3 <title>Extra-Dimensional Processes</title>
4 <link rel="stylesheet" type="text/css" href="pythia.css"/>
5 <link rel="shortcut icon" href="pythia32.gif"/>
9 <h2>Extra-Dimensional Processes</h2>
11 Scenarios with extra dimensions (ED) allow a multitude of processes.
12 Currently three different categories of processes are implemented.
13 The first involves the production of excited Kaluza Klein states
14 within so-called Randall-Sundrum (RS) scenarios, the second is
15 related to resonance production in TeV-1 sized extra dimensions
16 and the third relates to phenomena from large extra dimensions (LED).
17 Due to the close relation between the LED model and a so-called
18 unparticle model, similar unparticle processes are also kept in this
21 <h3>Randall-Sundrum Resonances, production processes</h3>
23 The graviton (G*) and gluon (KKgluon*) resonance states are assigned
24 PDG code 5100039 and 5100021 respectively. Decays into fermion, gluon
25 and photon pairs are handled with the correct angular distributions,
26 while other decay channels currently are handled isotropically.
29 <i>Warning:</i> The possible decays of a graviton into scalars
30 (i.e. Higgs and longitudinal Z/W) is currently not implemented and
31 in some scenarios, where for example the SM is allowed to propagate
32 in the ED bulk, these decay modes can be significant.
35 There are two lowest-order processes that together normally
36 should be sufficient for a simulation of <i>G^*</i> production.
38 <p/><code>flag </code><strong> ExtraDimensionsG*:all </strong>
39 (<code>default = <strong>off</strong></code>)<br/>
40 Common switch for the group of lowest-order <i>G^*</i> production
41 processes, i.e. the two ones below.
44 <p/><code>flag </code><strong> ExtraDimensionsG*:gg2G* </strong>
45 (<code>default = <strong>off</strong></code>)<br/>
46 Scatterings <i>g g -> G^*</i>.
50 <p/><code>flag </code><strong> ExtraDimensionsG*:ffbar2G* </strong>
51 (<code>default = <strong>off</strong></code>)<br/>
52 Scatterings <i>f fbar -> G^*</i>.
57 In addition there are three first-order processes included. These
58 are of less interest, but can be used for dedicated studies of the
59 high-<i>pT</i> tail of <i>G^*</i> production. As usual, it would
60 be double counting to include the lowest-order and first-order
61 processes simultaneously. Therefore the latter ones are not included
62 with the <code>ExtraDimensionsG*:all = on</code> option. In this set
63 of processes all decay angles are assumed isotropic.
65 <p/><code>flag </code><strong> ExtraDimensionsG*:gg2G*g </strong>
66 (<code>default = <strong>off</strong></code>)<br/>
67 Scatterings <i>g g -> G^* g</i>.
71 <p/><code>flag </code><strong> ExtraDimensionsG*:qg2G*q </strong>
72 (<code>default = <strong>off</strong></code>)<br/>
73 Scatterings <i>q g -> G^* q</i>.
77 <p/><code>flag </code><strong> ExtraDimensionsG*:qqbar2G*g </strong>
78 (<code>default = <strong>off</strong></code>)<br/>
79 Scatterings <i>q qbar -> G^* g</i>.
84 Currently there is one process for the production of a gluon resonance.
86 <p/><code>flag </code><strong> ExtraDimensionsG*:qqbar2KKgluon* </strong>
87 (<code>default = <strong>off</strong></code>)<br/>
88 Scatterings <i>q qbar -> g^*/KKgluon^*</i>.
92 <h3>Randall-Sundrum Resonances, parameters</h3>
94 In the above scenario the main free parameters are the masses, which
95 are set as usual. In addition there are the following coupling parameters.
96 The coupling <i>kappaMG</i> follows the conventions in [<a href="Bibliography.html" target="page">Bij01</a>],
97 where as the flavour dependent couplings follow the conventions used in
98 [<a href="Bibliography.html" target="page">Dav01</a>].
100 <p/><code>flag </code><strong> ExtraDimensionsG*:SMinBulk </strong>
101 (<code>default = <strong>off</strong></code>)<br/>
102 Parameter to choose between the two scenarios:
103 <i>off</i>, SM on the TeV brane (common <i>kappaMG</i> coupling);
104 <i>on</i>, SM in the ED bulk (flavour dependent couplings).
105 At the moment this parameter is only relevant for the lowest-order
106 graviton (<i>G*</i>) resonance.
109 <p/><code>parm </code><strong> ExtraDimensionsG*:kappaMG </strong>
110 (<code>default = <strong>0.054</strong></code>; <code>minimum = 0.0</code>)<br/>
111 dimensionless coupling, which enters quadratically in all partial
112 widths of the <i>G^*</i>. Is
113 <i>kappa m_G* = sqrt(2) x_1 k / Mbar_Pl</i>,
114 where <i>x_1 = 3.83</i> is the first zero of the <i>J_1</i> Bessel
115 function and <i>Mbar_Pl</i> is the modified Planck mass.
118 <p/><code>parm </code><strong> ExtraDimensionsG*:Gll </strong>
119 (<code>default = <strong>0.0</strong></code>; <code>minimum = 0.0</code>)<br/>
120 Coupling between graviton and leptons.
123 <p/><code>parm </code><strong> ExtraDimensionsG*:Gqq </strong>
124 (<code>default = <strong>0.0</strong></code>; <code>minimum = 0.0</code>)<br/>
125 Coupling between graviton and light quarks.
128 <p/><code>parm </code><strong> ExtraDimensionsG*:Gbb </strong>
129 (<code>default = <strong>0.0001</strong></code>; <code>minimum = 0.0</code>)<br/>
130 Coupling between graviton and bottom quark.
133 <p/><code>parm </code><strong> ExtraDimensionsG*:Gtt </strong>
134 (<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>)<br/>
135 Coupling between graviton and top quark.
138 <p/><code>parm </code><strong> ExtraDimensionsG*:GVV </strong>
139 (<code>default = <strong>0.000013</strong></code>; <code>minimum = 0.0</code>)<br/>
140 Coupling between graviton and vector bosons.
143 <p/><code>parm </code><strong> ExtraDimensionsG*:KKgqR </strong>
144 (<code>default = <strong>-0.2</strong></code>)<br/>
145 Coupling between KK-gluon and a right-handed light quark.
148 <p/><code>parm </code><strong> ExtraDimensionsG*:KKgqL </strong>
149 (<code>default = <strong>-0.2</strong></code>)<br/>
150 Coupling between KK-gluon and a left-handed light quark.
153 <p/><code>parm </code><strong> ExtraDimensionsG*:KKgbR </strong>
154 (<code>default = <strong>-0.2</strong></code>)<br/>
155 Coupling between KK-gluon and a right-handed bottom quark.
158 <p/><code>parm </code><strong> ExtraDimensionsG*:KKgbL </strong>
159 (<code>default = <strong>1.0</strong></code>)<br/>
160 Coupling between KK-gluon and a left-handed bottom quark.
163 <p/><code>parm </code><strong> ExtraDimensionsG*:KKgtR </strong>
164 (<code>default = <strong>4.0</strong></code>)<br/>
165 Coupling between KK-gluon and a right-handed top quark.
168 <p/><code>parm </code><strong> ExtraDimensionsG*:KKgtL </strong>
169 (<code>default = <strong>1.0</strong></code>)<br/>
170 Coupling between KK-gluon and a left-handed top quark.
173 <p/><code>mode </code><strong> ExtraDimensionsG*:KKintMode </strong>
174 (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/>
175 Choice of full <i>g^*/KK-gluon^*</i> structure or not in relevant
177 <br/><code>option </code><strong> 0</strong> : full <i>g^*/KK-gluon^*</i> structure, with
178 interference included.
179 <br/><code>option </code><strong> 1</strong> : only pure <i>gluon_{SM}</i> contribution.
180 <br/><code>option </code><strong> 2</strong> : only pure <i>gluon_{KK}</i> contribution.
183 <h3>TeV^-1 Sized Extra Dimension, production processes</h3>
185 This section contains a processes involving the production
186 of electroweak KK gauge bosons, i.e. <i>gamma_{KK}/Z_{KK}</i>,
187 in one TeV^-1 sized extra dimension. This scenario is described
188 in [<a href="Bibliography.html" target="page">Bel10</a>].
190 <p/><code>flag </code><strong> ExtraDimensionsTEV:ffbar2ffbar </strong>
191 (<code>default = <strong>off</strong></code>)<br/>
192 Scatterings <i>f fbar -> (gamma_{KK}/Z_{KK}) -> f fbar </i>,
196 <h3>TeV^-1 Sized Extra Dimension, parameters</h3>
198 Irrespective of the parameter options used, the particle produced,
199 <i>gamma_{KK}/Z_{KK}</i>, will always be assigned code 5000023
200 and open decay channels is purely dictated by what is set for the
203 <p/><code>mode </code><strong> ExtraDimensionsTEV:gmZmode </strong>
204 (<code>default = <strong>3</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)<br/>
205 Choice of full <i>gamma_{KK}/Z_{KK}</i> structure or not in relevant
207 <br/><code>option </code><strong> 0</strong> : full <i>gamma_{SM}/Z_{SM}</i> structure, with
208 interference included.
209 <br/><code>option </code><strong> 1</strong> : only pure <i>gamma_{SM}</i> contribution.
210 <br/><code>option </code><strong> 2</strong> : only pure <i>Z_{SM}</i> contribution.
211 <br/><code>option </code><strong> 3</strong> : full <i>gamma_{KK}/Z_{KK}</i> structure, with
212 interference included.
213 <br/><code>option </code><strong> 4</strong> : only pure <i>gamma_{KK}</i> contribution, with
214 SM interference included.
215 <br/><code>option </code><strong> 5</strong> : only pure <i>Z_{KK}</i> contribution, with SM
216 interference included.
219 <p/><code>parm </code><strong> ExtraDimensionsTEV:nMax </strong>
220 (<code>default = <strong>10</strong></code>; <code>minimum = 1</code>; <code>maximum = 100</code>)<br/>
221 The number of included KK excitations.
224 <p/><code>parm </code><strong> ExtraDimensionsTEV:mStar </strong>
225 (<code>default = <strong>4000.0</strong></code>; <code>minimum = 1000.0</code>)<br/>
226 The KK mass <i>m^*</i>, given by the inverse of the single extra
230 <h3>Large Extra Dimensions, production processes</h3>
232 The LED graviton, where the KK-modes normally are summed and do not
233 give rise to phenomena individually, is assigned PDG code 5000039.
234 The graviton emission and virtual graviton exchange processes uses
235 the same implementation as the corresponding unparticle processes,
236 which are all described in [<a href="Bibliography.html" target="page">Ask10</a>]. It is also possible to
237 generate monojet events from scalar graviton emission as described
238 in [<a href="Bibliography.html" target="page">Azu05</a>], by turning on the option <i>GravScalar</i>.
241 <i>Note:</i> As discussed in [<a href="Bibliography.html" target="page">Ask09</a>], for the graviton or
242 unparticle emission processes the underlying Breit-Wigner mass
243 distribution should be matched to the graviton mass spectrum in order
244 to achieve an optimal MC efficiency.
247 The following lowest order graviton emission processes are available.
249 <p/><code>flag </code><strong> ExtraDimensionsLED:monojet </strong>
250 (<code>default = <strong>off</strong></code>)<br/>
251 Common switch for the group of lowest-order <i>G jet</i> emission
252 processes, i.e. the three ones below.
255 <p/><code>flag </code><strong> ExtraDimensionsLED:gg2Gg </strong>
256 (<code>default = <strong>off</strong></code>)<br/>
257 Scatterings <i>g g -> G g</i>.
261 <p/><code>flag </code><strong> ExtraDimensionsLED:qg2Gq </strong>
262 (<code>default = <strong>off</strong></code>)<br/>
263 Scatterings <i>q g -> G q</i>.
267 <p/><code>flag </code><strong> ExtraDimensionsLED:qqbar2Gg </strong>
268 (<code>default = <strong>off</strong></code>)<br/>
269 Scatterings <i>q qbar -> G g</i>.
273 <p/><code>flag </code><strong> ExtraDimensionsLED:ffbar2GZ </strong>
274 (<code>default = <strong>off</strong></code>)<br/>
275 Scatterings <i>f fbar -> G Z</i>.
279 <p/><code>flag </code><strong> ExtraDimensionsLED:ffbar2Ggamma </strong>
280 (<code>default = <strong>off</strong></code>)<br/>
281 Scatterings <i>f fbar -> G gamma</i>. This process corresponds
282 to the photon limit of the <i>G Z</i> process, as described in
283 [<a href="Bibliography.html" target="page">Ask09</a>].
288 The following LED processes with virtual graviton exchange are
291 <p/><code>flag </code><strong> ExtraDimensionsLED:ffbar2gammagamma </strong>
292 (<code>default = <strong>off</strong></code>)<br/>
293 Scatterings <i>f fbar -> (LED G*) -> gamma gamma</i>. If the
294 graviton contribution is zero, the results corresponds to the
295 SM contribution, i.e. equivalent to
296 <code>PromptPhoton:ffbar2gammagamma</code>.
300 <p/><code>flag </code><strong> ExtraDimensionsLED:gg2gammagamma </strong>
301 (<code>default = <strong>off</strong></code>)<br/>
302 Scatterings <i>g g -> (LED G*) -> gamma gamma</i>.
306 <p/><code>flag </code><strong> ExtraDimensionsLED:ffbar2llbar </strong>
307 (<code>default = <strong>off</strong></code>)<br/>
308 Scatterings <i>f fbar -> (LED G*) -> l l </i>, where
309 <i>l</i> is a charged lepton. If the graviton contribution
310 is zero, the results corresponds to the SM contribution, i.e.
311 similar to <code>WeakSingleBoson:ffbar2gmZ</code>. Does not
312 include t-channel amplitude relevant for e^+e^- to e^+e^-
313 and no K-factor is used.
317 <p/><code>flag </code><strong> ExtraDimensionsLED:gg2llbar </strong>
318 (<code>default = <strong>off</strong></code>)<br/>
319 Scatterings <i>g g -> (LED G*) -> l l</i>.
323 <h3>Large Extra Dimensions, parameters</h3>
325 <p/><code>flag </code><strong> ExtraDimensionsLED:GravScalar </strong>
326 (<code>default = <strong>off</strong></code>)<br/>
327 Allow the monojet processes to produce scalar graviton emission
328 instead of the default tensor one. The scalar option is according
329 to the processes described in [<a href="Bibliography.html" target="page">Azu05</a>] and includes two
330 coupling constants below.
333 <p/><code>mode </code><strong> ExtraDimensionsLED:n </strong>
334 (<code>default = <strong>2</strong></code>; <code>minimum = 1</code>)<br/>
335 Number of extra dimensions.
338 <p/><code>parm </code><strong> ExtraDimensionsLED:MD </strong>
339 (<code>default = <strong>2000.</strong></code>; <code>minimum = 100.0</code>)<br/>
340 Fundamental scale of gravity in <i>D = 4 + n</i> dimensions.
343 <p/><code>parm </code><strong> ExtraDimensionsLED:LambdaT </strong>
344 (<code>default = <strong>2000.</strong></code>; <code>minimum = 100.0</code>)<br/>
345 Ultraviolet cutoff parameter for the virtual graviton exchange processes.
348 <p/><code>mode </code><strong> ExtraDimensionsLED:CutOffMode </strong>
349 (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 3</code>)<br/>
350 Options for when the hard scale of the process (e.g. <i>sHat</i>)
351 approaches or exceed the scale of validity of the low energy effective
352 theory (e.g. <i>M_D</i>). <i>Note:</i> Option 1 only concerns the
353 graviton emission processes and the form factor is currently not available
354 for the scalar graviton processes.
355 <br/><code>option </code><strong> 0</strong> : Do nothing, i.e. all values of <i>sHat</i> contribute.
357 <br/><code>option </code><strong> 1</strong> : Truncate contributing <i>sHat</i> region
358 ([<a href="Bibliography.html" target="page">Ask09</a>]).
359 <br/><code>option </code><strong> 2</strong> : Form factor, using <i>mu = renormScale2</i> .
360 <br/><code>option </code><strong> 3</strong> : Form factor, using <i>mu = E_jet</i>.
363 <p/><code>parm </code><strong> ExtraDimensionsLED:t </strong>
364 (<code>default = <strong>1.</strong></code>; <code>minimum = 0.001</code>)<br/>
365 Form factor parameter.
368 <p/><code>parm </code><strong> ExtraDimensionsLED:g </strong>
369 (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.0</code>)<br/>
370 Coupling related to scalar graviton emission.
373 <p/><code>parm </code><strong> ExtraDimensionsLED:c </strong>
374 (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.0</code>)<br/>
375 Coupling related to scalar graviton emission.
378 <h3>Unparticles, production processes</h3>
380 As mentioned above, the similar unparticle and graviton processes
381 share the same implementations. The unparticle processes, however,
382 only uses the dedicated unparticle parameters below. The unparticle
383 is also assigned the PDG code 5000039 and is therefore called
384 <i>Graviton</i> in the event record. The graviton and unparticle
385 emission as well as virtual graviton and unparticle exchange processes
386 are described in [<a href="Bibliography.html" target="page">Ask10</a>].
389 <i>Note:</i> As discussed in [<a href="Bibliography.html" target="page">Ask09</a>], for the graviton or
390 unparticle emission processes the underlying Breit-Wigner mass
391 distribution should be matched to the graviton mass spectrum in order
392 to achieve an optimal MC efficiency.
395 The following unparticle emission processes are available.
397 <p/><code>flag </code><strong> ExtraDimensionsUnpart:monojet </strong>
398 (<code>default = <strong>off</strong></code>)<br/>
399 Common switch for the group of lowest-order <i>U jet</i> emission
400 processes, i.e. the three ones below.
403 <p/><code>flag </code><strong> ExtraDimensionsUnpart:gg2Ug </strong>
404 (<code>default = <strong>off</strong></code>)<br/>
405 Scatterings <i>g g -> U g</i>.
409 <p/><code>flag </code><strong> ExtraDimensionsUnpart:qg2Uq </strong>
410 (<code>default = <strong>off</strong></code>)<br/>
411 Scatterings <i>q g -> U q</i>.
415 <p/><code>flag </code><strong> ExtraDimensionsUnpart:qqbar2Ug </strong>
416 (<code>default = <strong>off</strong></code>)<br/>
417 Scatterings <i>q qbar -> U g</i>.
421 <p/><code>flag </code><strong> ExtraDimensionsUnpart:ffbar2UZ </strong>
422 (<code>default = <strong>off</strong></code>)<br/>
423 Scatterings <i>f fbar -> U Z</i>.
427 <p/><code>flag </code><strong> ExtraDimensionsUnpart:ffbar2Ugamma </strong>
428 (<code>default = <strong>off</strong></code>)<br/>
429 Scatterings <i>f fbar -> U gamma</i>. This process corresponds
430 to the photon limit of the <i>U Z</i> process, as described in
431 [<a href="Bibliography.html" target="page">Ask09</a>].
436 The following processes with virtual unparticle exchange are available.
438 <p/><code>flag </code><strong> ExtraDimensionsUnpart:ffbar2gammagamma </strong>
439 (<code>default = <strong>off</strong></code>)<br/>
440 Scatterings <i>f fbar -> (U*) -> gamma gamma</i>. If the unparticle
441 contribution is zero in the spin-2 case, the results corresponds to
442 the SM contribution, i.e. equivalent to
443 <code>PromptPhoton:ffbar2gammagamma</code>.
447 <p/><code>flag </code><strong> ExtraDimensionsUnpart:gg2gammagamma </strong>
448 (<code>default = <strong>off</strong></code>)<br/>
449 Scatterings <i>g g -> (U*) -> gamma gamma</i>.
453 <p/><code>flag </code><strong> ExtraDimensionsUnpart:ffbar2llbar </strong>
454 (<code>default = <strong>off</strong></code>)<br/>
455 Scatterings <i>f fbar -> (U*) -> l lbar </i>, where
456 <i>l</i> is a charged lepton. If the unparticle contribution
457 is zero, the results corresponds to the SM contribution, i.e.
458 similar to <code>WeakSingleBoson:ffbar2gmZ</code>. Does not
459 include t-channel amplitude relevant for e^+e^- to e^+e^-
460 and no K-factor is used.
464 <p/><code>flag </code><strong> ExtraDimensionsUnpart:gg2llbar </strong>
465 (<code>default = <strong>off</strong></code>)<br/>
466 Scatterings <i>g g -> (U*) -> l lbar</i>.
470 <h3>Unparticles, parameters</h3>
472 <p/><code>mode </code><strong> ExtraDimensionsUnpart:spinU </strong>
473 (<code>default = <strong>2</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/>
477 <p/><code>parm </code><strong> ExtraDimensionsUnpart:dU </strong>
478 (<code>default = <strong>1.4</strong></code>; <code>minimum = 1.0</code>)<br/>
479 Scale dimension parameter.
482 <p/><code>parm </code><strong> ExtraDimensionsUnpart:LambdaU </strong>
483 (<code>default = <strong>2000.</strong></code>; <code>minimum = 100.0</code>)<br/>
484 Unparticle renormalization scale.
487 <p/><code>parm </code><strong> ExtraDimensionsUnpart:lambda </strong>
488 (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.0</code>)<br/>
489 Unparticle coupling to the SM fields.
492 <p/><code>parm </code><strong> ExtraDimensionsUnpart:ratio </strong>
493 (<code>default = <strong>1.0</strong></code>; <code>minimum = 1.0</code>; <code>maximum = 1.0</code>)<br/>
494 Ratio, <i>lambda'/lambda</i>, between the two possible coupling constants
495 of the spin-2 ME. <b>Warning:</b> A <i>ratio</i> value different from one
496 give rise to an IR divergence which makes the event generation very slow, so
497 this values is fixed to <i>ratio = 1</i> for the moment.
500 <p/><code>mode </code><strong> ExtraDimensionsUnpart:CutOffMode </strong>
501 (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 1</code>)<br/>
502 Options for when the hard scale of the process (e.g. <i>sHat</i>)
503 approaches or exceed the scale of validity of the low energy effective
504 theory (<i>Lambda_U</i>). This mode only concerns the unparticle
506 <br/><code>option </code><strong> 0</strong> : Do nothing, i.e. all values of <i>sHat</i>
508 <br/><code>option </code><strong> 1</strong> : Truncate contributing <i>sHat</i> region
509 ([<a href="Bibliography.html" target="page">Ask09</a>]).
512 <p/><code>mode </code><strong> ExtraDimensionsUnpart:gXX </strong>
513 (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/>
514 Chiral unparticle couplings, <i>gXX = gLL = gRR</i>. Only relevant
515 for lepton production from spin-1 unparticle exchange.
516 <br/><code>option </code><strong> 0</strong> : 1
517 <br/><code>option </code><strong> 1</strong> : -1
518 <br/><code>option </code><strong> 2</strong> : 0
521 <p/><code>mode </code><strong> ExtraDimensionsUnpart:gXY </strong>
522 (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/>
523 Chiral unparticle couplings, <i>gXY = gLR = gRL</i>. Only relevant
524 for lepton production from spin-1 unparticle exchange.
525 <br/><code>option </code><strong> 0</strong> : 1
526 <br/><code>option </code><strong> 1</strong> : -1
527 <br/><code>option </code><strong> 2</strong> : 0
533 <!-- Copyright (C) 2010 Torbjorn Sjostrand -->