     - 0.1
   * - :m:`b_{4}`
     - ``'b4'``
     - 0.2

The fields extend the ones in the :ref:`SM <fieldconventions>` by

.. list-table::
   :widths: 10 12
   :header-rows: 1
   :align: center

   * - Fields
     - |recola| identifier
   * - :m:`H_\mathrm{1}`
     - :code:`'H1'`
   * - :m:`H_\mathrm{2}`
     - :code:`'H2'`
   * - :m:`H^+`
     - :code:`'H+'`
   * - :m:`H^-`
     - :code:`'H-'`

where :m:`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 :ref:`SM power
counting <powercounting>`) that assumes the couplings :m:`a_2`,
:m:`b_2`` to scale as :m:`\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
:cite:`Blank:1997qa`. The mass correction to the second neutral Higgs-boson can be
printed by increasing the print level :py:meth:`set_print_level_parameters_rcl`.


Snippet code using the HT
*************************


.. tabs::

  .. code-tab:: py

      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()

  .. code-tab:: fortran

      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

  .. code-tab:: c++

      #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;
      }

Releases
^^^^^^^^

* :ht:`2.2.3` **newest**
* :ht:`2.2.2`


UFO model files
^^^^^^^^^^^^^^^
* :ht:`UFO`

.. rubric :: References

.. bibliography:: ../references.bib
   :filter: docname in docnames