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1<html>
2<head>
3<title>Left-Right-Symmetry Processes</title>
4<link rel="stylesheet" type="text/css" href="pythia.css"/>
5<link rel="shortcut icon" href="pythia32.gif"/>
6</head>
7<body>
8
9<h2>Left-Right-Symmetry Processes</h2>
10
11At current energies, the world is left-handed, i.e. the Standard Model
12contains an <i>SU(2)_L</i> group. Left-right symmetry at some larger
13scale implies the need for an <i>SU(2)_R</i> group. Thus the particle
14content is expanded by right-handed <i>Z_R^0</i> and <i>W_R^+-</i>
15and right-handed neutrinos. The Higgs fields have to be in a triplet
16representation, leading to doubly-charged Higgs particles, one set for
17each of the two <i>SU(2)</i> groups. Also the number of neutral and
18singly-charged Higgs states is increased relative to the Standard Model,
19but a search for the lowest-lying states of this kind is no different
20from e.g. the freedom already accorded by the MSSM Higgs scenarios.
21
22<p/>
23PYTHIA implements the scenario of [<a href="Bibliography.html" target="page">Hui97</a>].
24
25<p/>
26The <i>W_R^+-</i> has been implemented as a simple copy of the
27ordinary <i>W^+-</i>, with the exception that it couples to
28right-handed neutrinos instead of the ordinary left-handed ones.
29Thus the standard CKM matrix is used in the quark sector, and the
30same vector and axial coupling strengths, leaving only the mass as
31free parameter. The <i>Z_R^0</i> implementation (without interference
32with the photon or the ordinary <i>Z^0</i>) allows decays both to
33left- and right-handed neutrinos, as well as other fermions, according
34to one specific model ansatz. Obviously both the <i>W_R^+-</i>
35and the <i>Z_R^0</i> descriptions are  likely to be simplifications,
36but provide a starting point.
37
38<p/>
39For the doubly-charged Higgses, the main decay modes implemented are
40<i>H_L^++ -> W_L^+ W_L^+, l_i^+ l_j^+ </i> (<i>i, j</i> generation
41indices) and <i>H_R^++ -> W_R^+ W_R^+, l_i^+ l_j^+</i>.
42
43<p/>
44The right-handed neutrinos can be allowed to decay further. Assuming them
45to have a mass below that of <i>W_R^+-</i>, they decay to three-body
46states via a virtual <i>W_R^+-</i>, <i>nu_Rl -> l+- f fbar'</i>,
47where both lepton charges are allowed owing to the Majorana character
48of the neutrinos. If there is a significant mass splitting, also
49sequential decays <i>nu_Rl -> l+- l'-+  nu'_Rl</i> are allowed.
50Currently the decays are isotropic in phase space. If the neutrino
51masses are close to or above the <i>W_R^</i> ones, this description
52has to be substituted by a sequential decay via a real <i>W_R^</i> 
53(not implemented, but actually simpler to do than the one here).
54
55
56<h3>Production processes</h3>
57
58A few different production processes have been implemented, which normally
59would not overlap and therefore could be run together.
60
61<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:all &nbsp;</strong> 
62 (<code>default = <strong>off</strong></code>)<br/>
63Common switch for the group of implemented processes within a
64left-right-symmetric scenario.
65 
66
67<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ffbar2ZR &nbsp;</strong> 
68 (<code>default = <strong>off</strong></code>)<br/>
69Scatterings <i>f fbar -> Z_R^0</i>.
70Code 3101.
71 
72
73<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ffbar2WR &nbsp;</strong> 
74 (<code>default = <strong>off</strong></code>)<br/>
75Scatterings <i><f fbar' -> W_R^+</i>.
76Code 3102.
77 
78
79<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ll2HL &nbsp;</strong> 
80 (<code>default = <strong>off</strong></code>)<br/>
81Scatterings <i>l_i l_j -> H_L^--</i>.
82Code 3121.
83 
84
85<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HLe &nbsp;</strong> 
86 (<code>default = <strong>off</strong></code>)<br/>
87Scatterings <i>l_i gamma -> H_L^-- e^+</i>.
88Code 3122.
89 
90
91<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HLmu &nbsp;</strong> 
92 (<code>default = <strong>off</strong></code>)<br/>
93Scatterings <i>l_i gamma -> H_L^-- mu^+</i>.
94Code 3123.
95 
96
97<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HLtau &nbsp;</strong> 
98 (<code>default = <strong>off</strong></code>)<br/>
99Scatterings <i>l_i gamma -> H_L^-- tau^+</i>.
100Code 3124.
101 
102
103<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ff2HLff &nbsp;</strong> 
104 (<code>default = <strong>off</strong></code>)<br/>
105Scatterings <i>f_1 f_2 -> H_L^-- f_3 f_4</i> via <i>WW</i> fusion.
106Code 3125.
107 
108
109<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ffbar2HLHL &nbsp;</strong> 
110 (<code>default = <strong>off</strong></code>)<br/>
111Scatterings <i>f fbar ->  H_L^++ H_L^--</i>.
112Code 3126.
113 
114
115<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ll2HR &nbsp;</strong> 
116 (<code>default = <strong>off</strong></code>)<br/>
117Scatterings <i>l_i l_j -> H_R^--</i>.
118Code 3141.
119 
120
121<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HRe &nbsp;</strong> 
122 (<code>default = <strong>off</strong></code>)<br/>
123Scatterings <i>l_i gamma -> H_R^-- e^+</i>.
124Code 3142.
125 
126
127<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HRmu &nbsp;</strong> 
128 (<code>default = <strong>off</strong></code>)<br/>
129Scatterings <i>l_i gamma -> H_R^-- mu^+</i>.
130Code 3143.
131 
132
133<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:lgm2HRtau &nbsp;</strong> 
134 (<code>default = <strong>off</strong></code>)<br/>
135Scatterings <i>l_i gamma -> H_R^-- tau^+</i>.
136Code 3144.
137 
138
139<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ff2HRff &nbsp;</strong> 
140 (<code>default = <strong>off</strong></code>)<br/>
141Scatterings <i>f_1 f_2 -> H_R^-- f_3 f_4</i> via <i>WW</i> fusion.
142Code 3145.
143 
144
145<p/><code>flag&nbsp; </code><strong> LeftRightSymmmetry:ffbar2HRHR &nbsp;</strong> 
146 (<code>default = <strong>off</strong></code>)<br/>
147Scatterings <i>f fbar ->  H_R^++ H_L^--</i>.
148Code 3146.
149 
150
151<h3>Parameters</h3>
152
153The basic couplings of the model are
154
155<p/><code>parm&nbsp; </code><strong> LeftRightSymmmetry:gL &nbsp;</strong> 
156 (<code>default = <strong>0.64</strong></code>; <code>minimum = 0.0</code>)<br/>
157lefthanded coupling <i>g_L = e / sin(theta)</i>.
158 
159
160<p/><code>parm&nbsp; </code><strong> LeftRightSymmmetry:gR &nbsp;</strong> 
161 (<code>default = <strong>0.64</strong></code>; <code>minimum = 0.0</code>)<br/>
162righthanded coupling <i>g_R</i>, assumed the same as <i>g_L</i>.
163 
164
165<p/><code>parm&nbsp; </code><strong> LeftRightSymmmetry:vL &nbsp;</strong> 
166 (<code>default = <strong>5.</strong></code>; <code>minimum = 0.0</code>)<br/>
167vacuum expectation value <i>v_L</i> (in GeV) for the left-triplet.
168 
169
170<p/>
171The corresponding vacuum expectation value <i>v_R</i> is assumed
172given by <i>v_R = sqrt(2) M_WR / g_R</i> and is not stored explicitly.
173
174<p/>
175The Yukawa couplings of a lepton pair to a <i>H^--</i>, assumed the
176same for <i>H_L^--</i> and <i>H_R^--</i>, is described by a symmetric
1773-by-3 matrix. The default matrix is dominated by the diagonal elements
178and especially by the <i>tau tau</i> one.
179
180<p/><code>parm&nbsp; </code><strong> LeftRightSymmmetry:coupHee &nbsp;</strong> 
181 (<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>)<br/>
182Yukawa coupling for <i>H^-- -> e- e-</i>.
183 
184
185<p/><code>parm&nbsp; </code><strong> LeftRightSymmmetry:coupHmue &nbsp;</strong> 
186 (<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>)<br/>
187Yukawa coupling for <i>H^-- -> mu- e-</i>.
188 
189
190<p/><code>parm&nbsp; </code><strong> LeftRightSymmmetry:coupHmumu &nbsp;</strong> 
191 (<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>)<br/>
192Yukawa coupling for <i>H^-- -> mu- mu-</i>.
193 
194
195<p/><code>parm&nbsp; </code><strong> LeftRightSymmmetry:coupHtaue &nbsp;</strong> 
196 (<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>)<br/>
197Yukawa coupling for <i>H^-- -> tau- e-</i>.
198 
199
200<p/><code>parm&nbsp; </code><strong> LeftRightSymmmetry:coupHtaumu &nbsp;</strong> 
201 (<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>)<br/>
202Yukawa coupling for <i>H^-- -> tau- mu-</i>.
203 
204
205<p/><code>parm&nbsp; </code><strong> LeftRightSymmmetry:coupHtautau &nbsp;</strong> 
206 (<code>default = <strong>0.3</strong></code>; <code>minimum = 0.0</code>)<br/>
207Yukawa coupling for <i>H^-- -> tau- tau-</i>.
208 
209
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