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<title>Left-Right-Symmetry Processes</title>
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<h2>Left-Right-Symmetry Processes</h2>
At current energies, the world is left-handed, i.e. the Standard Model
contains an <i>SU(2)_L</i> group. Left-right symmetry at some larger
scale implies the need for an <i>SU(2)_R</i> group. Thus the particle
content is expanded by right-handed <i>Z_R^0</i> and <i>W_R^+-</i>
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 <i>SU(2)</i> 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 [<a href="Bibliography.html" target="page">Hui97</a>].
<p/>
The <i>W_R^+-</i> has been implemented as a simple copy of the
ordinary <i>W^+-</i>, 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 <i>Z_R^0</i> implementation (without interference
with the photon or the ordinary <i>Z^0</i>) allows decays both to
left- and right-handed neutrinos, as well as other fermions, according
to one specific model ansatz. Obviously both the <i>W_R^+-</i>
and the <i>Z_R^0</i> descriptions are likely to be simplifications,
but provide a starting point.
<p/>
For the doubly-charged Higgs bosons, the main decay modes implemented are
<i>H_L^++ → W_L^+ W_L^+, l_i^+ l_j^+ </i> (<i>i, j</i> generation
indices) and <i>H_R^++ → W_R^+ W_R^+, l_i^+ l_j^+</i>.
<p/>
The right-handed neutrinos can be allowed to decay further. Assuming them
to have a mass below that of <i>W_R^+-</i>, they decay to three-body
states via a virtual <i>W_R^+-</i>, <i>nu_Rl → l+- f fbar'</i>,
where both lepton charges are allowed owing to the Majorana character
of the neutrinos. If there is a significant mass splitting, also
sequential decays <i>nu_Rl → l+- l'-+ nu'_Rl</i> are allowed.
Currently the decays are isotropic in phase space. If the neutrino
masses are close to or above the <i>W_R^</i> ones, this description
has to be substituted by a sequential decay via a real <i>W_R^</i>
(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.
<p/><code>flag </code><strong> LeftRightSymmmetry:all </strong>
(<code>default = <strong>off</strong></code>)<br/>
Common switch for the group of implemented processes within a
left-right-symmetric scenario.
<p/><code>flag </code><strong> LeftRightSymmmetry:ffbar2ZR </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar → Z_R^0</i>.
Code 3101.
<p/><code>flag </code><strong> LeftRightSymmmetry:ffbar2WR </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i><f fbar' → W_R^+</i>.
Code 3102.
<p/><code>flag </code><strong> LeftRightSymmmetry:ll2HL </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i l_j → H_L^--</i>.
Code 3121.
<p/><code>flag </code><strong> LeftRightSymmmetry:lgm2HLe </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma → H_L^-- e^+</i>.
Code 3122.
<p/><code>flag </code><strong> LeftRightSymmmetry:lgm2HLmu </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma → H_L^-- mu^+</i>.
Code 3123.
<p/><code>flag </code><strong> LeftRightSymmmetry:lgm2HLtau </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma → H_L^-- tau^+</i>.
Code 3124.
<p/><code>flag </code><strong> LeftRightSymmmetry:ff2HLff </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f_1 f_2 → H_L^-- f_3 f_4</i> via <i>WW</i> fusion.
Code 3125.
<p/><code>flag </code><strong> LeftRightSymmmetry:ffbar2HLHL </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar → H_L^++ H_L^--</i>.
Code 3126.
<p/><code>flag </code><strong> LeftRightSymmmetry:ll2HR </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i l_j → H_R^--</i>.
Code 3141.
<p/><code>flag </code><strong> LeftRightSymmmetry:lgm2HRe </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma → H_R^-- e^+</i>.
Code 3142.
<p/><code>flag </code><strong> LeftRightSymmmetry:lgm2HRmu </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma → H_R^-- mu^+</i>.
Code 3143.
<p/><code>flag </code><strong> LeftRightSymmmetry:lgm2HRtau </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma → H_R^-- tau^+</i>.
Code 3144.
<p/><code>flag </code><strong> LeftRightSymmmetry:ff2HRff </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f_1 f_2 → H_R^-- f_3 f_4</i> via <i>WW</i> fusion.
Code 3145.
<p/><code>flag </code><strong> LeftRightSymmmetry:ffbar2HRHR </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar → H_R^++ H_R^--</i>.
Code 3146.
<h3>Parameters</h3>
The basic couplings of the model are
<p/><code>parm </code><strong> LeftRightSymmmetry:gL </strong>
(<code>default = <strong>0.64</strong></code>; <code>minimum = 0.0</code>)<br/>
lefthanded coupling <i>g_L = e / sin(theta)</i>.
<p/><code>parm </code><strong> LeftRightSymmmetry:gR </strong>
(<code>default = <strong>0.64</strong></code>; <code>minimum = 0.0</code>)<br/>
righthanded coupling <i>g_R</i>, assumed the same as <i>g_L</i>.
<p/><code>parm </code><strong> LeftRightSymmmetry:vL </strong>
(<code>default = <strong>5.</strong></code>; <code>minimum = 0.0</code>)<br/>
vacuum expectation value <i>v_L</i> (in GeV) for the left-triplet.
<p/>
The corresponding vacuum expectation value <i>v_R</i> is assumed
given by <i>v_R = sqrt(2) M_WR / g_R</i> and is not stored explicitly.
<p/>
The Yukawa couplings of a lepton pair to a <i>H^--</i>, assumed the
same for <i>H_L^--</i> and <i>H_R^--</i>, is described by a symmetric
3-by-3 matrix. The default matrix is dominated by the diagonal elements
and especially by the <i>tau tau</i> one.
<p/><code>parm </code><strong> LeftRightSymmmetry:coupHee </strong>
(<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>)<br/>
Yukawa coupling for <i>H^-- → e- e-</i>.
<p/><code>parm </code><strong> LeftRightSymmmetry:coupHmue </strong>
(<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>)<br/>
Yukawa coupling for <i>H^-- → mu- e-</i>.
<p/><code>parm </code><strong> LeftRightSymmmetry:coupHmumu </strong>
(<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>)<br/>
Yukawa coupling for <i>H^-- → mu- mu-</i>.
<p/><code>parm </code><strong> LeftRightSymmmetry:coupHtaue </strong>
(<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>)<br/>
Yukawa coupling for <i>H^-- → tau- e-</i>.
<p/><code>parm </code><strong> LeftRightSymmmetry:coupHtaumu </strong>
(<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>)<br/>
Yukawa coupling for <i>H^-- → tau- mu-</i>.
<p/><code>parm </code><strong> LeftRightSymmmetry:coupHtautau </strong>
(<code>default = <strong>0.3</strong></code>; <code>minimum = 0.0</code>)<br/>
Yukawa coupling for <i>H^-- → tau- tau-</i>.
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