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BeamRemnants.php @ 1

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first import of structure, PYTHIA8 and DELPHES
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2	<head>
3	<title>Beam Remnants</title>
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29
30	<h2>Beam Remnants</h2>
31
32	<h3>Introduction</h3>
33
34	The <code>BeamParticle</code> class contains information on all partons
35	extracted from a beam (so far). As each consecutive multiparton interaction
36	defines its respective incoming parton to the hard scattering a
37	new slot is added to the list. This information is modified when
38	the backwards evolution of the spacelike shower defines a new
39	initiator parton. It is used, both for the multiparton interactions
40	and the spacelike showers, to define rescaled parton densities based
41	on the <i>x</i> and flavours already extracted, and to distinguish
42	between valence, sea and companion quarks. Once the perturbative
43	evolution is finished, further beam remnants are added to obtain a
44	consistent set of flavours. The current physics framework is further
45	described in [<a href="Bibliography.php" target="page">Sjo04</a>].
46
47	<p/>
48	The introduction of <?php $filepath = $_GET["filepath"];
49	echo "<a href='MultipartonInteractions.php?filepath=".$filepath."' target='page'>";?>rescattering</a>
50	in the multiparton interactions framework further complicates the
51	processing of events. Specifically, when combined with showers,
52	the momentum of an individual parton is no longer uniquely associated
53	with one single subcollision. Nevertheless the parton is classified
54	with one system, owing to the technical and administrative complications
55	of more complete classifications. Therefore the addition of primordial
56	<i>kT</i> to the subsystem initiator partons does not automatically
57	guarantee overall <i>pT</i> conservation. Various tricks are used to
58	minimize the mismatch, with a brute force shift of all parton
59	<i>pT</i>'s as a final step.
60
61	<p/>
62	Much of the above information is stored in a vector of
63	<code>ResolvedParton</code> objects, which each contains flavour and
64	momentum information, as well as valence/companion information and more.
65	The <code>BeamParticle</code> method <code>list()</code> shows the
66	contents of this vector, mainly for debug purposes.
67
68	<p/>
69	The <code>BeamRemnants</code> class takes over for the final step
70	of adding primordial <i>kT</i> to the initiators and remnants,
71	assigning the relative longitudinal momentum sharing among the
72	remnants, and constructing the overall kinematics and colour flow.
73	This step couples the two sides of an event, and could therefore
74	not be covered in the <code>BeamParticle</code> class, which only
75	considers one beam at a time.
76
77	<p/>
78	The methods of these classes are not intended for general use,
79	and so are not described here.
80
81	<p/>
82	In addition to the parameters described on this page, note that the
83	choice of <?php $filepath = $_GET["filepath"];
84	echo "<a href='PDFSelection.php?filepath=".$filepath."' target='page'>";?>parton densities</a> is made
85	in the <code>Pythia</code> class. Then pointers to the pdf's are handed
86	on to <code>BeamParticle</code> at initialization, for all subsequent
87	usage.
88
89	<h3>Primordial <i>kT</i></h3>
90
91	The primordial <i>kT</i> of initiators of hard-scattering subsystems
92	are selected according to Gaussian distributions in <i>p_x</i> and
93	<i>p_y</i> separately. The widths of these distributions are chosen
94	to be dependent on the hard scale of the central process and on the mass
95	of the whole subsystem defined by the two initiators:
96	<br/><i>
97	sigma = (sigma_soft * Q_half + sigma_hard * Q) / (Q_half + Q)
98	* m / (m_half + m)
99	</i><br/>
100	Here <i>Q</i> is the hard-process renormalization scale for the
101	hardest process and the <i>pT</i> scale for subsequent multiparton
102	interactions, <i>m</i> the mass of the system, and
103	<i>sigma_soft</i>, <i>sigma_hard</i>, <i>Q_half</i> and
104	<i>m_half</i> parameters defined below. Furthermore each separately
105	defined beam remnant has a distribution of width <i>sigma_remn</i>,
106	independently of kinematical variables.
107
108	<br/><br/><strong>BeamRemnants:primordialKT</strong> <input type="radio" name="1" value="on" checked="checked"><strong>On</strong>
109	<input type="radio" name="1" value="off"><strong>Off</strong>
110	(<code>default = <strong>on</strong></code>)<br/>
111	Allow or not selection of primordial <i>kT</i> according to the
112	parameter values below.
113
114
115	<br/><br/><table><tr><td><strong>BeamRemnants:primordialKTsoft </td><td></td><td> <input type="text" name="2" value="0.5" size="20"/>   (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
116	The width <i>sigma_soft</i> in the above equation, assigned as a
117	primordial <i>kT</i> to initiators in the soft-interaction limit.
118
119
120	<br/><br/><table><tr><td><strong>BeamRemnants:primordialKThard </td><td></td><td> <input type="text" name="3" value="2.0" size="20"/>   (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
121	The width <i>sigma_hard</i> in the above equation, assigned as a
122	primordial <i>kT</i> to initiators in the hard-interaction limit.
123
124
125	<br/><br/><table><tr><td><strong>BeamRemnants:halfScaleForKT </td><td></td><td> <input type="text" name="4" value="1." size="20"/>   (<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
126	The scale <i>Q_half</i> in the equation above, defining the
127	half-way point between hard and soft interactions.
128
129
130	<br/><br/><table><tr><td><strong>BeamRemnants:halfMassForKT </td><td></td><td> <input type="text" name="5" value="1." size="20"/>   (<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
131	The scale <i>m_half</i> in the equation above, defining the
132	half-way point between low-mass and high-mass subsystems.
133	(Kinematics construction can easily fail if a system is assigned
134	a primordial <i>kT</i> value higher than its mass, so the
135	mass-dampening is intended to reduce some troubles later on.)
136
137
138	<br/><br/><table><tr><td><strong>BeamRemnants:primordialKTremnant </td><td></td><td> <input type="text" name="6" value="0.4" size="20"/>   (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
139	The width <i>sigma_remn</i>, assigned as a primordial <i>kT</i>
140	to beam-remnant partons.
141
142
143	<p/>
144	A net <i>kT</i> imbalance is obtained from the vector sum of the
145	primordial <i>kT</i> values of all initiators and all beam remnants.
146	This quantity is compensated by a shift shared equally between
147	all partons, except that the dampening factor <i>m / (m_half + m)</i>
148	is again used to suppress the role of small-mass systems.
149
150	<p/>
151	Note that the current <i>sigma</i> definition implies that
152	<i><pT^2> = <p_x^2>+ <p_y^2> = 2 sigma^2</i>.
153	It thus cannot be compared directly with the <i>sigma</i>
154	of nonperturbative hadronization, where each quark-antiquark
155	breakup corresponds to <i><pT^2> = sigma^2</i> and only
156	for hadrons it holds that <i><pT^2> = 2 sigma^2</i>.
157	The comparison is further complicated by the reduction of
158	primordial <i>kT</i> values by the overall compensation mechanism.
159
160	<br/><br/><strong>BeamRemnants:rescatterRestoreY</strong> <input type="radio" name="7" value="on"><strong>On</strong>
161	<input type="radio" name="7" value="off" checked="checked"><strong>Off</strong>
162	(<code>default = <strong>off</strong></code>)<br/>
163	Is only relevant when <?php $filepath = $_GET["filepath"];
164	echo "<a href='MultipartonInteractions.php?filepath=".$filepath."' target='page'>";?>rescattering</a>
165	is switched on in the multiparton interactions scenario. For a normal
166	interaction the rapidity and mass of a system is preserved when
167	primordial <i>kT</i> is introduced, by appropriate modification of the
168	incoming parton momenta. Kinematics construction is more complicated for
169	a rescattering, and two options are offered. Differences between these
170	can be used to explore systematic uncertainties in the rescattering
171	framework.<br/>
172	The default behaviour is to keep the incoming rescattered parton as is,
173	but to modify the unrescattered incoming parton so as to preserve the
174	invariant mass of the system. Thereby the rapidity of the rescattering
175	is modified.<br/>
176	The alternative is to retain the rapidity (and mass) of the rescattered
177	system when primordial <i>kT</i> is introduced. This is made at the
178	expense of a modified longitudinal momentum of the incoming rescattered
179	parton, so that it does not agree with the momentum it ought to have had
180	by the kinematics of the previous interaction.<br/>
181	For a double rescattering, when both incoming partons have already scattered,
182	there is no obvious way to retain the invariant mass of the system in the
183	first approach, so the second is always used.
184
185
186	<h3>Colour flow</h3>
187
188	The colour flows in the separate subprocesses defined in the
189	multiparton-interactions scenario are tied together via the assignment
190	of colour flow in the beam remnant. This is not an unambiguous
191	procedure, but currently no parameters are directly associated with it.
192	However, a simple "minimal" procedure of colour flow only via the beam
193	remnants does not result in a scenario in
194	agreement with data, notably not a sufficiently steep rise of
195	<i><pT>(n_ch)</i>. The true origin of this behaviour and the
196	correct mechanism to reproduce it remains one of the big unsolved issues
197	at the borderline between perturbative and nonperturbative QCD.
198	As a simple attempt, an additional step is introduced, wherein the gluons
199	of a lower-<i>pT</i> system are merged with the ones in a higher-pT one.
200
201	<br/><br/><strong>BeamRemnants:reconnectColours</strong> <input type="radio" name="8" value="on" checked="checked"><strong>On</strong>
202	<input type="radio" name="8" value="off"><strong>Off</strong>
203	(<code>default = <strong>on</strong></code>)<br/>
204	Allow or not a system to be merged with another one.
205
206
207	<br/><br/><table><tr><td><strong>BeamRemnants:reconnectRange </td><td></td><td> <input type="text" name="9" value="10.0" size="20"/>   (<code>default = <strong>10.0</strong></code>; <code>minimum = 0.</code>; <code>maximum = 10.</code>)</td></tr></table>
208	A system with a hard scale <i>pT</i> can be merged with one of a
209	harder scale with a probability that is
210	<i>pT0_Rec^2 / (pT0_Rec^2 + pT^2)</i>, where
211	<i>pT0_Rec</i> is <code>reconnectRange</code> times <i>pT0</i>,
212	the latter being the same energy-dependent dampening parameter as
213	used for multiparton interactions.
214	Thus it is easy to merge a low-<i>pT</i> system with any other,
215	but difficult to merge two high-<i>pT</i> ones with each other.
216
217
218	<p/>
219	The procedure is used iteratively. Thus first the reconnection probability
220	<i>P = pT0_Rec^2 / (pT0_Rec^2 + pT^2)</i> of the lowest-<i>pT</i>
221	system is found, and gives the probability for merger with the
222	second-lowest one. If not merged, it is tested with the third-lowest one,
223	and so on. For the <i>m</i>'th higher system the reconnection
224	probability thus becomes <i>(1 - P)^(m-1) P</i>. That is, there is
225	no explicit dependence on the higher <i>pT</i> scale, but implicitly
226	there is via the survival probability of not already having been merged
227	with a lower-<i>pT</i> system. Also note that the total reconnection
228	probability for the lowest-<i>pT</i> system in an event with <i>n</i>
229	systems becomes <i>1 - (1 - P)^(n-1)</i>. Once the fate of the
230	lowest-<i>pT</i> system has been decided, the second-lowest is considered
231	with respect to the ones above it, then the third-lowest, and so on.
232
233	<p/>
234	Once it has been decided which systems should be joined, the actual merging
235	is carried out in the opposite direction. That is, first the hardest
236	system is studied, and all colour dipoles in it are found (including to
237	the beam remnants, as defined by the holes of the incoming partons).
238	Next each softer system to be merged is studied in turn. Its gluons are,
239	in decreasing <i>pT</i> order, inserted on the colour dipole <i>i,j</i>
240	that gives the smallest <i>(p_g p_i)(p_g p_j)/(p_i p_j)</i>, i.e.
241	minimizes the "disturbance" on the existing dipole, in terms of
242	<i>pT^2</i> or <i>Lambda</i> measure (string length). The insertion
243	of the gluon means that the old dipole is replaced by two new ones.
244	Also the (rather few) quark-antiquark pairs that can be traced back to
245	a gluon splitting are treated in close analogy with the gluon case.
246	Quark lines that attach directly to the beam remnants cannot be merged
247	but are left behind.
248
249	<p/>
250	The joining procedure can be viewed as a more sophisticated variant of
251	the one introduced already in [<a href="Bibliography.php" target="page">Sjo87</a>]. Clearly it is ad hoc.
252	It hopefully captures some elements of truth. The lower <i>pT</i> scale
253	a system has the larger its spatial extent and therefore the larger its
254	overlap with other systems. It could be argued that one should classify
255	individual initial-state partons by <i>pT</i> rather than the system
256	as a whole. However, for final-state radiation, a soft gluon radiated off
257	a hard parton is actually produced at late times and therefore probably
258	less likely to reconnect. In the balance, a classification by system
259	<i>pT</i> scale appears sensible as a first try.
260
261	<p/>
262	Note that the reconnection is carried out before resonance decays are
263	considered. Colour inside a resonance therefore is not reconnected.
264	This is a deliberate choice, but certainly open to discussion and
265	extensions at a later stage, as is the rest of this procedure.
266
267	<h3>Further variables</h3>
268
269	<br/><br/><table><tr><td><strong>BeamRemnants:maxValQuark </td><td></td><td> <input type="text" name="10" value="3" size="20"/>   (<code>default = <strong>3</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)</td></tr></table>
270	The maximum valence quark kind allowed in acceptable incoming beams,
271	for which multiparton interactions are simulated. Default is that hadrons
272	may contain <i>u</i>, <i>d</i> and <i>s</i> quarks,
273	but not <i>c</i> and <i>b</i> ones, since sensible
274	kinematics has not really been worked out for the latter.
275
276
277	<br/><br/><table><tr><td><strong>BeamRemnants:companionPower </td><td></td><td> <input type="text" name="11" value="4" size="20"/>   (<code>default = <strong>4</strong></code>; <code>minimum = 0</code>; <code>maximum = 4</code>)</td></tr></table>
278	When a sea quark has been found, a companion antisea quark ought to be
279	nearby in <i>x</i>. The shape of this distribution can be derived
280	from the gluon mother distribution convoluted with the
281	<i>g -> q qbar</i> splitting kernel. In practice, simple solutions
282	are only feasible if the gluon shape is assumed to be of the form
283	<i>g(x) ~ (1 - x)^p / x</i>, where <i>p</i> is an integer power,
284	the parameter above. Allowed values correspond to the cases programmed.
285	<br/>
286	Since the whole framework is approximate anyway, this should be good
287	enough. Note that companions typically are found at small <i>Q^2</i>,
288	if at all, so the form is supposed to represent <i>g(x)</i> at small
289	<i>Q^2</i> scales, close to the lower cutoff for multiparton interactions.
290
291
292	<p/>
293	When assigning relative momentum fractions to beam-remnant partons,
294	valence quarks are chosen according to a distribution like
295	<i>(1 - x)^power / sqrt(x)</i>. This <i>power</i> is given below
296	for quarks in mesons, and separately for <i>u</i> and <i>d</i>
297	quarks in the proton, based on the approximate shape of low-<i>Q^2</i>
298	parton densities. The power for other baryons is derived from the
299	proton ones, by an appropriate mixing. The <i>x</i> of a diquark
300	is chosen as the sum of its two constituent <i>x</i> values, and can
301	thus be above unity. (A common rescaling of all remnant partons and
302	particles will fix that.) An additional enhancement of the diquark
303	momentum is obtained by its <i>x</i> value being rescaled by the
304	<code>valenceDiqEnhance</code> factor.
305
306	<br/><br/><table><tr><td><strong>BeamRemnants:valencePowerMeson </td><td></td><td> <input type="text" name="12" value="0.8" size="20"/>   (<code>default = <strong>0.8</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
307	The abovementioned power for valence quarks in mesons.
308
309
310	<br/><br/><table><tr><td><strong>BeamRemnants:valencePowerUinP </td><td></td><td> <input type="text" name="13" value="3.5" size="20"/>   (<code>default = <strong>3.5</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
311	The abovementioned power for valence <i>u</i> quarks in protons.
312
313
314	<br/><br/><table><tr><td><strong>BeamRemnants:valencePowerDinP </td><td></td><td> <input type="text" name="14" value="2.0" size="20"/>   (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
315	The abovementioned power for valence <i>d</i> quarks in protons.
316
317
318	<br/><br/><table><tr><td><strong>BeamRemnants:valenceDiqEnhance </td><td></td><td> <input type="text" name="15" value="2.0" size="20"/>   (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.5</code>; <code>maximum = 10.</code>)</td></tr></table>
319	Enhancement factor for valence diqaurks in baryons, relative to the
320	simple sum of the two constituent quarks.
321
322
323	<br/><br/><strong>BeamRemnants:allowJunction</strong> <input type="radio" name="16" value="on" checked="checked"><strong>On</strong>
324	<input type="radio" name="16" value="off"><strong>Off</strong>
325	(<code>default = <strong>on</strong></code>)<br/>
326	The <code>off</code> option is intended for debug purposes only, as
327	follows. When more than one valence quark is kicked out of a baryon
328	beam, as part of the multiparton interactions scenario, the subsequent
329	hadronization is described in terms of a junction string topology.
330	This description involves a number of technical complications that
331	may make the program more unstable. As an alternative, by switching
332	this option off, junction configurations are rejected (which gives
333	an error message that the remnant flavour setup failed), and the
334	multiparton interactions and showers are redone until a
335	junction-free topology is found.
336
337
338	<input type="hidden" name="saved" value="1"/>
339
340	<?php
341	echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?>
342
343	<table width="100%"><tr><td align="right"><input type="submit" value="Save Settings" /></td></tr></table>
344	</form>
345
346	<?php
347
348	if($_POST["saved"] == 1)
349	{
350	$filepath = $_POST["filepath"];
351	$handle = fopen($filepath, 'a');
352
353	if($_POST["1"] != "on")
354	{
355	$data = "BeamRemnants:primordialKT = ".$_POST["1"]."\n";
356	fwrite($handle,$data);
357	}
358	if($_POST["2"] != "0.5")
359	{
360	$data = "BeamRemnants:primordialKTsoft = ".$_POST["2"]."\n";
361	fwrite($handle,$data);
362	}
363	if($_POST["3"] != "2.0")
364	{
365	$data = "BeamRemnants:primordialKThard = ".$_POST["3"]."\n";
366	fwrite($handle,$data);
367	}
368	if($_POST["4"] != "1.")
369	{
370	$data = "BeamRemnants:halfScaleForKT = ".$_POST["4"]."\n";
371	fwrite($handle,$data);
372	}
373	if($_POST["5"] != "1.")
374	{
375	$data = "BeamRemnants:halfMassForKT = ".$_POST["5"]."\n";
376	fwrite($handle,$data);
377	}
378	if($_POST["6"] != "0.4")
379	{
380	$data = "BeamRemnants:primordialKTremnant = ".$_POST["6"]."\n";
381	fwrite($handle,$data);
382	}
383	if($_POST["7"] != "off")
384	{
385	$data = "BeamRemnants:rescatterRestoreY = ".$_POST["7"]."\n";
386	fwrite($handle,$data);
387	}
388	if($_POST["8"] != "on")
389	{
390	$data = "BeamRemnants:reconnectColours = ".$_POST["8"]."\n";
391	fwrite($handle,$data);
392	}
393	if($_POST["9"] != "10.0")
394	{
395	$data = "BeamRemnants:reconnectRange = ".$_POST["9"]."\n";
396	fwrite($handle,$data);
397	}
398	if($_POST["10"] != "3")
399	{
400	$data = "BeamRemnants:maxValQuark = ".$_POST["10"]."\n";
401	fwrite($handle,$data);
402	}
403	if($_POST["11"] != "4")
404	{
405	$data = "BeamRemnants:companionPower = ".$_POST["11"]."\n";
406	fwrite($handle,$data);
407	}
408	if($_POST["12"] != "0.8")
409	{
410	$data = "BeamRemnants:valencePowerMeson = ".$_POST["12"]."\n";
411	fwrite($handle,$data);
412	}
413	if($_POST["13"] != "3.5")
414	{
415	$data = "BeamRemnants:valencePowerUinP = ".$_POST["13"]."\n";
416	fwrite($handle,$data);
417	}
418	if($_POST["14"] != "2.0")
419	{
420	$data = "BeamRemnants:valencePowerDinP = ".$_POST["14"]."\n";
421	fwrite($handle,$data);
422	}
423	if($_POST["15"] != "2.0")
424	{
425	$data = "BeamRemnants:valenceDiqEnhance = ".$_POST["15"]."\n";
426	fwrite($handle,$data);
427	}
428	if($_POST["16"] != "on")
429	{
430	$data = "BeamRemnants:allowJunction = ".$_POST["16"]."\n";
431	fwrite($handle,$data);
432	}
433	fclose($handle);
434	}
435
436	?>
437	</body>
438	</html>
439
440	<!-- Copyright (C) 2012 Torbjorn Sjostrand -->

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