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1	<html>
2	<head>
3	<title>Resonance Decays</title>
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29
30	<h2>Resonance Decays</h2>
31
32	The <code>ResonanceDecays</code> class performs the sequential decays of
33	all resonances formed in the hard process. Note the important distinction
34	between "resonances" and other "particles" made in PYTHIA.
35	<ul>
36	<li>
37	The list of resonances contains <i>gamma^*/Z^0</i>, <i>W^+-</i>, top,
38	the Higgs, and essentially all new particles of Beyond-the-Standard-Model
39	physics: further Higgses, sfermions, gauginos, techniparticles, and so on.
40	The partial widths to different decay channels are perturbatively
41	calculable, given the parameters of the respective model, and branching
42	ratios may be allowed to vary across a (reasonably broad) resonance peak.
43	Usually resonances are short-lived, and therefore it makes sense to consider
44	their decays immediately after the primary hard process has been set up.
45	Furthermore, in several cases the decay angular distributions are encoded
46	as part of the specific process, e.g. the <i>W</i> decays differently in
47	<i>f fbar -> W^+-</i>, <i>f fbar -> W^+ W^-</i> and
48	<i>h^0 -> W^+ W^- </i>. All of these particles are (in PYTHIA) only
49	produced as part of the hard process itself, i.e. they are not produced
50	in showers or hadronization processes. Therefore the restriction to
51	specific decay channels can be consistently taken into account as a
52	corresponding reduction in the cross section of a process. Finally, note
53	that all of these resonances have an on-shell mass above 20 GeV, with the
54	exception of some hypothetical weakly interacting and stable particles
55	such as the gravitino.
56	</li>
57	<li>
58	The other particles include normal hadrons and the Standard-Model leptons,
59	including the <i>tau^+-</i>. These can be produced in the normal
60	hadronization and decay description, which involve unknown nonperturbative
61	parameters and multistep chains that cannot be predicted beforehand:
62	a hard process like <i>g g -> g g</i> can develop a shower with a
63	<i>g -> b bbar</i> branching, where the <i>b</i> hadronizes to a
64	<i>B^0bar</i> that oscillates to a <i>B^0</i> that decays to a
65	<i>tau^+</i>. Therefore any change of branching ratios - most of which
66	are determined from data rather than from first principles anyway -
67	will not be taken into account in the cross section of a process.
68	Exceptions exist, but most particles in this class are made to decay
69	isotropically. Finally, note that all of these particles have a mass
70	below 20 GeV.
71	</li>
72	</ul>
73
74	There is one ambiguous case in this classification, namely the photon.
75	The <i>gamma^*/Z^0</i> combination contains a low-mass peak when
76	produced in a hard process. On the other hand, photons can participate
77	in shower evolution, and therefore a photon originally assumed
78	massless can be assigned an arbitrarily high mass when it is allowed
79	to branch into a fermion pair. In some cases this could lead to
80	doublecounting, e.g. between processes such as
81	<i>f fbar -> (gamma^/Z^0) (gamma^/Z^0)</i>,
82	<i>f fbar -> (gamma^*/Z^0) gamma</i> and
83	<i>f fbar -> gamma gamma</i>. Here it make sense to limit the
84	lower mass allowed for the <i>gamma^*/Z^0</i> combination,
85	in <code>23:mMin</code>, to be the same as the upper limit allowed
86	for an off-shell photon in the shower evolution, in
87	<code>TimeShower:mMaxGamma</code>. By default this matching is done
88	at 10 GeV.
89
90	<p/>
91	In spite of the above-mentioned differences, the resonances and the
92	other particles are all stored in one common
93	<?php $filepath = $_GET["filepath"];
94	echo "<a href='ParticleData.php?filepath=".$filepath."' target='page'>";?>particle data table</a>, so as to offer a
95	uniform interface to <?php $filepath = $_GET["filepath"];
96	echo "<a href='ParticleDataScheme.php?filepath=".$filepath."' target='page'>";?>setting and
97	getting</a> properties such as name, mass, charge and decay modes,
98	also for the <?php $filepath = $_GET["filepath"];
99	echo "<a href='ParticleProperties.php?filepath=".$filepath."' target='page'>";?>particle properties</a>
100	in the event record. Some methods are specific to resonances, however,
101	in particular for the calculation of partial widths and thereby of
102	branching ratio. For resonances these can be calculated dynamically,
103	set up at initialization for the nominal mass and then updated to the
104	current mass when these are picked according to a Breit-Wigner resonance
105	shape.
106
107	<h3>Resonance Decays and Cross Sections</h3>
108
109	As already hinted above, you have the possibility to set the allowed
110	decay channels of resonances, see
111	<?php $filepath = $_GET["filepath"];
112	echo "<a href='ParticleDataScheme.php?filepath=".$filepath."' target='page'>";?>Particle Data Scheme</a> description.
113	For instance, if you study the process <i>q qbar -> H^0 Z^0</i>
114	you could specify that the <i>Z^0</i> should decay only to
115	lepton pairs, the <i>H^0</i> only to <i>W^+ W^-</i>, the
116	<i>W^+</i> only to a muon and a neutrino, while the <i>W^-</i>
117	can decay to anything. Unfortunately there are limits to the
118	flexibility: you cannot set a resonance to have different properties
119	in different places of a process, e.g. if instead
120	<i>H^0 -> Z^0 Z^0</i> in the above process then the three
121	<i>Z^0</i>'s would all obey the same rules.
122
123	<p/>
124	The restrictions on the allowed final states of a process is directly
125	reflected in the cross section of it. That is, if some final states
126	are excluded then the cross section is reduced accordingly. Such
127	restrictions are built up recursively in cases of sequential decay
128	chains. The restrictions are also reflected in the compositions of
129	those events that actually do get to be generated. For instance,
130	the relative rates of <i>H^0 -> W^+ W^-</i> and
131	<i>H^0 -> Z^0 Z^0</i> are shifted when the allowed sets of
132	<i>W^+-</i> and <i>Z^0</i> decay channels are changed.
133
134	<p/>
135	We remind that only those particles that Pythia treat as resonances
136	enjoy this property, and only those that are considered as part of the
137	hard process and its assocaited resonance decays.
138
139	<p/>
140	There is one key restriction on resonances:
141	<br/><br/><table><tr><td><strong>ResonanceWidths:minWidth </td><td></td><td> <input type="text" name="1" value="1e-20" size="20"/>   (<code>default = <strong>1e-20</strong></code>; <code>minimum = 1e-30</code>)</td></tr></table>
142	Minimal allowed width of a resonance, in GeV. If the width falls below
143	this number the resonance is considered stable and will not be allowed
144	to decay. This is mainly intended as a technical parameter, to avoid
145	disasters in cases where no open decay channels exists at all. It could
146	be used for real-life decisions as well, however, but then typically
147	would have to be much bigger than the default value. Special caution
148	would be needed if coloured resonance particles were made stable, since
149	the program would not necessarily know how to hadronize them, and
150	therefore fail at that stage.
151
152
153	<p/>
154	In spite of this technical parameter choice, it is possible to set
155	a lifetime for a resonance, and thereby to obtain displaced vertices.
156	If a resonance is allowed to decay it will do so, irrespective of
157	the location of the decay vertex. This is unlike
158	<?php $filepath = $_GET["filepath"];
159	echo "<a href='ParticleDecays.php?filepath=".$filepath."' target='page'>";?>normal particle decays</a>,
160	where it is possible to define some region around the primary
161	vertex within which all decays should happen, with particles
162	leaving that region considered stable. The logic is that resonances
163	as a rule are too short-lived for secondary vertices,
164	so if you pick a scenario with a long-lived but unstable resonance
165	it is because you <i>want</i> to study secondary vertices.
166	How to interface those decays to a detector simulation program then
167	is another story, to be solved separately. Do note that a special
168	treatment is needed for coloured long-lived resonances, that form
169	<?php $filepath = $_GET["filepath"];
170	echo "<a href='Rhadrons.php?filepath=".$filepath."' target='page'>";?>R-hadrons</a>, and where charge and flavour
171	may change between the production and decay vertices.
172
173	<h3>Special properties and methods for resonances</h3>
174
175	The method <code>ParticleData::isResonance(id)</code> allows you to
176	query whether a given particle species is considered a resonance or not.
177	You can also change the default value of this flag in the normal way,
178	e.g. <code>pythia.readString("id:isResonance = true")</code>.
179
180	<p/>
181	An option with a forced width can be set with the
182	<code>id:doForceWidth</code> flag as above, and queried with
183	<code>ParticleData::doForceWidth(id)</code>. It is by default
184	<code>off</code>, and should normally so remain. If switched
185	<code>on</code> then the width stored in <code>id:mWidth</code> is
186	strictly used to describe the Breit-Wigner of the resonance. This is
187	unlike the normal behaviour of standard resonances such as the
188	<i>Z^0</i>, <i>W^+-</i>, <i>t</i> or <i>h^0</i>, which have
189	explicit decay-widths formulae encoded, in classes derived from the
190	<code><?php $filepath = $_GET["filepath"];
191	echo "<a href='SemiInternalResonances.php?filepath=".$filepath."' target='page'>";?>ResonanceWidths</a></code>
192	base class. These formulae are used, e.g., to derive all the Higgs partial
193	widths as a function of the Higgs mass you choose, and at initialization
194	overwrites the existing total width value. The reason for forcing the
195	width to another value specified by you would normally more have to do
196	with experimental issues than with physics ones, e.g. how sensitive your
197	detector would be to changes in the Higgs width by a factor of two.
198	A warning is that such a rescaling could modify the cross section of
199	a process correspondingly for some processes, while leaving it
200	(essentially) unchanged for others (as would seem most logical),
201	depending on how these were encoded. A further warning is that,
202	if you use this facility for <i>Z^0</i> or <i>Z'^0</i> with
203	<i>gamma^/Z^0</i> or <i>gamma^/Z^0/Z'^0</i> interference on,
204	then also the handling of this interference is questionable.
205	So, if you need to use the width-rescaling option, be extremely cautios.
206
207	<p/>
208	If a resonance does not have a class of its own, with hardcoded equations
209	for all relevant partial widths, then a simpler object will be created
210	at initialization. This object will take the total width and branching
211	ratios as is (with the optional variations explained in the next section),
212	and thus the rescaling approach brings no further freedom.
213
214	<p/>
215	Mainly for internal usage, the
216	<code><?php $filepath = $_GET["filepath"];
217	echo "<a href='ParticleDataScheme.php?filepath=".$filepath."' target='page'>";?>ParticleData</a></code> contain
218	some special methods that are only meaningful for resonances:
219	<ul>
220	<li><code>resInit(...)</code> to initialize a resonance, possibly
221	including a recalculation of the nominal width to match the nominal
222	mass;</li>
223	<li><code>resWidth(...)</code> to calculate the partial and total widths
224	at the currently selected mass;</li>
225	<li><code>resWidthOpen(...)</code> to calculate the partial and total
226	widths of those channels left open by user switches, at the currently
227	selected mass;</li>
228	<li><code>resWidthStore(...)</code> to calculate the partial and total
229	widths of those channels left open by user switches, at the currently
230	selected mass, and store those as input for a subsequent selection of
231	decay channel;</li>
232	<li><code>resOpenFrac(...)</code> to return the fraction of the total
233	width that is open by the decay channel selection made by users (based on
234	the choice of <code><?php $filepath = $_GET["filepath"];
235	echo "<a href='ParticleDataScheme.php?filepath=".$filepath."' target='page'>";?>onMode</a></code>
236	for the various decay channels, recursively calculated for sequential
237	decays);</li>
238	<li><code>resWidthRescaleFactor(...)</code> returns the factor by which
239	the internally calculated PYTHIA width has to be rescaled to give the
240	user-enforced width;</li>
241	<li><code>resWidthChan(...)</code> to return the width for one particular
242	channel (currently only used for Higgs decays, to obtain instate coupling
243	from outstate width).</li>
244	</ul>
245	These methods actually provide an interface to the classes derived from
246	the <code>ResonanceWidths</code> base class, to describe various
247	resonances.
248
249	<h3>Modes for Matrix Element Processing</h3>
250
251	The <code>meMode()</code> value for a decay mode is used to specify
252	<?php $filepath = $_GET["filepath"];
253	echo "<a href='ParticleDecays.php?filepath=".$filepath."' target='page'>";?>nonisotropic decays or the conversion of
254	a parton list into a set of hadrons</a> in some channels of normal
255	particles. For resonances it can also take a third function, namely
256	to describe how the branching ratios and widths of a resonance should
257	be rescaled as a function of the current mass of the decaying resonance.
258	The rules are especially useful when new channels are added to an
259	existing particle, or a completely new resonance added.
260
261	<ul>
262	<li>0 : channels for which hardcoded partial-width expressions are
263	expected to exist in the derived class of the respective resonance.
264	Should no such code exist then the partial width defaults to zero.
265	</li>
266	<li>1 - 99 : same as 0, but normally not used for resonances.</li>
267	<li>100 : calculate the partial width of the channel from its stored
268	branching ratio times the stored total width. This value remains unchanged
269	when the resonance fluctuates in mass. Specifically there are no
270	threshold corrections. That is, if the resonance fluctuates down in
271	mass, to below the nominal threshold, it is assumed that one of the
272	daughters could also fluctuate down to keep the channel open. (If not,
273	there may be problems later on.)
274	</li>
275	<li>101 : calculate the partial width of the channel from its stored
276	branching ratio times the stored total width. Multiply by a step threshold,
277	i.e. the channel is switched off when the sum of the daughter on-shell
278	masses is above the current mother mass.</li>
279	<li>102 : calculate the partial width of the channel from its stored
280	branching ratio times the stored total width. Multiply by a smooth
281	threshold factor
282	<i>beta = sqrt( (1 - m_1^2/m_2 - m_2^2/m^2)^2 - 4 m_1^2 m_2^2/m^4)</i>
283	for two-body decays and <i>sqrt(1 - Sum_i m_i / m)</i> for multibody
284	ones. The former correctly encodes the size of the phase space but
285	misses out on any nontrivial matrix-element behaviour, while the latter
286	obviously is a very crude simplification of the correct phase-space
287	expression. Specifically, it is thereby assumed that the stored branching
288	ratio and total width did not take into account such a factor.</li>
289	<li>103 : use the same kind of behaviour and threshold factor as for
290	102 above, but assume that such a threshold factor has been used when
291	the default branching ratio and total width were calculated, so that one
292	should additionally divide by the on-shell threshold factor. Specifically,
293	this will give back the stored branching ratios for on-shell mass,
294	unlike the 102 option. To avoid division by zero, or in general
295	unreasonably big rescaling factors, a lower limit
296	<code>minThreshold</code> (see below) on the value of the on-shell
297	threshold factor is imposed. (In cases where a big rescaling is
298	intentional, code 102 would be more appropriate.) </li>
299	</ul>
300
301	<br/><br/><table><tr><td><strong>ResonanceWidths:minThreshold </td><td></td><td> <input type="text" name="2" value="0.1" size="20"/>   (<code>default = <strong>0.1</strong></code>; <code>minimum = 0.01</code>)</td></tr></table>
302	Used uniquely for <code>meMode = 103</code> to set the minimal value
303	assumed for the threshold factor,
304	<i>sqrt( (1 - m_1^2/m_2 - m_2^2/m^2)^2 - 4 m_1^2 m_2^2/m^4)</i>
305	for two-body decays and <i>sqrt(1 - Sum_i m_i / m)</i> for multibody
306	ones. Thus the inverse of this number sets an upper limit for how
307	much the partial width of a channel can increase from the on-shell
308	value to the value for asymptotically large resonance masses. Is mainly
309	intended as a safety measure, to avoid unintentionally large rescalings.
310
311
312	<p/>
313	All of these <code>meMode</code>'s may coexist for the same resonance.
314	This would be the case e.g. if you want to add a few new channels to an
315	already existing resonance, where the old partial widths come hardcoded
316	while the new ones are read in from an external file. The typical example
317	would be an MSSM Higgs sector, where partial widths to SM particles are
318	already encoded, <code>meMode = 0</code>, while decay rates to sparticles
319	are read in from some external calculation and maybe would be best
320	approximated by using <code>meMode = 103</code>. Indeed the default
321	particle table in PYTHIA uses 103 for all channels that are expected
322	to be provided by external input.
323
324	<p/>
325	Some further clarification may be useful. At initialization the existing
326	total width and on-shell branching ratios will be updated. For channels
327	with <code>meMode < 100</code> the originally stored branching ratios
328	are irrelevant, since the existing code will anyway be used to calculate
329	the partial widths from scratch. For channels with <code>meMode = 100</code>
330	or bigger, instead the stored branching ratio is used together with the
331	originally stored total width to define the correct on-shell partial width.
332	The sum of partial widths then gives the new total width, and from there
333	new branching ratios are defined.
334
335	<p/>
336	In these operations the original sum of branching ratios need not be
337	normalized to unity. For instance, you may at input have a stored total
338	width of 1 GeV and a sum of branching ratios of 2. After initialization
339	the width will then have been changed to 2 GeV and the sum of branching
340	ratios rescaled to unity. This might happen e.g. if you add a few channels
341	to an existing resonance, without changing the branching ratios of the
342	existing channels or the total width of the resonance.
343
344	<p/>
345	In order to simulate the Breit-Wigner shape correctly, it is important
346	that all channels that contribute to the total width are included in the
347	above operations. This must be kept separate from the issue of which
348	channels you want to have switched on for a particular study, to be
349	considered next.
350
351	<p/>
352
353	In the event-generation process, when an off-shell resonance mass has been
354	selected, the width and branching ratios are re-evaluated for this new mass.
355	At this stage also the effects of restrictions on allowed decay modes are
356	taken into account, as set by the <code>onMode</code> switch for each
357	separate decay channel. Thus a channel may be on or off, with different
358	choices of open channels between the particle and its antiparticle.
359	In addition, even when a channel is on, the decay may be into another
360	resonance with its selection of allowed channels. It is these kinds of
361	restrictions that lead to the <i>Gamma_out</i> possibly being
362	smaller than <i>Gamma_tot</i>. As a reminder, the Breit-Wigner for
363	decays behaves like <i>Gamma_out / ((s - m^2)^2 + s * Gamma_tot^2)</i>,
364	where the width in the numerator is only to those channels being studied,
365	but the one in the denominator to all channels of the particle. These
366	ever-changing numbers are not directly visible to the user, but are only
367	stored in a work area.
368
369	<input type="hidden" name="saved" value="1"/>
370
371	<?php
372	echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?>
373
374	<table width="100%"><tr><td align="right"><input type="submit" value="Save Settings" /></td></tr></table>
375	</form>
376
377	<?php
378
379	if($_POST["saved"] == 1)
380	{
381	$filepath = $_POST["filepath"];
382	$handle = fopen($filepath, 'a');
383
384	if($_POST["1"] != "1e-20")
385	{
386	$data = "ResonanceWidths:minWidth = ".$_POST["1"]."\n";
387	fwrite($handle,$data);
388	}
389	if($_POST["2"] != "0.1")
390	{
391	$data = "ResonanceWidths:minThreshold = ".$_POST["2"]."\n";
392	fwrite($handle,$data);
393	}
394	fclose($handle);
395	}
396
397	?>
398	</body>
399	</html>
400
401	<!-- Copyright (C) 2012 Torbjorn Sjostrand -->
402

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