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first import of structure, PYTHIA8 and DELPHES
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2	<head>
3	<title>Fragmentation</title>
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19	<?php
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24	echo "<font color='red'>NO FILE SELECTED YET.. PLEASE DO SO </font><a href='SaveSettings.php'>HERE</a><br/><br/>"; }
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28	<form method='post' action='Fragmentation.php'>
29
30	<h2>Fragmentation</h2>
31
32	Fragmentation in PYTHIA is based on the Lund string model
33	[<a href="Bibliography.php" target="page">And83, Sjo84</a>]. Several different aspects are involved in
34	the physics description, which here therefore is split accordingly.
35	This also, at least partly, reflect the set of classes involved in
36	the fragmentation machinery.
37
38	<p/>
39	The variables collected here have a very wide span of usefulness.
40	Some would be central in any hadronization tuning exercise, others
41	should not be touched except by experts.
42
43	<p/>
44	The fragmentation flavour-choice machinery is also used in a few
45	other places of the program, notably particle decays, and is thus
46	described on the separate <?php $filepath = $_GET["filepath"];
47	echo "<a href='FlavourSelection.php?filepath=".$filepath."' target='page'>";?>Flavour
48	Selection</a> page.
49
50	<h3>Fragmentation functions</h3>
51
52	The <code>StringZ</code> class handles the choice of longitudinal
53	lightcone fraction <i>z</i> according to one of two possible
54	shape sets.
55
56	<p/>
57	The Lund symmetric fragmentation function [<a href="Bibliography.php" target="page">And83</a>] is the
58	only alternative for light quarks. It is of the form
59	<br/><i>
60	f(z) = (1/z) * (1-z)^a * exp(-b m_T^2 / z)
61	</i><br/>
62	with the two main free parameters <i>a</i> and <i>b</i> to be
63	tuned to data. They are stored in
64
65	<br/><br/><table><tr><td><strong>StringZ:aLund </td><td></td><td> <input type="text" name="1" value="0.3" size="20"/>   (<code>default = <strong>0.3</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 2.0</code>)</td></tr></table>
66	The <i>a</i> parameter of the Lund symmetric fragmentation function.
67
68
69	<br/><br/><table><tr><td><strong>StringZ:bLund </td><td></td><td> <input type="text" name="2" value="0.8" size="20"/>   (<code>default = <strong>0.8</strong></code>; <code>minimum = 0.2</code>; <code>maximum = 2.0</code>)</td></tr></table>
70	The <i>b</i> parameter of the Lund symmetric fragmentation function.
71
72
73	<p/>
74	In principle, each flavour can have a different <i>a</i>. Then,
75	for going from an old flavour <i>i</i> to a new <i>j</i> one
76	the shape is
77	<br/><i>
78	f(z) = (1/z) * z^{a_i} * ((1-z)/z)^{a_j} * exp(-b * m_T^2 / z)
79	</i><br/>
80	This is only implemented for diquarks relative to normal quarks:
81
82	<br/><br/><table><tr><td><strong>StringZ:aExtraDiquark </td><td></td><td> <input type="text" name="3" value="0.5" size="20"/>   (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 2.0</code>)</td></tr></table>
83	allows a larger <i>a</i> for diquarks, with total
84	<i>a = aLund + aExtraDiquark</i>.
85
86
87	<p/>
88	Finally, the Bowler modification [<a href="Bibliography.php" target="page">Bow81</a>] introduces an extra
89	factor
90	<br/><i>
91	1/z^{r_Q * b * m_Q^2}
92	</i><br/>
93	for heavy quarks. To keep some flexibility, a multiplicative factor
94	<i>r_Q</i> is introduced, which ought to be unity (provided that
95	quark masses were uniquely defined) but can be set in
96
97	<br/><br/><table><tr><td><strong>StringZ:rFactC </td><td></td><td> <input type="text" name="4" value="1.0" size="20"/>   (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 2.0</code>)</td></tr></table>
98	<i>r_c</i>, i.e. the above parameter for <i>c</i> quarks.
99
100
101	<br/><br/><table><tr><td><strong>StringZ:rFactB </td><td></td><td> <input type="text" name="5" value="0.67" size="20"/>   (<code>default = <strong>0.67</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 2.0</code>)</td></tr></table>
102	<i>r_b</i>, i.e. the above parameter for <i>b</i> quarks.
103
104
105	<br/><br/><table><tr><td><strong>StringZ:rFactH </td><td></td><td> <input type="text" name="6" value="1.0" size="20"/>   (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 2.0</code>)</td></tr></table>
106	<i>r_h</i>, i.e. the above parameter for heavier hypothetical quarks,
107	or in general any new coloured particle long-lived enough to hadronize.
108
109
110	<p/>
111	As an alternative, it is possible to switch over to the
112	Peterson/SLAC formula [<a href="Bibliography.php" target="page">Pet83</a>]
113	<br/><i>
114	f(z) = 1 / ( z * (1 - 1/z - epsilon/(1-z))^2 )
115	</i><br/>
116	for charm, bottom and heavier (defined as above) by the three flags
117
118	<br/><br/><strong>StringZ:usePetersonC</strong> <input type="radio" name="7" value="on"><strong>On</strong>
119	<input type="radio" name="7" value="off" checked="checked"><strong>Off</strong>
120	(<code>default = <strong>off</strong></code>)<br/>
121	use Peterson for <i>c</i> quarks.
122
123
124	<br/><br/><strong>StringZ:usePetersonB</strong> <input type="radio" name="8" value="on"><strong>On</strong>
125	<input type="radio" name="8" value="off" checked="checked"><strong>Off</strong>
126	(<code>default = <strong>off</strong></code>)<br/>
127	use Peterson for <i>b</i> quarks.
128
129
130	<br/><br/><strong>StringZ:usePetersonH</strong> <input type="radio" name="9" value="on"><strong>On</strong>
131	<input type="radio" name="9" value="off" checked="checked"><strong>Off</strong>
132	(<code>default = <strong>off</strong></code>)<br/>
133	use Peterson for hypothetical heavier quarks.
134
135
136	<p/>
137	When switched on, the corresponding epsilon values are chosen to be
138
139	<br/><br/><table><tr><td><strong>StringZ:epsilonC </td><td></td><td> <input type="text" name="10" value="0.05" size="20"/>   (<code>default = <strong>0.05</strong></code>; <code>minimum = 0.01</code>; <code>maximum = 0.25</code>)</td></tr></table>
140	<i>epsilon_c</i>, i.e. the above parameter for <i>c</i> quarks.
141
142
143	<br/><br/><table><tr><td><strong>StringZ:epsilonB </td><td></td><td> <input type="text" name="11" value="0.005" size="20"/>   (<code>default = <strong>0.005</strong></code>; <code>minimum = 0.001</code>; <code>maximum = 0.025</code>)</td></tr></table>
144	<i>epsilon_b</i>, i.e. the above parameter for <i>b</i> quarks.
145
146
147	<br/><br/><table><tr><td><strong>StringZ:epsilonH </td><td></td><td> <input type="text" name="12" value="0.005" size="20"/>   (<code>default = <strong>0.005</strong></code>; <code>minimum = 0.0001</code>; <code>maximum = 0.25</code>)</td></tr></table>
148	<i>epsilon_h</i>, i.e. the above parameter for hypothetical heavier
149	quarks, normalized to the case where <i>m_h = m_b</i>. The actually
150	used parameter is then <i>epsilon = epsilon_h * (m_b^2 / m_h^2)</i>.
151	This allows a sensible scaling to a particle with an unknown higher
152	mass without the need for a user intervention.
153
154
155	<h3>Fragmentation <i>pT</i></h3>
156
157	The <code>StringPT</code> class handles the choice of fragmentation
158	<i>pT</i>. At each string breaking the quark and antiquark of the pair are
159	supposed to receive opposite and compensating <i>pT</i> kicks according
160	to a Gaussian distribution in <i>p_x</i> and <i>p_y</i> separately.
161	Call <i>sigma_q</i> the width of the <i>p_x</i> and <i>p_y</i>
162	distributions separately, i.e.
163	<br/><i>
164	d(Prob) = exp( -(p_x^2 + p_y^2) / 2 sigma_q^2).
165	</i><br/>
166	Then the total squared width is
167	<br/><i>
168	<pT^2> = <p_x^2> + <p_y^2> = 2 sigma_q^2 = sigma^2.
169	</i><br/>
170	It is this latter number that is stored in
171
172	<br/><br/><table><tr><td><strong>StringPT:sigma </td><td></td><td> <input type="text" name="13" value="0.304" size="20"/>   (<code>default = <strong>0.304</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
173	the width <i>sigma</i> in the fragmentation process.
174
175
176	<p/>
177	Since a normal hadron receives <i>pT</i> contributions for two string
178	breakings, it has a <i><p_x^2>_had = <p_y^2>_had = sigma^2</i>,
179	and thus <i><pT^2>_had = 2 sigma^2</i>.
180
181	<p/>
182	Some studies on isolated particles at LEP has indicated the need for
183	a slightly enhanced rate in the high-<i>pT</i> tail of the above
184	distribution. This would have to be reviewed in the context of a
185	complete retune of parton showers and hadronization, but for the
186	moment we stay with the current recipe, to boost the above <i>pT</i>
187	by a factor <i>enhancedWidth</i> for a small fraction
188	<i>enhancedFraction</i> of the breakups, where
189
190	<br/><br/><table><tr><td><strong>StringPT:enhancedFraction </td><td></td><td> <input type="text" name="14" value="0.01" size="20"/>   (<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.</code>)</td></tr></table>
191	<i>enhancedFraction</i>,the fraction of string breaks with enhanced
192	width.
193
194
195	<br/><br/><table><tr><td><strong>StringPT:enhancedWidth </td><td></td><td> <input type="text" name="15" value="2.0" size="20"/>   (<code>default = <strong>2.0</strong></code>; <code>minimum = 1.0</code>; <code>maximum = 10.0</code>)</td></tr></table>
196	<i>enhancedWidth</i>,the enhancement of the width in this fraction.
197
198
199	<h3>Jet joining procedure</h3>
200
201	String fragmentation is carried out iteratively from both string ends
202	inwards, which means that the two chains of hadrons have to be joined up
203	somewhere in the middle of the event. This joining is described by
204	parameters that in principle follows from the standard fragmentation
205	parameters, but in a way too complicated to parametrize. The dependence
206	is rather mild, however, so for a sensible range of variation the
207	parameters in this section should not be touched.
208
209	<br/><br/><table><tr><td><strong>StringFragmentation:stopMass </td><td></td><td> <input type="text" name="16" value="1.0" size="20"/>   (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 2.0</code>)</td></tr></table>
210	Is used to define a <i>W_min = m_q1 + m_q2 + stopMass</i>,
211	where <i>m_q1</i> and <i>m_q2</i> are the masses of the two
212	current endpoint quarks or diquarks.
213
214
215	<br/><br/><table><tr><td><strong>StringFragmentation:stopNewFlav </td><td></td><td> <input type="text" name="17" value="2.0" size="20"/>   (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 2.0</code>)</td></tr></table>
216	Add to <i>W_min</i> an amount <i>stopNewFlav * m_q_last</i>,
217	where <i>q_last</i> is the last <i>q qbar</i> pair produced
218	between the final two hadrons.
219
220
221	<br/><br/><table><tr><td><strong>StringFragmentation:stopSmear </td><td></td><td> <input type="text" name="18" value="0.2" size="20"/>   (<code>default = <strong>0.2</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 0.5</code>)</td></tr></table>
222	The <i>W_min</i> above is then smeared uniformly in the range
223	<i>W_min_smeared = W_min * [ 1 - stopSmear, 1 + stopSmear ]</i>.
224
225
226	<p/>
227	This <i>W_min_smeared</i> is then compared with the current remaining
228	<i>W_transverse</i> to determine if there is energy left for further
229	particle production. If not, i.e. if
230	<i>W_transverse < W_min_smeared</i>, the final two particles are
231	produced from what is currently left, if possible. (If not, the
232	fragmentation process is started over.)
233
234	<h3>Simplifying systems</h3>
235
236	There are a few situations when it is meaningful to simplify the
237	original task, one way or another.
238
239	<br/><br/><table><tr><td><strong>HadronLevel:mStringMin </td><td></td><td> <input type="text" name="19" value="1." size="20"/>   (<code>default = <strong>1.</strong></code>; <code>minimum = 0.5</code>; <code>maximum = 1.5</code>)</td></tr></table>
240	Decides whether a partonic system should be considered as a normal
241	string or a ministring, the latter only producing one or two primary
242	hadrons. The system mass should be above <i>mStringMin</i> plus the
243	sum of quark/diquark constituent masses for a normal string description,
244	else the ministring scenario is used.
245
246
247	<br/><br/><table><tr><td><strong>FragmentationSystems:mJoin </td><td></td><td> <input type="text" name="20" value="0.3" size="20"/>   (<code>default = <strong>0.3</strong></code>; <code>minimum = 0.2</code>; <code>maximum = 1.</code>)</td></tr></table>
248	When two colour-connected partons are very nearby, with at least
249	one being a gluon, they can be joined into one, to avoid technical
250	problems of very small string regions. The requirement for joining is
251	that the invariant mass of the pair is below <i>mJoin</i>, where a
252	gluon only counts with half its momentum, i.e. with its contribution
253	to the string region under consideration. (Note that, for technical
254	reasons, the 0.2 GeV lower limit is de facto hardcoded.)
255
256
257	<br/><br/><table><tr><td><strong>FragmentationSystems:mJoinJunction </td><td></td><td> <input type="text" name="21" value="1.0" size="20"/>   (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.5</code>; <code>maximum = 2.</code>)</td></tr></table>
258	When the invariant mass of two of the quarks in a three-quark junction
259	string system becomes too small, the system is simplified to a
260	quark-diquark simple string. The requirement for this simplification
261	is that the diquark mass, minus the two quark masses, falls below
262	<i>mJoinJunction</i>. Gluons on the string between the junction and
263	the respective quark, if any, are counted as part of the quark
264	four-momentum. Those on the two combined legs are clustered with the
265	diquark when it is formed.
266
267
268	<h3>Ministrings</h3>
269
270	The <code>MiniStringFragmentation</code> machinery is only used when a
271	string system has so small invariant mass that normal string fragmentation
272	is difficult/impossible. Instead one or two particles are produced,
273	in the former case shuffling energy-momentum relative to another
274	colour singlet system in the event, while preserving the invariant
275	mass of that system. With one exception parameters are the same as
276	defined for normal string fragmentation, to the extent that they are
277	at all applicable in this case.
278
279	A discussion of the relevant physics is found in [<a href="Bibliography.php" target="page">Nor00</a>].
280	The current implementation does not completely abide to the scheme
281	presented there, however, but has in part been simplified. (In part
282	for greater clarity, in part since the class is not quite finished yet.)
283
284	<br/><br/><table><tr><td><strong>MiniStringFragmentation:nTry </td><td></td><td> <input type="text" name="22" value="2" size="20"/>   (<code>default = <strong>2</strong></code>; <code>minimum = 1</code>; <code>maximum = 10</code>)</td></tr></table>
285	Whenever the machinery is called, first this many attempts are made
286	to pick two hadrons that the system fragments to. If the hadrons are
287	too massive the attempt will fail, but a new subsequent try could
288	involve other flavour and hadrons and thus still succeed.
289	After <i>nTry</i> attempts, instead an attempt is made to produce a
290	single hadron from the system. Should also this fail, some further
291	attempts at obtaining two hadrons will be made before eventually
292	giving up.
293
294
295	<h3>Junction treatment</h3>
296
297	A junction topology corresponds to an Y arrangement of strings
298	i.e. where three string pieces have to be joined up in a junction.
299	Such topologies can arise if several valence quarks are kicked out
300	from a proton beam, or in baryon-number-violating SUSY decays.
301	Special attention is necessary to handle the region just around
302	the junction, where the baryon number topologically is located.
303	The junction fragmentation scheme is described in [<a href="Bibliography.php" target="page">Sjo03</a>].
304	The parameters in this section should not be touched except by experts.
305
306	<br/><br/><table><tr><td><strong>StringFragmentation:eNormJunction </td><td></td><td> <input type="text" name="23" value="2.0" size="20"/>   (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.5</code>; <code>maximum = 10</code>)</td></tr></table>
307	Used to find the effective rest frame of the junction, which is
308	complicated when the three string legs may contain additional
309	gluons between the junction and the endpoint. To this end,
310	a pull is defined as a weighed sum of the momenta on each leg,
311	where the weight is <i>exp(- eSum / eNormJunction)</i>, with
312	<i>eSum</i> the summed energy of all partons closer to the junction
313	than the currently considered one (in the junction rest frame).
314	Should in principle be (close to) <i>sqrt((1 + a) / b)</i>, with
315	<i>a</i> and <i>b</i> the parameters of the Lund symmetric
316	fragmentation function.
317
318
319	<br/><br/><table><tr><td><strong>StringFragmentation:eBothLeftJunction </td><td></td><td> <input type="text" name="24" value="1.0" size="20"/>   (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.5</code>)</td></tr></table>
320	Retry (up to 10 times) when the first two considered strings in to a
321	junction both have a remaining energy (in the junction rest frame)
322	above this number.
323
324
325	<br/><br/><table><tr><td><strong>StringFragmentation:eMaxLeftJunction </td><td></td><td> <input type="text" name="25" value="10.0" size="20"/>   (<code>default = <strong>10.0</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
326	Retry (up to 10 times) when the first two considered strings in to a
327	junction has a highest remaining energy (in the junction rest frame)
328	above a random energy evenly distributed between
329	<i>eBothLeftJunction</i> and
330	<i>eBothLeftJunction + eMaxLeftJunction</i>
331	(drawn anew for each test).
332
333
334	<br/><br/><table><tr><td><strong>StringFragmentation:eMinLeftJunction </td><td></td><td> <input type="text" name="26" value="0.2" size="20"/>   (<code>default = <strong>0.2</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
335	Retry (up to 10 times) when the invariant mass-squared of the final leg
336	and the leftover momentum of the first two treated legs falls below
337	<i>eMinLeftJunction</i> times the energy of the final leg (in the
338	junction rest frame).
339
340
341	<input type="hidden" name="saved" value="1"/>
342
343	<?php
344	echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?>
345
346	<table width="100%"><tr><td align="right"><input type="submit" value="Save Settings" /></td></tr></table>
347	</form>
348
349	<?php
350
351	if($_POST["saved"] == 1)
352	{
353	$filepath = $_POST["filepath"];
354	$handle = fopen($filepath, 'a');
355
356	if($_POST["1"] != "0.3")
357	{
358	$data = "StringZ:aLund = ".$_POST["1"]."\n";
359	fwrite($handle,$data);
360	}
361	if($_POST["2"] != "0.8")
362	{
363	$data = "StringZ:bLund = ".$_POST["2"]."\n";
364	fwrite($handle,$data);
365	}
366	if($_POST["3"] != "0.5")
367	{
368	$data = "StringZ:aExtraDiquark = ".$_POST["3"]."\n";
369	fwrite($handle,$data);
370	}
371	if($_POST["4"] != "1.0")
372	{
373	$data = "StringZ:rFactC = ".$_POST["4"]."\n";
374	fwrite($handle,$data);
375	}
376	if($_POST["5"] != "0.67")
377	{
378	$data = "StringZ:rFactB = ".$_POST["5"]."\n";
379	fwrite($handle,$data);
380	}
381	if($_POST["6"] != "1.0")
382	{
383	$data = "StringZ:rFactH = ".$_POST["6"]."\n";
384	fwrite($handle,$data);
385	}
386	if($_POST["7"] != "off")
387	{
388	$data = "StringZ:usePetersonC = ".$_POST["7"]."\n";
389	fwrite($handle,$data);
390	}
391	if($_POST["8"] != "off")
392	{
393	$data = "StringZ:usePetersonB = ".$_POST["8"]."\n";
394	fwrite($handle,$data);
395	}
396	if($_POST["9"] != "off")
397	{
398	$data = "StringZ:usePetersonH = ".$_POST["9"]."\n";
399	fwrite($handle,$data);
400	}
401	if($_POST["10"] != "0.05")
402	{
403	$data = "StringZ:epsilonC = ".$_POST["10"]."\n";
404	fwrite($handle,$data);
405	}
406	if($_POST["11"] != "0.005")
407	{
408	$data = "StringZ:epsilonB = ".$_POST["11"]."\n";
409	fwrite($handle,$data);
410	}
411	if($_POST["12"] != "0.005")
412	{
413	$data = "StringZ:epsilonH = ".$_POST["12"]."\n";
414	fwrite($handle,$data);
415	}
416	if($_POST["13"] != "0.304")
417	{
418	$data = "StringPT:sigma = ".$_POST["13"]."\n";
419	fwrite($handle,$data);
420	}
421	if($_POST["14"] != "0.01")
422	{
423	$data = "StringPT:enhancedFraction = ".$_POST["14"]."\n";
424	fwrite($handle,$data);
425	}
426	if($_POST["15"] != "2.0")
427	{
428	$data = "StringPT:enhancedWidth = ".$_POST["15"]."\n";
429	fwrite($handle,$data);
430	}
431	if($_POST["16"] != "1.0")
432	{
433	$data = "StringFragmentation:stopMass = ".$_POST["16"]."\n";
434	fwrite($handle,$data);
435	}
436	if($_POST["17"] != "2.0")
437	{
438	$data = "StringFragmentation:stopNewFlav = ".$_POST["17"]."\n";
439	fwrite($handle,$data);
440	}
441	if($_POST["18"] != "0.2")
442	{
443	$data = "StringFragmentation:stopSmear = ".$_POST["18"]."\n";
444	fwrite($handle,$data);
445	}
446	if($_POST["19"] != "1.")
447	{
448	$data = "HadronLevel:mStringMin = ".$_POST["19"]."\n";
449	fwrite($handle,$data);
450	}
451	if($_POST["20"] != "0.3")
452	{
453	$data = "FragmentationSystems:mJoin = ".$_POST["20"]."\n";
454	fwrite($handle,$data);
455	}
456	if($_POST["21"] != "1.0")
457	{
458	$data = "FragmentationSystems:mJoinJunction = ".$_POST["21"]."\n";
459	fwrite($handle,$data);
460	}
461	if($_POST["22"] != "2")
462	{
463	$data = "MiniStringFragmentation:nTry = ".$_POST["22"]."\n";
464	fwrite($handle,$data);
465	}
466	if($_POST["23"] != "2.0")
467	{
468	$data = "StringFragmentation:eNormJunction = ".$_POST["23"]."\n";
469	fwrite($handle,$data);
470	}
471	if($_POST["24"] != "1.0")
472	{
473	$data = "StringFragmentation:eBothLeftJunction = ".$_POST["24"]."\n";
474	fwrite($handle,$data);
475	}
476	if($_POST["25"] != "10.0")
477	{
478	$data = "StringFragmentation:eMaxLeftJunction = ".$_POST["25"]."\n";
479	fwrite($handle,$data);
480	}
481	if($_POST["26"] != "0.2")
482	{
483	$data = "StringFragmentation:eMinLeftJunction = ".$_POST["26"]."\n";
484	fwrite($handle,$data);
485	}
486	fclose($handle);
487	}
488
489	?>
490	</body>
491	</html>
492
493	<!-- Copyright (C) 2012 Torbjorn Sjostrand -->
494

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