<chapter name="Left-Right-Symmetry Processes">
<h2>Left-Right-Symmetry Processes</h2>
At current energies, the world is left-handed, i.e. the Standard Model
contains an <ei>SU(2)_L</ei> group. Left-right symmetry at some larger
scale implies the need for an <ei>SU(2)_R</ei> group. Thus the particle
content is expanded by right-handed <ei>Z_R^0</ei> and <ei>W_R^+-</ei>
and right-handed neutrinos. The Higgs fields have to be in a triplet
representation, leading to doubly-charged Higgs particles, one set for
each of the two <ei>SU(2)</ei> groups. Also the number of neutral and
singly-charged Higgs states is increased relative to the Standard Model,
but a search for the lowest-lying states of this kind is no different
from e.g. the freedom already accorded by the MSSM Higgs scenarios.
<p/>
PYTHIA implements the scenario of <ref>Hui97</ref>.
<p/>
The <ei>W_R^+-</ei> has been implemented as a simple copy of the
ordinary <ei>W^+-</ei>, with the exception that it couples to
right-handed neutrinos instead of the ordinary left-handed ones.
Thus the standard CKM matrix is used in the quark sector, and the
same vector and axial coupling strengths, leaving only the mass as
free parameter. The <ei>Z_R^0</ei> implementation (without interference
with the photon or the ordinary <ei>Z^0</ei>) allows decays both to
left- and right-handed neutrinos, as well as other fermions, according
to one specific model ansatz. Obviously both the <ei>W_R^+-</ei>
and the <ei>Z_R^0</ei> descriptions are likely to be simplifications,
but provide a starting point.
<p/>
For the doubly-charged Higgs bosons, the main decay modes implemented are
<ei>H_L^++ → W_L^+ W_L^+, l_i^+ l_j^+ </ei> (<ei>i, j</ei> generation
indices) and <ei>H_R^++ → W_R^+ W_R^+, l_i^+ l_j^+</ei>.
<p/>
The right-handed neutrinos can be allowed to decay further. Assuming them
to have a mass below that of <ei>W_R^+-</ei>, they decay to three-body
states via a virtual <ei>W_R^+-</ei>, <ei>nu_Rl → l+- f fbar'</ei>,
where both lepton charges are allowed owing to the Majorana character
of the neutrinos. If there is a significant mass splitting, also
sequential decays <ei>nu_Rl → l+- l'-+ nu'_Rl</ei> are allowed.
Currently the decays are isotropic in phase space. If the neutrino
masses are close to or above the <ei>W_R^</ei> ones, this description
has to be substituted by a sequential decay via a real <ei>W_R^</ei>
(not implemented, but actually simpler to do than the one here).
<h3>Production processes</h3>
A few different production processes have been implemented, which normally
would not overlap and therefore could be run together.
<flag name="LeftRightSymmmetry:all" default="off">
Common switch for the group of implemented processes within a
left-right-symmetric scenario.
</flag>
<flag name="LeftRightSymmmetry:ffbar2ZR" default="off">
Scatterings <ei>f fbar → Z_R^0</ei>.
Code 3101.
</flag>
<flag name="LeftRightSymmmetry:ffbar2WR" default="off">
Scatterings <ei><f fbar' → W_R^+</ei>.
Code 3102.
</flag>
<flag name="LeftRightSymmmetry:ll2HL" default="off">
Scatterings <ei>l_i l_j → H_L^--</ei>.
Code 3121.
</flag>
<flag name="LeftRightSymmmetry:lgm2HLe" default="off">
Scatterings <ei>l_i gamma → H_L^-- e^+</ei>.
Code 3122.
</flag>
<flag name="LeftRightSymmmetry:lgm2HLmu" default="off">
Scatterings <ei>l_i gamma → H_L^-- mu^+</ei>.
Code 3123.
</flag>
<flag name="LeftRightSymmmetry:lgm2HLtau" default="off">
Scatterings <ei>l_i gamma → H_L^-- tau^+</ei>.
Code 3124.
</flag>
<flag name="LeftRightSymmmetry:ff2HLff" default="off">
Scatterings <ei>f_1 f_2 → H_L^-- f_3 f_4</ei> via <ei>WW</ei> fusion.
Code 3125.
</flag>
<flag name="LeftRightSymmmetry:ffbar2HLHL" default="off">
Scatterings <ei>f fbar → H_L^++ H_L^--</ei>.
Code 3126.
</flag>
<flag name="LeftRightSymmmetry:ll2HR" default="off">
Scatterings <ei>l_i l_j → H_R^--</ei>.
Code 3141.
</flag>
<flag name="LeftRightSymmmetry:lgm2HRe" default="off">
Scatterings <ei>l_i gamma → H_R^-- e^+</ei>.
Code 3142.
</flag>
<flag name="LeftRightSymmmetry:lgm2HRmu" default="off">
Scatterings <ei>l_i gamma → H_R^-- mu^+</ei>.
Code 3143.
</flag>
<flag name="LeftRightSymmmetry:lgm2HRtau" default="off">
Scatterings <ei>l_i gamma → H_R^-- tau^+</ei>.
Code 3144.
</flag>
<flag name="LeftRightSymmmetry:ff2HRff" default="off">
Scatterings <ei>f_1 f_2 → H_R^-- f_3 f_4</ei> via <ei>WW</ei> fusion.
Code 3145.
</flag>
<flag name="LeftRightSymmmetry:ffbar2HRHR" default="off">
Scatterings <ei>f fbar → H_R^++ H_R^--</ei>.
Code 3146.
</flag>
<h3>Parameters</h3>
The basic couplings of the model are
<parm name="LeftRightSymmmetry:gL" default="0.64" min="0.0">
lefthanded coupling <ei>g_L = e / sin(theta)</ei>.
</parm>
<parm name="LeftRightSymmmetry:gR" default="0.64" min="0.0">
righthanded coupling <ei>g_R</ei>, assumed the same as <ei>g_L</ei>.
</parm>
<parm name="LeftRightSymmmetry:vL" default="5." min="0.0">
vacuum expectation value <ei>v_L</ei> (in GeV) for the left-triplet.
</parm>
<p/>
The corresponding vacuum expectation value <ei>v_R</ei> is assumed
given by <ei>v_R = sqrt(2) M_WR / g_R</ei> and is not stored explicitly.
<p/>
The Yukawa couplings of a lepton pair to a <ei>H^--</ei>, assumed the
same for <ei>H_L^--</ei> and <ei>H_R^--</ei>, is described by a symmetric
3-by-3 matrix. The default matrix is dominated by the diagonal elements
and especially by the <ei>tau tau</ei> one.
<parm name="LeftRightSymmmetry:coupHee" default="0.1" min="0.0">
Yukawa coupling for <ei>H^-- → e- e-</ei>.
</parm>
<parm name="LeftRightSymmmetry:coupHmue" default="0.01" min="0.0">
Yukawa coupling for <ei>H^-- → mu- e-</ei>.
</parm>
<parm name="LeftRightSymmmetry:coupHmumu" default="0.1" min="0.0">
Yukawa coupling for <ei>H^-- → mu- mu-</ei>.
</parm>
<parm name="LeftRightSymmmetry:coupHtaue" default="0.01" min="0.0">
Yukawa coupling for <ei>H^-- → tau- e-</ei>.
</parm>
<parm name="LeftRightSymmmetry:coupHtaumu" default="0.01" min="0.0">
Yukawa coupling for <ei>H^-- → tau- mu-</ei>.
</parm>
<parm name="LeftRightSymmmetry:coupHtautau" default="0.3" min="0.0">
Yukawa coupling for <ei>H^-- → tau- tau-</ei>.
</parm>
</chapter>
<!-- Copyright (C) 2014 Torbjorn Sjostrand -->
Marcin Chrzaszcz