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<html>
<head>
<title>Left-Right-Symmetry Processes</title>
<link rel="stylesheet" type="text/css" href="pythia.css"/>
<link rel="shortcut icon" href="pythia32.gif"/>
</head>
<body>

<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&nbsp; </code><strong> LeftRightSymmmetry:all &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:ffbar2ZR &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar -> Z_R^0</i>. 
Code 3101.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ffbar2WR &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i><f fbar' -> W_R^+</i>. 
Code 3102.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ll2HL &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i l_j -> H_L^--</i>. 
Code 3121.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HLe &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma -> H_L^-- e^+</i>. 
Code 3122.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HLmu &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma -> H_L^-- mu^+</i>. 
Code 3123.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HLtau &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma -> H_L^-- tau^+</i>. 
Code 3124.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ff2HLff &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:ffbar2HLHL &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar ->  H_L^++ H_L^--</i>. 
Code 3126.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ll2HR &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i l_j -> H_R^--</i>. 
Code 3141.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HRe &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma -> H_R^-- e^+</i>. 
Code 3142.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HRmu &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma -> H_R^-- mu^+</i>. 
Code 3143.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HRtau &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>l_i gamma -> H_R^-- tau^+</i>. 
Code 3144.
  

<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ff2HRff &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:ffbar2HRHR &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar ->  H_R^++ H_L^--</i>. 
Code 3146.
  

<h3>Parameters</h3>

The basic couplings of the model are

<p/><code>parm&nbsp; </code><strong> LeftRightSymmmetry:gL &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:gR &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:vL &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:coupHee &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:coupHmue &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:coupHmumu &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:coupHtaue &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:coupHtaumu &nbsp;</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&nbsp; </code><strong> LeftRightSymmmetry:coupHtautau &nbsp;</strong> 
 (<code>default = <strong>0.3</strong></code>; <code>minimum = 0.0</code>)<br/>
Yukawa coupling for <i>H^-- -> tau- tau-</i>.
  

</body>
</html>

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