3 <title>Hidden Valley Processes</title>
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28 <form method='post' action='HiddenValleyProcesses.php'>
30 <h2>Hidden Valley Processes</h2>
32 This Hidden Valley (HV) scenario has been developed specifically
33 to allow the study of visible consequences of radiation in a
34 hidden sector, by recoil effect. A key aspect is therefore that
35 the normal timelike showering machinery has been expanded with a
36 third kind of radiation, in addition to the QCD and QED ones.
37 These three kinds of radiation are fully interleaved, i.e.
38 evolution occurs in a common <i>pT</i>-ordered sequence.
39 The scenario is described in [<a href="Bibliography.php" target="page">Car10</a>].
41 <h2>Particle content and properties</h2>
43 For simplicity we assume that the HV contains an unbroken <b>SU(N)</b>
44 gauge symmetry. This is used in the calculation of production cross
45 sections. These could be rescaled by hand for other gauge groups.
47 <br/><br/><table><tr><td><strong>HiddenValley:Ngauge </td><td></td><td> <input type="text" name="1" value="3" size="20"/> (<code>default = <strong>3</strong></code>; <code>minimum = 1</code>)</td></tr></table>
48 is <b>U(1)</b> for <code>Ngauge = 1</code>, is <b>SU(N)</b> if
49 <code>Ngauge > 1</code>. Note that pair production cross sections
50 contains a factor of <code>Ngauge</code> for new particles
51 in the fundamental representation of this group.
55 A minimal HV particle content has been introduced. Firstly, there is
56 a set of 12 particles that mirrors the Standard Model flavour
57 structure, and is charged under both the SM and the HV symmetry groups.
58 Each new particle couples flavour-diagonally to a corresponding SM
59 state, and has the same SM charge and colour, but in addition is in
60 the fundamental representation of the HV colour, as follows:
61 <br/><code>Dv</code>, identity 4900001, partner to the normal
63 <br/><code>Uv</code>, identity 4900002, partner to the normal
65 <br/><code>Sv</code>, identity 4900003, partner to the normal
67 <br/><code>Cv</code>, identity 4900004, partner to the normal
69 <br/><code>Bv</code>, identity 4900005, partner to the normal
71 <br/><code>Tv</code>, identity 4900006, partner to the normal
73 <br/><code>Ev</code>, identity 4900011, partner to the normal
74 <code>e</code> lepton;
75 <br/><code>nuEv</code>, identity 4900012, partner to the normal
76 <code>nue</code> neutrino;
77 <br/><code>MUv</code>, identity 4900013, partner to the normal
78 <code>mu</code> lepton;
79 <br/><code>nuMUv</code>, identity 4900014, partner to the normal
80 <code>numu</code> neutrino;
81 <br/><code>TAUv</code>, identity 4900015, partner to the normal
82 <code>tau</code> lepton;
83 <br/><code>nuTAUv</code>, identity 4900016, partner to the normal
84 <code>nutau</code> neutrino.
85 <br/>Collectively we will refer to these states as <code>Fv</code>;
86 note, however, that they need not be fermions themselves.
89 In addition the model contains the HV gauge particle, either
90 a HV gluon or a HV photon, but not both; see <code>Ngauge</code>
92 <br/><code>gv</code>, identity 4900021, is the massless
93 gauge boson of the HV <b>SU(N)</b> group;
94 <br/><code>gammav</code>, identity 4900022, is the massless
95 gauge boson of the HV <b>U(1)</b> group.
98 Finally, there is a new massive particle with only HV charge sitting
99 in the fundamental representation of the HV gauge group:
100 <br/><code>qv</code>, identity 4900101.
102 <p/>The typical scenario would be for pair production of one of the
103 states presented first above, e.g. <i>g g -> Dv Dvbar</i>.
104 Such a <i>Dv</i> can radiate gluons and photons like an SM quark,
105 but in addition HV gluons or HV photons in a similar fashion.
106 Eventually the <i>Dv</i> will decay like <i>Dv -> d + qv</i>.
107 The strength of this decay is not set as such, but is implicit in
108 your choice of width for the <i>Dv</i> state.
109 Thereafter the <i>d</i> and <i>qv</i> can radiate
110 further within their respective sectors. The fate of the
111 <i>qv</i>, <i>gv</i> or <i>gammav</i>, once formed,
112 is not considered further: they remain invisible.
115 Only the spin of the HV gluon or HV photon is determined unambiguously
116 to be unity; for the others you can make your choice.
118 <br/><br/><table><tr><td><strong>HiddenValley:spinFv </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table>
119 The spin of the HV partners of the SM fermions, e.g.
120 <ei>Dv</ei>, <ei>Uv</ei>, <ei>Ev</ei> and <ei>nuEv</ei>.
122 <input type="radio" name="2" value="0"><strong>0 </strong>: spin 0.<br/>
123 <input type="radio" name="2" value="1" checked="checked"><strong>1 </strong>: spin 1/2.<br/>
124 <input type="radio" name="2" value="2"><strong>2 </strong>: spin 1/2.<br/>
126 <br/><br/><table><tr><td><strong>HiddenValley:spinqv </td><td> (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 1</code>)</td></tr></table>
127 The spin of <ei>qv</ei> when the <ei>Fv</ei> (the HV partners of
128 the SM fermions) have spin 1/2. (While, if they have spin 0 or 1,
129 the <ei>qv</ei> spin is fixed at 1/2.)
131 <input type="radio" name="3" value="0" checked="checked"><strong>0 </strong>: spin 0.<br/>
132 <input type="radio" name="3" value="1"><strong>1 </strong>: spin 0.<br/>
134 <br/><br/><table><tr><td><strong>HiddenValley:kappa </td><td></td><td> <input type="text" name="4" value="1." size="20"/> (<code>default = <strong>1.</strong></code>)</td></tr></table>
135 If the <i>Fv</i> have spin 1 then their production
136 cross section depends on the presence of ananomalous magnetic dipole
137 moment, i.e. of a <i>kappa</i> different from unity. For other spins
138 this parameter is not used.
142 You should set the <i>Fv</i> and <i>qv</i> masses appropriately,
143 with the latter smaller than the former two to allow decays.
145 <h2>Production processes</h2>
147 <br/><br/><strong>HiddenValley:all</strong> <input type="radio" name="5" value="on"><strong>On</strong>
148 <input type="radio" name="5" value="off" checked="checked"><strong>Off</strong>
149 (<code>default = <strong>off</strong></code>)<br/>
150 Common switch for the group of all hard Hidden Valley processes,
151 as listed separately in the following.
154 <br/><br/><strong>HiddenValley:gg2DvDvbar</strong> <input type="radio" name="6" value="on"><strong>On</strong>
155 <input type="radio" name="6" value="off" checked="checked"><strong>Off</strong>
156 (<code>default = <strong>off</strong></code>)<br/>
157 Pair production <i>g g -> Dv Dvbar</i>.
161 <br/><br/><strong>HiddenValley:gg2UvUvbar</strong> <input type="radio" name="7" value="on"><strong>On</strong>
162 <input type="radio" name="7" value="off" checked="checked"><strong>Off</strong>
163 (<code>default = <strong>off</strong></code>)<br/>
164 Pair production <i>g g -> Uv Uvbar</i>.
168 <br/><br/><strong>HiddenValley:gg2SvSvbar</strong> <input type="radio" name="8" value="on"><strong>On</strong>
169 <input type="radio" name="8" value="off" checked="checked"><strong>Off</strong>
170 (<code>default = <strong>off</strong></code>)<br/>
171 Pair production <i>g g -> Sv Svbar</i>.
175 <br/><br/><strong>HiddenValley:gg2CvCvbar</strong> <input type="radio" name="9" value="on"><strong>On</strong>
176 <input type="radio" name="9" value="off" checked="checked"><strong>Off</strong>
177 (<code>default = <strong>off</strong></code>)<br/>
178 Pair production <i>g g -> Cv Cvbar</i>.
182 <br/><br/><strong>HiddenValley:gg2BvBvbar</strong> <input type="radio" name="10" value="on"><strong>On</strong>
183 <input type="radio" name="10" value="off" checked="checked"><strong>Off</strong>
184 (<code>default = <strong>off</strong></code>)<br/>
185 Pair production <i>g g -> Bv Bvbar</i>.
189 <br/><br/><strong>HiddenValley:gg2TvTvbar</strong> <input type="radio" name="11" value="on"><strong>On</strong>
190 <input type="radio" name="11" value="off" checked="checked"><strong>Off</strong>
191 (<code>default = <strong>off</strong></code>)<br/>
192 Pair production <i>g g -> Tv Tvbar</i>.
196 <br/><br/><strong>HiddenValley:qqbar2DvDvbar</strong> <input type="radio" name="12" value="on"><strong>On</strong>
197 <input type="radio" name="12" value="off" checked="checked"><strong>Off</strong>
198 (<code>default = <strong>off</strong></code>)<br/>
199 Pair production <i>q qbar -> Dv Dvbar</i>
200 via intermediate gluon.
204 <br/><br/><strong>HiddenValley:qqbar2UvUvbar</strong> <input type="radio" name="13" value="on"><strong>On</strong>
205 <input type="radio" name="13" value="off" checked="checked"><strong>Off</strong>
206 (<code>default = <strong>off</strong></code>)<br/>
207 Pair production <i>q qbar -> Uv Uvbar</i>
208 via intermediate gluon.
212 <br/><br/><strong>HiddenValley:qqbar2SvSvbar</strong> <input type="radio" name="14" value="on"><strong>On</strong>
213 <input type="radio" name="14" value="off" checked="checked"><strong>Off</strong>
214 (<code>default = <strong>off</strong></code>)<br/>
215 Pair production <i>q qbar -> Sv Svbar</i>
216 via intermediate gluon.
220 <br/><br/><strong>HiddenValley:qqbar2CvCvbar</strong> <input type="radio" name="15" value="on"><strong>On</strong>
221 <input type="radio" name="15" value="off" checked="checked"><strong>Off</strong>
222 (<code>default = <strong>off</strong></code>)<br/>
223 Pair production <i>q qbar -> Cv Cvbar</i>
224 via intermediate gluon.
228 <br/><br/><strong>HiddenValley:qqbar2BvBvbar</strong> <input type="radio" name="16" value="on"><strong>On</strong>
229 <input type="radio" name="16" value="off" checked="checked"><strong>Off</strong>
230 (<code>default = <strong>off</strong></code>)<br/>
231 Pair production <i>q qbar -> Bv Bvbar</i>
232 via intermediate gluon.
236 <br/><br/><strong>HiddenValley:qqbar2TvTvbar</strong> <input type="radio" name="17" value="on"><strong>On</strong>
237 <input type="radio" name="17" value="off" checked="checked"><strong>Off</strong>
238 (<code>default = <strong>off</strong></code>)<br/>
239 Pair production <i>q qbar -> Tv Tvbar</i>
240 via intermediate gluon.
244 <br/><br/><strong>HiddenValley:ffbar2DvDvbar</strong> <input type="radio" name="18" value="on"><strong>On</strong>
245 <input type="radio" name="18" value="off" checked="checked"><strong>Off</strong>
246 (<code>default = <strong>off</strong></code>)<br/>
247 Pair production <i>f fbar -> Dv Dvbar</i>
248 via intermediate <i>gamma*/Z^*</i>.
252 <br/><br/><strong>HiddenValley:ffbar2UvUvbar</strong> <input type="radio" name="19" value="on"><strong>On</strong>
253 <input type="radio" name="19" value="off" checked="checked"><strong>Off</strong>
254 (<code>default = <strong>off</strong></code>)<br/>
255 Pair production <i>f fbar -> Uv Uvbar</i>
256 via intermediate <i>gamma*/Z^*</i>.
260 <br/><br/><strong>HiddenValley:ffbar2SvSvbar</strong> <input type="radio" name="20" value="on"><strong>On</strong>
261 <input type="radio" name="20" value="off" checked="checked"><strong>Off</strong>
262 (<code>default = <strong>off</strong></code>)<br/>
263 Pair production <i>f fbar -> Sv Svbar</i>
264 via intermediate <i>gamma*/Z^*</i>.
268 <br/><br/><strong>HiddenValley:ffbar2CvCvbar</strong> <input type="radio" name="21" value="on"><strong>On</strong>
269 <input type="radio" name="21" value="off" checked="checked"><strong>Off</strong>
270 (<code>default = <strong>off</strong></code>)<br/>
271 Pair production <i>f fbar -> Cv Cvbar</i>
272 via intermediate <i>gamma*/Z^*</i>.
276 <br/><br/><strong>HiddenValley:ffbar2BvBvbar</strong> <input type="radio" name="22" value="on"><strong>On</strong>
277 <input type="radio" name="22" value="off" checked="checked"><strong>Off</strong>
278 (<code>default = <strong>off</strong></code>)<br/>
279 Pair production <i>f fbar -> Bv Bvbar</i>
280 via intermediate <i>gamma*/Z^*</i>.
284 <br/><br/><strong>HiddenValley:ffbar2TvTvbar</strong> <input type="radio" name="23" value="on"><strong>On</strong>
285 <input type="radio" name="23" value="off" checked="checked"><strong>Off</strong>
286 (<code>default = <strong>off</strong></code>)<br/>
287 Pair production <i>f fbar -> Tv Tvbar</i>
288 via intermediate <i>gamma*/Z^*</i>.
292 <br/><br/><strong>HiddenValley:ffbar2EvEvbar</strong> <input type="radio" name="24" value="on"><strong>On</strong>
293 <input type="radio" name="24" value="off" checked="checked"><strong>Off</strong>
294 (<code>default = <strong>off</strong></code>)<br/>
295 Pair production <i>f fbar -> Ev Evbar</i>
296 via intermediate <i>gamma*/Z^*</i>.
300 <br/><br/><strong>HiddenValley:ffbar2nuEvnuEvbar</strong> <input type="radio" name="25" value="on"><strong>On</strong>
301 <input type="radio" name="25" value="off" checked="checked"><strong>Off</strong>
302 (<code>default = <strong>off</strong></code>)<br/>
303 Pair production <i>f fbar -> nuEv nuEvbar</i>
304 via intermediate <i>gamma*/Z^*</i>.
308 <br/><br/><strong>HiddenValley:ffbar2MUvMUvbar</strong> <input type="radio" name="26" value="on"><strong>On</strong>
309 <input type="radio" name="26" value="off" checked="checked"><strong>Off</strong>
310 (<code>default = <strong>off</strong></code>)<br/>
311 Pair production <i>f fbar -> MUv MUvbar</i>
312 via intermediate <i>gamma*/Z^*</i>.
316 <br/><br/><strong>HiddenValley:ffbar2nuMUvnuMUvbar</strong> <input type="radio" name="27" value="on"><strong>On</strong>
317 <input type="radio" name="27" value="off" checked="checked"><strong>Off</strong>
318 (<code>default = <strong>off</strong></code>)<br/>
319 Pair production <i>f fbar -> nuMUv nuMUvbar</i>
320 via intermediate <i>gamma*/Z^*</i>.
324 <br/><br/><strong>HiddenValley:ffbar2TAUvTAUvbar</strong> <input type="radio" name="28" value="on"><strong>On</strong>
325 <input type="radio" name="28" value="off" checked="checked"><strong>Off</strong>
326 (<code>default = <strong>off</strong></code>)<br/>
327 Pair production <i>f fbar -> TAUv TAUvbar</i>
328 via intermediate <i>gamma*/Z^*</i>.
332 <br/><br/><strong>HiddenValley:ffbar2nuTAUvnuTAUvbar</strong> <input type="radio" name="29" value="on"><strong>On</strong>
333 <input type="radio" name="29" value="off" checked="checked"><strong>Off</strong>
334 (<code>default = <strong>off</strong></code>)<br/>
335 Pair production <i>f fbar -> nuTAUv nuTAUvbar</i>
336 via intermediate <i>gamma*/Z^*</i>.
340 <h2>Timelike showers</h2>
342 One key point of this HV scenario is that radiation off the
343 HV-charged particles is allowed. This is done by the standard
344 final-state showering machinery. (HV particles are not produced
345 in initial-state radiation.) All the (anti)particles <i>Fv</i>
346 and <i>qv</i> have one (negative) unit of HV charge. That is,
347 radiation closely mimics the one in QCD. Both QCD, QED and HV
348 radiation are interleaved in one common sequence of decreasing
349 emission <i>pT</i> scales. Each radiation kind defines a set of
350 dipoles, usually spanned between a radiating parton and its recoil
351 partner, such that the invariant mass of the pair is not changed
352 when a radiation occurs. This need not follow from trivial colour
353 assignments, but is often obvious. For instance, in a decay
354 <i>Qv -> q + qv</i> the QCD dipole is between the <i>q</i> and
355 the hole after <i>Qv</i>, but <i>qv</i> becomes the recoiler
356 should a radiation occur, while the role of <i>q</i> and <i>qv</i>
357 is reversed for HV radiation.
359 <p/>This also includes matrix-element corrections for a number
360 of decay processes, with colour, spin and mass effects included
361 [<a href="Bibliography.php" target="page">Nor01</a>]. They were calculated within the context of the
362 particle content of the MSSM, however, which does not include spin 1
363 particles with unit colour charge. In such cases spin 0 is assumed
364 instead. By experience, the main effects come from mass and colour
365 flow anyway, so this is not a bad approximation. (Furthermore the
366 MSSM formulae allow for <i>gamma_5</i> factors from wave
367 functions or vertices; these are even less important.)
369 <p/>An emitted <i>gv</i> can branch in its turn,
370 <i>gv -> gv + gv</i>. This radiation may affect momenta
371 in the visible sector by recoil effect, but this is a minor
372 effect relative to the primary emission of the <i>gv</i>.
374 <br/><br/><strong>HiddenValley:FSR</strong> <input type="radio" name="30" value="on"><strong>On</strong>
375 <input type="radio" name="30" value="off" checked="checked"><strong>Off</strong>
376 (<code>default = <strong>off</strong></code>)<br/>
377 switch on final-state shower of <i>gv</i> or <i>gammav</i>
378 in a HV production process.
381 <br/><br/><table><tr><td><strong>HiddenValley:alphaFSR </td><td></td><td> <input type="text" name="31" value="0.1" size="20"/> (<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>)</td></tr></table>
382 fixed alpha scale of <i>gv/gammav</i> emission; corresponds to
383 <i>alpha_strong</i> of QCD or <i>alpha_em</i> of QED. For
384 shower branchings such as <i>Dv -> Dv + gv</i> the coupling is
385 multiplied by <i>C_F = (N^2 - 1) / (2 * N)</i> for an
386 <b>SU(N)</b> group and for <i>gv -> gv + gv</i> by <i>N</i>.
389 <br/><br/><table><tr><td><strong>HiddenValley:pTminFSR </td><td></td><td> <input type="text" name="32" value="0.4" size="20"/> (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>)</td></tr></table>
390 lowest allowed <i>pT</i> of emission. Chosen with same default
391 as in normal QCD showers.
394 <input type="hidden" name="saved" value="1"/>
397 echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?>
399 <table width="100%"><tr><td align="right"><input type="submit" value="Save Settings" /></td></tr></table>
404 if($_POST["saved"] == 1)
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442 fwrite($handle,$data);
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447 fwrite($handle,$data);
449 if($_POST["9"] != "off")
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452 fwrite($handle,$data);
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462 fwrite($handle,$data);
464 if($_POST["12"] != "off")
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467 fwrite($handle,$data);
469 if($_POST["13"] != "off")
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472 fwrite($handle,$data);
474 if($_POST["14"] != "off")
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477 fwrite($handle,$data);
479 if($_POST["15"] != "off")
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482 fwrite($handle,$data);
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502 fwrite($handle,$data);
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507 fwrite($handle,$data);
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512 fwrite($handle,$data);
514 if($_POST["22"] != "off")
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517 fwrite($handle,$data);
519 if($_POST["23"] != "off")
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522 fwrite($handle,$data);
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527 fwrite($handle,$data);
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532 fwrite($handle,$data);
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537 fwrite($handle,$data);
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542 fwrite($handle,$data);
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547 fwrite($handle,$data);
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552 fwrite($handle,$data);
554 if($_POST["30"] != "off")
556 $data = "HiddenValley:FSR = ".$_POST["30"]."\n";
557 fwrite($handle,$data);
559 if($_POST["31"] != "0.1")
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562 fwrite($handle,$data);
564 if($_POST["32"] != "0.4")
566 $data = "HiddenValley:pTminFSR = ".$_POST["32"]."\n";
567 fwrite($handle,$data);
576 <!-- Copyright (C) 2010 Torbjorn Sjostrand -->