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30<h2>Event Analysis</h2>
31
32<h3>Introduction</h3>
33
34The routines in this section are intended to be used to analyze
35event properties. As such they are not part of the main event
36generation chain, but can be used in comparisons between Monte
37Carlo events and real data. They are rather free-standing, but
38assume that input is provided in the PYTHIA 8
39<code>Event</code> format, and use a few basic facilities such
40as four-vectors. Their ordering is mainly by history; for current
41LHC applications the final one, <code>SlowJet</code>, is of
42special interest.
43
44<p/>
45In addition to the methods presented here, there is also the
46possibility to make use of <?php $filepath = $_GET["filepath"];
47echo "<a href='JetFinders.php?filepath=".$filepath."' target='page'>";?>external
48jet finders </a>.
49
50<h3>Sphericity</h3>
51
52The standard sphericity tensor is
53<br/><i>
54    S^{ab} = (sum_i p_i^a p_i^b) / (sum_i p_i^2)
55</i><br/>
56where the <i>sum i</i> runs over the particles in the event,
57<i>a, b = x, y, z,</i> and <i>p</i> without such an index is
58the absolute size of the three-momentum . This tensor can be
59diagonalized to find eigenvalues and eigenvectors.
60
61<p/>
62The above tensor can be generalized by introducing a power
63<i>r</i>, such that
64<br/><i>
65    S^{ab} = (sum_i p_i^a p_i^b p_i^{r-2}) / (sum_i p_i^r)
66</i><br/>
67In particular, <i>r = 1</i> gives a linear dependence on momenta
68and thus a collinear safe definition, unlike sphericity.
69
70<p/> 
71To do sphericity analyses you have to set up a <code>Sphericity</code>
72instance, and then feed in events to it, one at a time. The results
73for the latest event are available as output from a few methods.
74
75<a name="method1"></a>
76<p/><strong>Sphericity::Sphericity(double power = 2., int select = 2) &nbsp;</strong> <br/>
77create a sphericity analysis object, where
78<br/><code>argument</code><strong> power </strong> (<code>default = <strong>2.</strong></code>) : 
79is the power <i>r</i> defined above, i.e.
80<br/><code>argumentoption </code><strong> 2.</strong> : gives Spericity, and   
81<br/><code>argumentoption </code><strong> 1.</strong> : gives the linear form. 
82 
83<br/><code>argument</code><strong> select </strong> (<code>default = <strong>2</strong></code>) : 
84tells which particles are analyzed,
85<br/><code>argumentoption </code><strong> 1</strong> : all final-state particles, 
86<br/><code>argumentoption </code><strong> 2</strong> : all observable final-state particles,
87i.e. excluding neutrinos and other particles without strong or
88electromagnetic interactions (the <code>isVisible()</code>
89particle method), and
90 
91<br/><code>argumentoption </code><strong> 3</strong> : only charged final-state particles. 
92 
93 
94
95<a name="method2"></a>
96<p/><strong>bool Sphericity::analyze( const Event& event, ostream& os = cout) &nbsp;</strong> <br/>
97perform a sphericity analysis, where
98<br/><code>argument</code><strong> event </strong>  : is an object of the <code>Event</code> class,
99most likely the <code>pythia.event</code> one.
100 
101<br/><code>argument</code><strong> os </strong> (<code>default = <strong>cout</strong></code>) :  is the output stream for
102error messages. (The method does not rely on the <code>Info</code>
103mchinery for error messages.)
104 
105<br/>If the routine returns <code>false</code> the
106analysis failed, e.g. if too few particles are present to analyze.
107 
108
109<p/>
110After the analysis has been performed, a few methods are available
111to return the result of the analysis of the latest event:
112
113<a name="method3"></a>
114<p/><strong>double Sphericity::sphericity() &nbsp;</strong> <br/>
115gives the sphericity (or equivalent if <i>r</i> is not 2),
116 
117
118<a name="method4"></a>
119<p/><strong>double Sphericity::aplanarity() &nbsp;</strong> <br/>
120gives the aplanarity (with the same comment),
121 
122
123<a name="method5"></a>
124<p/><strong>double Sphericity::eigenValue(int i) &nbsp;</strong> <br/>
125gives one of the three eigenvalues for <i>i</i> = 1, 2 or 3, in
126descending order,
127 
128
129<a name="method6"></a>
130<p/><strong>Vec4 Sphericity::eventAxis(i) &nbsp;</strong> <br/>
131gives the matching normalized eigenvector, as a <code>Vec4</code>
132with vanishing time/energy component.
133 
134
135<a name="method7"></a>
136<p/><strong>void Sphericity::list(ostream& os = cout) &nbsp;</strong> <br/>
137provides a listing of the above information.
138 
139
140<p/>
141There is also one method that returns information accumulated for all
142the events analyzed so far.
143
144<a name="method8"></a>
145<p/><strong>int Sphericity::nError() &nbsp;</strong> <br/>
146tells the number of times <code>analyze(...)</code> failed to analyze
147events, i.e. returned <code>false</code>.
148 
149
150<h3>Thrust</h3>
151
152Thrust is obtained by varying the thrust axis so that the longitudinal
153momentum component projected onto it is maximized, and thrust itself is
154then defined as the sum of absolute longitudinal momenta divided by
155the sum of absolute momenta. The major axis is found correspondingly
156in the plane transverse to thrust, and the minor one is then defined
157to be transverse to both. Oblateness is the difference between the major
158and the minor values.
159
160<p/>
161The calculation of thrust is more computer-time-intensive than e.g.
162linear sphericity, introduced above, and has no specific advantages except
163historical precedent. In the PYTHIA 6 implementation the search was
164speeded up at the price of then not being guaranteed to hit the absolute
165maximum. The current implementation studies all possibilities, but at
166the price of being slower, with time consumption for an event with
167<i>n</i> particles growing like <i>n^3</i>.
168
169<p/> 
170To do thrust analyses you have to set up a <code>Thrust</code>
171instance, and then feed in events to it, one at a time. The results
172for the latest event are available as output from a few methods.
173
174<a name="method9"></a>
175<p/><strong>Thrust::Thrust(int select = 2) &nbsp;</strong> <br/>
176create a thrust analysis object, where
177<br/><code>argument</code><strong> select </strong> (<code>default = <strong>2</strong></code>) : 
178tells which particles are analyzed,
179<br/><code>argumentoption </code><strong> 1</strong> : all final-state particles, 
180<br/><code>argumentoption </code><strong> 2</strong> : all observable final-state particles,
181i.e. excluding neutrinos and other particles without strong or
182electromagnetic interactions (the <code>isVisible()</code>
183particle method), and
184 
185<br/><code>argumentoption </code><strong> 3</strong> : only charged final-state particles. 
186 
187 
188
189<a name="method10"></a>
190<p/><strong>bool Thrust::analyze( const Event& event, ostream& os = cout) &nbsp;</strong> <br/>
191perform a thrust analysis, where
192<br/><code>argument</code><strong> event </strong>  : is an object of the <code>Event</code> class,
193most likely the <code>pythia.event</code> one.
194 
195<br/><code>argument</code><strong> os </strong> (<code>default = <strong>cout</strong></code>) :  is the output stream for
196error messages. (The method does not rely on the <code>Info</code>
197mchinery for error messages.)
198 
199<br/>If the routine returns <code>false</code> the
200analysis failed, e.g. if too few particles are present to analyze.
201 
202
203<p/>
204After the analysis has been performed, a few methods are available
205to return the result of the analysis of the latest event:
206
207<a name="method11"></a>
208<p/><strong>double Thrust::thrust() &nbsp;</strong> <br/>
209 
210<strong>double Thrust::tMajor() &nbsp;</strong> <br/>
211 
212<strong>double Thrust::tMinor() &nbsp;</strong> <br/>
213 
214<strong>double Thrust::oblateness() &nbsp;</strong> <br/>
215gives the thrust, major, minor and oblateness values, respectively,
216 
217
218<a name="method12"></a>
219<p/><strong>Vec4 Thrust::eventAxis(int i) &nbsp;</strong> <br/>
220gives the matching normalized event-axis vectors, for <i>i</i> = 1, 2 or 3
221corresponding to thrust, major or minor, as a <code>Vec4</code> with
222vanishing time/energy component.
223 
224
225<a name="method13"></a>
226<p/><strong>void Thrust::list(ostream& os = cout) &nbsp;</strong> <br/>
227provides a listing of the above information.
228 
229
230<p/>
231There is also one method that returns information accumulated for all
232the events analyzed so far.
233
234<a name="method14"></a>
235<p/><strong>int Thrust::nError() &nbsp;</strong> <br/>
236tells the number of times <code>analyze(...)</code> failed to analyze
237events, i.e. returned <code>false</code>.
238 
239
240<h3>ClusterJet</h3>
241
242<code>ClusterJet</code> (a.k.a. <code>LUCLUS</code> and
243<code>PYCLUS</code>) is a clustering algorithm of the type used for
244analyses of <i>e^+e^-</i> events, see the PYTHIA 6 manual. All
245visible particles in the events are clustered into jets. A few options
246are available for some well-known distance measures. Cutoff
247distances can either be given in terms of a scaled quadratic quantity
248like <i>y = pT^2/E^2</i> or an unscaled linear one like <i>pT</i>.
249
250<p/> 
251Note that we have deliberately chosen not to include the <i>e^+e^-</i>
252equivalents of the Cambridge/Aachen and anti-<i>kRT</i> algorithms.
253These tend to be good at clustering the densely populated (in angle)
254cores of jets, but less successful for the sparsely populated transverse
255regions, where many jets may come to consist of a single low-momentum
256particle. In hadron collisions such jets could easily be disregarded,
257while in <i>e^+e^-</i> annihilation all particles derive back from the
258hard process.
259
260<p/> 
261To do jet finding analyses you have to set up a <code>ClusterJet</code>
262instance, and then feed in events to it, one at a time. The results
263for the latest event are available as output from a few methods.
264
265<a name="method15"></a>
266<p/><strong>ClusterJet::ClusterJet(string measure = &quot;Lund&quot;, int select = 2, int massSet = 2, bool precluster = false, bool reassign = false) &nbsp;</strong> <br/>
267create a <code>ClusterJet</code> instance, where
268<br/><code>argument</code><strong> measure </strong> (<code>default = <strong>&quot;Lund&quot;</strong></code>) : distance measure,
269to be provided as a character string (actually, only the first character
270is necessary)
271<br/><code>argumentoption </code><strong> &quot;Lund&quot;</strong> : the Lund <i>pT</i> distance,
272 
273<br/><code>argumentoption </code><strong> &quot;JADE&quot;</strong> : the JADE mass distance, and
274 
275<br/><code>argumentoption </code><strong> &quot;Durham&quot;</strong> : the Durham <i>kT</i> measure.
276 
277 
278<br/><code>argument</code><strong> select </strong> (<code>default = <strong>2</strong></code>) : 
279tells which particles are analyzed,
280<br/><code>argumentoption </code><strong> 1</strong> : all final-state particles, 
281<br/><code>argumentoption </code><strong> 2</strong> : all observable final-state particles,
282i.e. excluding neutrinos and other particles without strong or
283electromagnetic interactions (the <code>isVisible()</code> particle
284method), and
285 
286<br/><code>argumentoption </code><strong> 3</strong> : only charged final-state particles. 
287 
288<br/><code>argument</code><strong> massSet </strong> (<code>default = <strong>2</strong></code>) : masses assumed for the particles
289used in the analysis
290<br/><code>argumentoption </code><strong> 0</strong> : all massless, 
291<br/><code>argumentoption </code><strong> 1</strong> : photons are massless while all others are
292assigned the <i>pi+-</i> mass, and
293 
294<br/><code>argumentoption </code><strong> 2</strong> : all given their correct masses. 
295 
296<br/><code>argument</code><strong> precluster </strong> (<code>default = <strong>false</strong></code>) :
297perform or not a early preclustering step, where nearby particles
298are lumped together so as to speed up the subsequent normal clustering.
299 
300<br/><code>argument</code><strong> reassign </strong> (<code>default = <strong>false</strong></code>) : 
301reassign all particles to the nearest jet each time after two jets
302have been joined.
303 
304 
305
306<a name="method16"></a>
307<p/><strong>ClusterJet::analyze( const Event& event, double yScale, double pTscale, int nJetMin = 1, int nJetMax = 0, ostream& os = cout) &nbsp;</strong> <br/>
308performs a jet finding analysis, where
309<br/><code>argument</code><strong> event </strong>  : is an object of the <code>Event</code> class,
310most likely the <code>pythia.event</code> one.
311 
312<br/><code>argument</code><strong> yScale </strong>  : 
313is the cutoff joining scale, below which jets are joined. Is given
314in quadratic dimensionless quantities. Either <code>yScale</code>
315or <code>pTscale</code> must be set nonvanishing, and the larger of
316the two dictates the actual value.
317 
318<br/><code>argument</code><strong> pTscale </strong>  : 
319is the cutoff joining scale, below which jets are joined. Is given
320in linear quantities, such as <i>pT</i> or <i>m</i> depending on
321the measure used, but always in units of GeV. Either <code>yScale</code>
322or <code>pTscale</code> must be set nonvanishing, and the larger of
323the two dictates the actual value.
324 
325<br/><code>argument</code><strong> nJetMin </strong> (<code>default = <strong>1</strong></code>) : 
326the minimum number of jets to be reconstructed. If used, it can override
327the <code>yScale</code> and <code>pTscale</code> values.
328 
329<br/><code>argument</code><strong> nJetMax </strong> (<code>default = <strong>0</strong></code>) : 
330the maximum number of jets to be reconstructed. Is not used if below
331<code>nJetMin</code>. If used, it can override the <code>yScale</code>
332and <code>pTscale</code> values. Thus e.g.
333<code>nJetMin = nJetMax = 3</code> can be used to reconstruct exactly
3343 jets.
335 
336<br/><code>argument</code><strong> os </strong> (<code>default = <strong>cout</strong></code>) :  is the output stream for
337error messages. (The method does not rely on the <code>Info</code>
338mchinery for error messages.)
339 
340<br/>If the routine returns <code>false</code> the analysis failed,
341e.g. because the number of particles was smaller than the minimum number
342of jets requested.
343 
344
345<p/>
346After the analysis has been performed, a few <code>ClusterJet</code>
347class methods are available to return the result of the analysis:
348
349<a name="method17"></a>
350<p/><strong>int ClusterJet::size() &nbsp;</strong> <br/>
351gives the number of jets found, with jets numbered 0 through
352<code>size() - 1</code>.
353 
354
355<a name="method18"></a>
356<p/><strong>Vec4 ClusterJet::p(int i) &nbsp;</strong> <br/>
357gives a <code>Vec4</code> corresponding to the four-momentum defined by
358the sum of all the contributing particles to the <i>i</i>'th jet.
359 
360
361<a name="method19"></a>
362<p/><strong>int ClusterJet::mult(int i) &nbsp;</strong> <br/>
363the number of particles that have been clustered into the <i>i</i>'th jet.
364 
365
366<a name="method20"></a>
367<p/><strong>int ClusterJet::jetAssignment(int i) &nbsp;</strong> <br/>
368gives the index of the jet that the particle <i>i</i> of the event
369record belongs to,
370 
371
372<a name="method21"></a>
373<p/><strong>void ClusterJet::list(ostream& os = cout) &nbsp;</strong> <br/>
374provides a listing of the reconstructed jets.
375 
376
377<a name="method22"></a>
378<p/><strong>int ClusterJet::distanceSize() &nbsp;</strong> <br/>
379the number of most recent clustering scales that have been stored
380for readout with the next method. Normally this would be five,
381but less if fewer clustering steps occured.
382 
383
384<a name="method23"></a>
385<p/><strong>double ClusterJet::distance(int i) &nbsp;</strong> <br/>
386clustering scales, with <code>distance(0)</code> being the most
387recent one, i.e. normally the highest, up to <code>distance(4)</code>
388being the fifth most recent. That is, with <i>n</i> being the final
389number of jets, <code>ClusterJet::size()</code>, the scales at which
390<i>n+1</i> jets become <i>n</i>, <i>n+2</i> become <i>n+1</i>,
391and so on till <i>n+5</i> become <i>n+4</i>. Nonexisting clustering
392scales are returned as zero. The physical interpretation of a scale is
393as provided by the respective distance measure (Lund, JADE, Durham).
394 
395
396<p/>
397There is also one method that returns information accumulated for all
398the events analyzed so far.
399
400<a name="method24"></a>
401<p/><strong>int ClusterJet::nError() &nbsp;</strong> <br/>
402tells the number of times <code>analyze(...)</code> failed to analyze
403events, i.e. returned <code>false</code>.
404 
405
406<h3>CellJet</h3>
407
408<code>CellJet</code> (a.k.a. <code>PYCELL</code>) is a simple cone jet
409finder in the UA1 spirit, see the PYTHIA 6 manual. It works in an
410<i>(eta, phi, eT)</i> space, where <i>eta</i> is pseudorapidity,
411<i>phi</i> azimuthal angle and <i>eT</i> transverse energy.
412It will draw cones in <i>R = sqrt(Delta-eta^2 + Delta-phi^2)</i>
413around seed cells. If the total <i>eT</i> inside the cone exceeds
414the threshold, a jet is formed, and the cells are removed from further
415analysis. There are no split or merge procedures, so later-found jets
416may be missing some of the edge regions already used up by previous
417ones. Not all particles in the event are assigned to jets; leftovers
418may be viewed as belonging to beam remnants or the underlying event.
419It is not used by any experimental collaboration, but is closely
420related to the more recent and better theoretically motivated
421anti-<i>kT</i> algorithm [<a href="Bibliography.php" target="page">Cac08</a>].   
422
423<p/> 
424To do jet finding analyses you have to set up a <code>CellJet</code>
425instance, and then feed in events to it, one at a time. Especially note
426that, if you want to use the options where energies are smeared in
427order so emulate detector imperfections, you must hand in an external
428random number generator, preferably the one residing in the
429<code>Pythia</code> class. The results for the latest event are
430available as output from a few methods.
431
432<a name="method25"></a>
433<p/><strong>CellJet::CellJet(double etaMax = 5., int nEta = 50, int nPhi = 32, int select = 2, int smear = 0, double resolution = 0.5, double upperCut = 2., double threshold = 0., Rndm* rndmPtr = 0) &nbsp;</strong> <br/>
434create a <code>CellJet</code> instance, where
435<br/><code>argument</code><strong> etaMax </strong> (<code>default = <strong>5.</strong></code>) : 
436the maximum +-pseudorapidity that the detector is assumed to cover.
437 
438<br/><code>argument</code><strong> nEta </strong> (<code>default = <strong>50</strong></code>) : 
439the number of equal-sized bins that the <i>+-etaMax</i> range
440is assumed to be divided into.
441 
442<br/><code>argument</code><strong> nPhi </strong> (<code>default = <strong>32</strong></code>) : 
443the number of equal-sized bins that the <i>phi</i> range
444<i>+-pi</i> is assumed to be divided into.
445 
446<br/><code>argument</code><strong> select </strong> (<code>default = <strong>2</strong></code>) : 
447tells which particles are analyzed,
448<br/><code>argumentoption </code><strong> 1</strong> : all final-state particles, 
449<br/><code>argumentoption </code><strong> 2</strong> : all observable final-state particles,
450i.e. excluding neutrinos and other particles without strong or
451electromagnetic interactions (the <code>isVisible()</code> particle
452method),
453and 
454<br/><code>argumentoption </code><strong> 3</strong> : only charged final-state particles. 
455 
456<br/><code>argument</code><strong> smear </strong> (<code>default = <strong>0</strong></code>) :
457strategy to smear the actual <i>eT</i> bin by bin,
458<br/><code>argumentoption </code><strong> 0</strong> : no smearing, 
459<br/><code>argumentoption </code><strong> 1</strong> : smear the <i>eT</i> according to a Gaussian
460with width <i>resolution * sqrt(eT)</i>, with the Gaussian truncated
461at 0 and <i>upperCut * eT</i>, 
462<br/><code>argumentoption </code><strong> 2</strong> : smear the <i>e = eT * cosh(eta)</i> according
463to a Gaussian with width <i>resolution * sqrt(e)</i>, with the
464Gaussian truncated at 0 and <i>upperCut * e</i>. 
465 
466<br/><code>argument</code><strong> resolution </strong> (<code>default = <strong>0.5</strong></code>) :
467see above.
468 
469<br/><code>argument</code><strong> upperCut </strong> (<code>default = <strong>2.</strong></code>) :
470see above.
471 
472<br/><code>argument</code><strong> threshold </strong> (<code>default = <strong>0 GeV</strong></code>) :
473completely neglect all bins with an <i>eT &lt; threshold</i>.
474 
475<br/><code>argument</code><strong> rndmPtr </strong> (<code>default = <strong>0</strong></code>) :
476the random-number generator used to select the smearing described
477above. Must be handed in for smearing to be possible. If your
478<code>Pythia</code> class instance is named <code>pythia</code>,
479then <code>&pythia.rndm</code> would be the logical choice.
480 
481 
482
483<a name="method26"></a>
484<p/><strong>bool CellJet::analyze( const Event& event, double eTjetMin = 20., double coneRadius = 0.7, double eTseed = 1.5, ostream& os = cout) &nbsp;</strong> <br/>
485performs a jet finding analysis, where
486<br/><code>argument</code><strong> event </strong>  : is an object of the <code>Event</code> class,
487most likely the <code>pythia.event</code> one.
488 
489<br/><code>argument</code><strong> eTjetMin </strong> (<code>default = <strong>20. GeV</strong></code>) : 
490is the minimum transverse energy inside a cone for this to be
491accepted as a jet.
492 
493<br/><code>argument</code><strong> coneRadius </strong> (<code>default = <strong>0.7</strong></code>) : 
494 is the size of the cone in <i>(eta, phi)</i> space drawn around
495the geometric center of the jet.
496 
497<br/><code>argument</code><strong> eTseed </strong> (<code>default = <strong>1.5 GeV</strong></code>) : 
498the mimimum <i>eT</i> in a cell for this to be acceptable as
499the trial center of a jet.
500 
501<br/><code>argument</code><strong> os </strong> (<code>default = <strong>cout</strong></code>) :  is the output stream for
502error messages. (The method does not rely on the <code>Info</code>
503mchinery for error messages.)
504 
505<br/>If the routine returns <code>false</code> the analysis failed,
506but currently this is not foreseen ever to happen.
507 
508
509<p/>
510After the analysis has been performed, a few <code>CellJet</code>
511class methods are available to return the result of the analysis:
512
513<a name="method27"></a>
514<p/><strong>int CellJet::size() &nbsp;</strong> <br/>
515gives the number of jets found, with jets numbered 0 through
516<code>size() - 1</code>,
517 
518
519<a name="method28"></a>
520<p/><strong>double CellJet::eT(i) &nbsp;</strong> <br/>
521gives the <i>eT</i> of the <i>i</i>'th jet, where jets have been
522ordered with decreasing <i>eT</i> values,
523 
524
525<a name="method29"></a>
526<p/><strong>double CellJet::etaCenter(int i) &nbsp;</strong> <br/>
527 
528<strong>double CellJet::phiCenter(int i) &nbsp;</strong> <br/>
529gives the <i>eta</i> and <i>phi</i> coordinates of the geometrical
530center of the <i>i</i>'th jet,
531 
532
533<a name="method30"></a>
534<p/><strong>double CellJet::etaWeighted(int i) &nbsp;</strong> <br/>
535 
536<strong>double CellJet::phiWeighted(int i) &nbsp;</strong> <br/>
537gives the <i>eta</i> and <i>phi</i> coordinates of the
538<i>eT</i>-weighted center of the <i>i</i>'th jet,
539 
540
541<a name="method31"></a>
542<p/><strong>int CellJet::multiplicity(int i) &nbsp;</strong> <br/>
543gives the number of particles clustered into the <i>i</i>'th jet,
544 
545
546<a name="method32"></a>
547<p/><strong>Vec4 CellJet::pMassless(int i) &nbsp;</strong> <br/>
548gives a <code>Vec4</code> corresponding to the four-momentum defined
549by the <i>eT</i> and the weighted center of the <i>i</i>'th jet,
550 
551
552<a name="method33"></a>
553<p/><strong>Vec4 CellJet::pMassive(int i) &nbsp;</strong> <br/>
554gives a <code>Vec4</code> corresponding to the four-momentum defined by
555the sum of all the contributing cells to the <i>i</i>'th jet, where
556each cell contributes a four-momentum as if all the <i>eT</i> is
557deposited in the center of the cell,
558 
559
560<a name="method34"></a>
561<p/><strong>double CellJet::m(int i) &nbsp;</strong> <br/>
562gives the invariant mass of the <i>i</i>'th jet, defined by the
563<code>pMassive</code> above,
564 
565
566<a name="method35"></a>
567<p/><strong>void CellJet::list() &nbsp;</strong> <br/>
568provides a listing of the above information (except <code>pMassless</code>,
569for reasons of space).
570 
571
572<p/>
573There is also one method that returns information accumulated for all
574the events analyzed so far.
575<a name="method36"></a>
576<p/><strong>int CellJet::nError() &nbsp;</strong> <br/>
577tells the number of times <code>analyze(...)</code> failed to analyze
578events, i.e. returned <code>false</code>.
579 
580
581<h3>SlowJet</h3>
582
583<code>SlowJet</code> is a simple program for doing jet finding according
584to either of the <i>kT</i>, anti-<i>kT</i>, and Cambridge/Aachen
585algorithms, in a cylindrical coordinate frame. The name is obviously
586an homage to the <code>FastJet</code> program [<a href="Bibliography.php" target="page">Cac06</a>].
587That package contains many more algorithms, with many more options,
588and, above all, is <i>much</i> faster. Therefore <code>SlowJet</code>
589is not so much intended for massive processing of data or Monte Carlo
590files as for simple first tests. Nevertheless, within the advertised
591capabilities of <code>SlowJet</code>, it has been checked to find
592identically the same jets as <code>FastJet</code>. The time consumption
593typically is around or below that to generate an LHC <i>pp</i> event
594in the first place, so is not prohibitive. But the time rises rapidly
595for large multiplicities, so obviously <code>SlowJet</code> can not
596be used for tricks like distributing a dense grid of pseudoparticles
597to be able to define jet areas, like <code>FastJet</code> can, and also
598not for events with much pileup or other noise.
599
600<p/> 
601The first step is to decide which particles should be included in the
602analysis, and with what four-momenta. The <code>SlowJet</code> constructor
603allows to pick a maximum pseudorapidity defined by the extent of the
604assumed detector, to pick among some standard options of which particles
605to analyze, and to allow for some standard mass assumptions, like that
606all charged particles have the pion mass. Obviously this is only a
607restricted set of possibilities.
608
609<p/> 
610Full flexibility can be obtained by deriving from the base class
611<code>SlowJetHook</code> to write your own <code>include</code> method.
612This will be presented with one final-state particle at a time, and
613should return <code>true</code> for those particles that should be
614analyzed. It is also possible to return modified four-momenta and masses,
615to take into account detector smearing effects or particle identity
616misassignments, but you must respect <i>E^2 - p^2 = m^2</i>.
617
618<p/> 
619Alternatively you can modify the event record itself, or a copy of it
620(if you want to keep the original intact). For instance, only final
621particles are considered in the analysis, i.e. particles with positive
622status code, so negative status code should then be assigned to those
623particles that you do not want to see analyzed. Again four-momenta and
624masses can be modified, subject to <i>E^2 - p^2 = m^2</i>.
625
626<p/> 
627The jet reconstructions is then based on sequential recombination with
628progressive removal, using the <i>E</i> recombination scheme. To be
629more specific, the algorithm works as follows.
630<ol>
631<li>Each particle to be analyzed defines an original cluster. It has a
632well-defined four-momentum and mass at input. From this information the
633triplet <i>(pT, y, phi)</i> is calculated, i.e. the transverse momentum,
634rapidity and azimuthal angle of the cluster.</li>
635<li>Define distance measures of all clusters <i>i</i> to the beam
636<br/><i>d_iB = pT_i^2p</i><br/>
637and of all pairs <i>(i,j)</i> relative to each other
638<br/><i>d_ij = min( pT_i^2p, pT_j^2p) DeltaR_ij^2 / R^2 </i><br/>
639where
640<br/><i>DeltaR_ij^2 = (y_i - y_j)^2 + (phi_i - phi_j)^2.</i><br/>  
641The jet algorithm is determined by the user-selected <i>p</i> value,
642where <i>p = -1</i> corresponds to the anti-<i>kT</i> one,
643<i>p = 0</i> to the Cambridge/Aachen one and <i>p = 1</i> to the
644<i>kT</i> one. Also <i>R</i> is chosen by the user, to give an
645approximate measure of the size of jets. However, note that jets need
646not have a circular shape in <i>(y, phi)</i> space, so <i>R</i>
647can not straight off be interpreted as a jet radius.</li>
648<li>Find the smallest of all <i>d_iB</i> and <i>d_ij</i>.</li>
649<li>If this is a <i>d_iB</i> then cluster <i>i</i> is removed from
650the clusters list and instead added to the jets list.
651Optionally, a <i>pTjetMin</i> requirement is imposed, where only
652clusters with <i>pT > pTjetMin</i> are added to the jets list.
653If so, some of the analyzed particles will not be part of any final
654jet.</li>
655<li>If instead te smallest measure is a <i>d_ij</i> then the
656four-momenta of the <i>i</i> and <i>j</i> clusters are added
657to define a single new cluster. Convert this four-momentum to a new
658<i>(pT, y, phi)</i> triplet and update the list of <i>d_iB</i>
659and <i>d_ij</i>.</li>
660<li>Return to step 3 until no clusters remain.</li>
661</ol>
662
663<p/> 
664To do jet finding analyses you first have to set up a <code>SlowJet</code>
665instance, where the arguments of the constructor specifies the details
666of the subsequent analyses. Thereafter you can feed in events to it,
667one at a time, and have them analyzed by the <code>analyze</code> method.
668Information on the resulting jets can be extracted by a few different methods.
669The minimal procedure only requires one call per event to do the analysis.
670We will begin by presenting it, and only afterwards some extensions.
671
672<a name="method37"></a>
673<p/><strong>SlowJet::SlowJet(double power, double R, double pTjetMin = 0.,double etaMax = 25., int select = 2, int massSet = 2, SlowJetHook* sjHookPtr = 0) &nbsp;</strong> <br/>
674create a <code>SlowJet</code> instance, where
675<br/><code>argument</code><strong> power </strong>  : 
676tells (half) the power of the transverse-momentum dependence of the
677distance measure,
678<br/><code>argumentoption </code><strong> -1</strong> : the anti-<i>kT</i> algorithm, 
679<br/><code>argumentoption </code><strong> 0</strong> : the Cambridge/Aachen algorithm, and 
680<br/><code>argumentoption </code><strong> 1</strong> : the <i>kT</i> algorithm. 
681 
682<br/><code>argument</code><strong> R </strong>  : 
683the <i>R</i> size parameter, which is crudely related to the radius of
684the jet cone in <i>(y, phi)</i> space around the center of the jet.
685 
686<br/><code>argument</code><strong> pTjetMin </strong> (<code>default = <strong>0.0 GeV</strong></code>) :
687the minimum transverse momentum required for a cluster
688to become a jet. By default all clusters become jets, and therefore
689all analyzed particles are assigned to a jet.
690For comparisons with perturbative QCD, however, it is only meaningful
691to consider jets with a significant <i>pT</i>.
692 
693<br/><code>argument</code><strong> etaMax </strong> (<code>default = <strong>25.</strong></code>) : 
694the maximum +-pseudorapidity that the detector is assumed to cover.
695If you pick a value above 20 there is assumed to be full coverage
696(obviously only meaningful for theoretical studies).
697 
698<br/><code>argument</code><strong> select </strong> (<code>default = <strong>2</strong></code>) : 
699tells which particles are analyzed,
700<br/><code>argumentoption </code><strong> 1</strong> : all final-state particles, 
701<br/><code>argumentoption </code><strong> 2</strong> : all observable final-state particles,
702i.e. excluding neutrinos and other particles without strong or
703electromagnetic interactions (the <code>isVisible()</code> particle
704method),
705and 
706<br/><code>argumentoption </code><strong> 3</strong> : only charged final-state particles. 
707 
708<br/><code>argument</code><strong> massSet </strong> (<code>default = <strong>2</strong></code>) : masses assumed for the particles
709used in the analysis
710<br/><code>argumentoption </code><strong> 0</strong> : all massless, 
711<br/><code>argumentoption </code><strong> 1</strong> : photons are massless while all others are
712assigned the <i>pi+-</i> mass, and
713 
714<br/><code>argumentoption </code><strong> 2</strong> : all given their correct masses. 
715 
716<br/><code>argument</code><strong> sjHookPtr </strong> (<code>default = <strong>0</strong></code>) : 
717gives the possibility to send in your own selection routine for which
718particles should be part of the analysis; see further below on the
719<code>SlowJetHook</code> class. If this pointer is sent in nonzero,
720<code>etaMax</code> and <code>massSet</code> are disregarded,
721and <code>select</code> only gives the basic selection, to which
722the user can add further requirements.
723 
724 
725
726<a name="method38"></a>
727<p/><strong>bool SlowJet::analyze( const Event& event) &nbsp;</strong> <br/>
728performs a jet finding analysis, where
729<br/><code>argument</code><strong> event </strong>  : is an object of the <code>Event</code> class,
730most likely the <code>pythia.event</code> one.
731 
732<br/>If the routine returns <code>false</code> the analysis failed,
733but currently this is not foreseen ever to happen.
734 
735
736<p/>
737After the analysis has been performed, a few <code>SlowJet</code>
738class methods are available to return the result of the analysis:
739
740<a name="method39"></a>
741<p/><strong>int SlowJet::sizeOrig() &nbsp;</strong> <br/>
742gives the original number of particles (and thus clusters) that the
743analysis starts with.
744 
745
746<a name="method40"></a>
747<p/><strong>int SlowJet::sizeJet() &nbsp;</strong> <br/>
748gives the number of jets found, with jets numbered 0 through
749<code>sizeJet() - 1</code>, and ordered in terms of decreasing
750transverse momentum values w.r.t. the beam axis,
751 
752
753<a name="method41"></a>
754<p/><strong>double SlowJet::pT(i) &nbsp;</strong> <br/>
755gives the transverse momentum <i>pT</i> of the <i>i</i>'th jet,
756 
757
758<a name="method42"></a>
759<p/><strong>double SlowJet::y(int i) &nbsp;</strong> <br/>
760 
761<strong>double SlowJet::phi(int i) &nbsp;</strong> <br/>
762gives the rapidity <i>y</i> and azimuthal angle <i>phi</i>
763of the center of the <i>i</i>'th jet (defined by the vector sum
764of constituent four-momenta),
765 
766
767<a name="method43"></a>
768<p/><strong>Vec4 SlowJet::p(int i) &nbsp;</strong> <br/>
769 
770<strong>double SlowJet::m(int i) &nbsp;</strong> <br/>
771gives a <code>Vec4</code> corresponding to the four-momentum
772sum of the particles assigned to the <i>i</i>'th jet, and
773the invariant mass of this four-vector,
774 
775
776<a name="method44"></a>
777<p/><strong>int SlowJet::multiplicity(int i) &nbsp;</strong> <br/>
778gives the number of particles clustered into the <i>i</i>'th jet,
779 
780
781<a name="method45"></a>
782<p/><strong>int SlowJet::jetAssignment(int i) &nbsp;</strong> <br/>
783gives the index of the jet that the particle <i>i</i> of the event
784record belongs to, or -1 if there is no jet containing particle
785<i>i</i>,
786 
787
788<a name="method46"></a>
789<p/><strong>void SlowJet::removeJet(int i) &nbsp;</strong> <br/>
790removes the <i>i</i>'th jet,
791 
792
793<a name="method47"></a>
794<p/><strong>void SlowJet::list() &nbsp;</strong> <br/>
795provides a listing of the above information.
796 
797
798<p/> 
799These are the basic methods. For more sophisticated usage
800it is possible to trace the clustering, one step at a time. If so, the
801<code>setup</code> method should be used to read in the event and find
802the initial smallest distance. Each subsequent <code>doStep</code>
803will then do one cluster joining and find the new smallest distance.
804You can therefore interrogate which clusters will be joined next
805before the joining actually is performed. Alternatively you can take
806several steps in one go, or take steps down to a predetermined number
807of jets plus remaining clusters.
808
809<a name="method48"></a>
810<p/><strong>bool SlowJet::setup( const Event& event) &nbsp;</strong> <br/>
811selects the particles to be analyzed, calculates initial distances,
812and finds the initial smallest distance.
813<br/><code>argument</code><strong> event </strong>  : is an object of the <code>Event</code> class,
814most likely the <code>pythia.event</code> one.
815 
816<br/>If the routine returns <code>false</code> the setup failed,
817but currently this is not foreseen ever to happen.
818 
819
820<a name="method49"></a>
821<p/><strong>bool SlowJet::doStep() &nbsp;</strong> <br/>
822do the next step of the clustering. This can either be that two
823clusters are joined to one, or that a cluster is promoted to a jet
824(which is discarded if its <i>pT</i> value is below
825<code>pTjetMin</code>).
826<br/>The routine will only return <code>false</code> if there are no
827clusters left.
828 
829
830<a name="method50"></a>
831<p/><strong>bool SlowJet::doNSteps(int nStep) &nbsp;</strong> <br/>
832calls the <code>doStep()</code> method <code>nStep</code> times,
833if possible. Will return <code>false</code> if the list of clusters
834is emptied before then. The stored jet information is still perfectly
835fine; it is only the number of steps that is wrong.
836 
837
838<a name="method51"></a>
839<p/><strong>bool SlowJet::stopAtN(int nStop) &nbsp;</strong> <br/>
840calls the <code>doStep()</code> method until a total of <code>nStop</code>
841jet and cluster objects remain. Will return <code>false</code> if this
842is not possible, specifically if the number of objects already is smaller
843than <code>nStop</code> when the method is called. The stored jet and
844cluster information is still perfectly fine; it only does not have the
845expected multiplicity.
846 
847
848<a name="method52"></a>
849<p/><strong>int SlowJet::sizeAll() &nbsp;</strong> <br/>
850gives the total current number of jets and clusters. The jets are
851numbered 0 through <code>sizeJet() - 1</code>, while the clusters
852are numbered <code>sizeJet()</code> through <code>sizeAll() - 1</code>.
853(Internally jets and clusters are represented by two separate arrays,
854but are here presented in one flat range.) Note that the jets are ordered
855in decreasing <i>pT</i>, while the clusters are not ordered.
856 
857
858<p/>
859With this extension, the methods <code>double pT(int i)</code>,
860<code>double y(int i)</code>, <code>double phi(int i)</code>,
861<code>Vec4 p(int i)</code>, <code>double m(int i)</code> and
862<code>int multiplicity(int i)</code> can be used as before.
863Furthermore, <code>list()</code> generalizes
864
865<a name="method53"></a>
866<p/><strong>void SlowJet::list(bool listAll = false, ostream& os = cout) &nbsp;</strong> <br/>
867provides a listing of the above information.
868<br/><code>argument</code><strong> listAll </strong>  :  lists both jets and clusters if <code>true</code>,
869else only jets.
870 
871 
872 
873<p/>
874Three further methods can be used to check what will happen next.
875
876<a name="method54"></a>
877<p/><strong>int SlowJet::iNext() &nbsp;</strong> <br/>
878 
879<strong>int SlowJet::jNext() &nbsp;</strong> <br/>
880 
881<strong>double SlowJet::dNext() &nbsp;</strong> <br/>
882if the next step is to join two clusters, then the methods give
883the <i>(i,j, d_ij)</i> values, if instead to promote
884a cluster to a jet then <i>(i, -1, d_iB)</i>.
885If no clusters remain then <i>(-1, -1, 0.)</i>. Note that
886the cluster numbers are offset as described above, i.e. they begin at
887<code>sizeJet()</code>, which of course easily could be subtracted off.
888Also note that the jet and cluster lists are (moderately) reshuffled
889in each new step.
890 
891 
892<p/>
893Finally, and separately, the <code>SlowJetHook</code> class can be used
894for a more smart selection of which particles to include in the analysis.
895For instance, isolated and/or high-<i>pT</i> muons, electrons and
896photons should presumably be identified separately at an early stage,
897and then not clustered to jets.
898 
899<p/>
900Technically, it works like with <?php $filepath = $_GET["filepath"];
901echo "<a href='UserHooks.php?filepath=".$filepath."' target='page'>";?>User Hooks</a>.
902That is, PYTHIA contains the base class. You write a derived class.
903In the main program you create an instance of this class, and hand it
904in to <code>SlowJet</code>; in this case already as part of the
905constructor.
906
907<p/> 
908The following methods should be defined in your derived class.
909
910<a name="method55"></a>
911<p/><strong>SlowJetHook::SlowJetHook() &nbsp;</strong> <br/>
912 
913<strong>virtual SlowJetHook::~SlowJetHook() &nbsp;</strong> <br/>
914the constructor and destructor need not do anything, and if so you
915need not write your own destructor.
916 
917
918<a name="method56"></a>
919<p/><strong>virtual bool SlowJetHook::include(int iSel, const Event& event, Vec4& pSel, double& mSel) &nbsp;</strong> <br/>
920is the main method that you will need to write. It will be called
921once for each final-state particle in an event, subject to the
922value of the <code>select</code> switch in the <code>SlowJet</code>
923constructor. The value <code>select = 2</code> may be convenient
924since then you do not need to remove e.g. neutrinos yourself, but
925use <code>select = 1</code> for full control. The method should then
926return <code>true</code> if you want to see particle included in the
927jet clustering, and <code>false</code> if not.
928<br/><code>argument</code><strong> iSel </strong>  : is the index in the event record of the
929currently studied particle.
930 
931<br/><code>argument</code><strong> event </strong>  : is an object of the <code>Event</code> class,
932most likely the <code>pythia.event</code> one, where the currently
933studied particle is found.
934 
935<br/><code>argument</code><strong> pSel </strong>  :  is at input the four-momentum of the
936currently studied particle. You can change the values, e.g. to take
937into account energy smearing in the detector, to define the initial
938cluster value, without corrupting the event record itself.
939 
940<br/><code>argument</code><strong> mSel </strong>  :  is at input the mass of the currently studied
941particle. You can change the value, e.g. to take into account
942particle misidentification, to define the initial cluster value,
943without corrupting the event record itself. Note that the changes of
944<code>pSel</code> and <code>mSel</code> must be coordinated such that
945<i>E^2 - p^2 = m^2</i> holds.
946 
947 
948
949<p/> 
950It is also possible to define further methods of your own.
951One such could e.g. be called directly in the main program before the
952<code>analyze</code> method is called, to identify and bookkeep
953some event properties you may not want to reanalyze for each
954individual particle.
955
956</body>
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958
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