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-
-<h2>Event Analysis</h2>
-
-<h3>Introduction</h3>
-
-The routines in this section are intended to be used to analyze
-event properties. As such they are not part of the main event
-generation chain, but can be used in comparisons between Monte
-Carlo events and real data. They are rather free-standing, but
-assume that input is provided in the PYTHIA 8
-<code>Event</code> format, and use a few basic facilities such
-as four-vectors. Their ordering is mainly by history; for current
-LHC applications the final one, <code>SlowJet</code>, is of
-special interest.
-
-<p/>
-In addition to the methods presented here, there is also the
-possibility to make use of <?php $filepath = $_GET["filepath"];
-echo "<a href='JetFinders.php?filepath=".$filepath."' target='page'>";?>external
-jet finders </a>.
-
-<h3>Sphericity</h3>
-
-The standard sphericity tensor is
-<br/><i>
- S^{ab} = (sum_i p_i^a p_i^b) / (sum_i p_i^2)
-</i><br/>
-where the <i>sum i</i> runs over the particles in the event,
-<i>a, b = x, y, z,</i> and <i>p</i> without such an index is
-the absolute size of the three-momentum . This tensor can be
-diagonalized to find eigenvalues and eigenvectors.
-
-<p/>
-The above tensor can be generalized by introducing a power
-<i>r</i>, such that
-<br/><i>
- S^{ab} = (sum_i p_i^a p_i^b p_i^{r-2}) / (sum_i p_i^r)
-</i><br/>
-In particular, <i>r = 1</i> gives a linear dependence on momenta
-and thus a collinear safe definition, unlike sphericity.
-
-<p/>
-To do sphericity analyses you have to set up a <code>Sphericity</code>
-instance, and then feed in events to it, one at a time. The results
-for the latest event are available as output from a few methods.
-
-<a name="method1"></a>
-<p/><strong>Sphericity::Sphericity(double power = 2., int select = 2) </strong> <br/>
-create a sphericity analysis object, where
-<br/><code>argument</code><strong> power </strong> (<code>default = <strong>2.</strong></code>) :
-is the power <i>r</i> defined above, i.e.
-<br/><code>argumentoption </code><strong> 2.</strong> : gives Spericity, and
-<br/><code>argumentoption </code><strong> 1.</strong> : gives the linear form.
-
-<br/><code>argument</code><strong> select </strong> (<code>default = <strong>2</strong></code>) :
-tells which particles are analyzed,
-<br/><code>argumentoption </code><strong> 1</strong> : all final-state particles,
-<br/><code>argumentoption </code><strong> 2</strong> : all observable final-state particles,
-i.e. excluding neutrinos and other particles without strong or
-electromagnetic interactions (the <code>isVisible()</code>
-particle method), and
-
-<br/><code>argumentoption </code><strong> 3</strong> : only charged final-state particles.
-
-
-
-<a name="method2"></a>
-<p/><strong>bool Sphericity::analyze( const Event& event, ostream& os = cout) </strong> <br/>
-perform a sphericity analysis, where
-<br/><code>argument</code><strong> event </strong> : is an object of the <code>Event</code> class,
-most likely the <code>pythia.event</code> one.
-
-<br/><code>argument</code><strong> os </strong> (<code>default = <strong>cout</strong></code>) : is the output stream for
-error messages. (The method does not rely on the <code>Info</code>
-mchinery for error messages.)
-
-<br/>If the routine returns <code>false</code> the
-analysis failed, e.g. if too few particles are present to analyze.
-
-
-<p/>
-After the analysis has been performed, a few methods are available
-to return the result of the analysis of the latest event:
-
-<a name="method3"></a>
-<p/><strong>double Sphericity::sphericity() </strong> <br/>
-gives the sphericity (or equivalent if <i>r</i> is not 2),
-
-
-<a name="method4"></a>
-<p/><strong>double Sphericity::aplanarity() </strong> <br/>
-gives the aplanarity (with the same comment),
-
-
-<a name="method5"></a>
-<p/><strong>double Sphericity::eigenValue(int i) </strong> <br/>
-gives one of the three eigenvalues for <i>i</i> = 1, 2 or 3, in
-descending order,
-
-
-<a name="method6"></a>
-<p/><strong>Vec4 Sphericity::eventAxis(i) </strong> <br/>
-gives the matching normalized eigenvector, as a <code>Vec4</code>
-with vanishing time/energy component.
-
-
-<a name="method7"></a>
-<p/><strong>void Sphericity::list(ostream& os = cout) </strong> <br/>
-provides a listing of the above information.
-
-
-<p/>
-There is also one method that returns information accumulated for all
-the events analyzed so far.
-
-<a name="method8"></a>
-<p/><strong>int Sphericity::nError() </strong> <br/>
-tells the number of times <code>analyze(...)</code> failed to analyze
-events, i.e. returned <code>false</code>.
-
-
-<h3>Thrust</h3>
-
-Thrust is obtained by varying the thrust axis so that the longitudinal
-momentum component projected onto it is maximized, and thrust itself is
-then defined as the sum of absolute longitudinal momenta divided by
-the sum of absolute momenta. The major axis is found correspondingly
-in the plane transverse to thrust, and the minor one is then defined
-to be transverse to both. Oblateness is the difference between the major
-and the minor values.
-
-<p/>
-The calculation of thrust is more computer-time-intensive than e.g.
-linear sphericity, introduced above, and has no specific advantages except
-historical precedent. In the PYTHIA 6 implementation the search was
-speeded up at the price of then not being guaranteed to hit the absolute
-maximum. The current implementation studies all possibilities, but at
-the price of being slower, with time consumption for an event with
-<i>n</i> particles growing like <i>n^3</i>.
-
-<p/>
-To do thrust analyses you have to set up a <code>Thrust</code>
-instance, and then feed in events to it, one at a time. The results
-for the latest event are available as output from a few methods.
-
-<a name="method9"></a>
-<p/><strong>Thrust::Thrust(int select = 2) </strong> <br/>
-create a thrust analysis object, where
-<br/><code>argument</code><strong> select </strong> (<code>default = <strong>2</strong></code>) :
-tells which particles are analyzed,
-<br/><code>argumentoption </code><strong> 1</strong> : all final-state particles,
-<br/><code>argumentoption </code><strong> 2</strong> : all observable final-state particles,
-i.e. excluding neutrinos and other particles without strong or
-electromagnetic interactions (the <code>isVisible()</code>
-particle method), and
-
-<br/><code>argumentoption </code><strong> 3</strong> : only charged final-state particles.
-
-
-
-<a name="method10"></a>
-<p/><strong>bool Thrust::analyze( const Event& event, ostream& os = cout) </strong> <br/>
-perform a thrust analysis, where
-<br/><code>argument</code><strong> event </strong> : is an object of the <code>Event</code> class,
-most likely the <code>pythia.event</code> one.
-
-<br/><code>argument</code><strong> os </strong> (<code>default = <strong>cout</strong></code>) : is the output stream for
-error messages. (The method does not rely on the <code>Info</code>
-mchinery for error messages.)
-
-<br/>If the routine returns <code>false</code> the
-analysis failed, e.g. if too few particles are present to analyze.
-
-
-<p/>
-After the analysis has been performed, a few methods are available
-to return the result of the analysis of the latest event:
-
-<a name="method11"></a>
-<p/><strong>double Thrust::thrust() </strong> <br/>
-
-<strong>double Thrust::tMajor() </strong> <br/>
-
-<strong>double Thrust::tMinor() </strong> <br/>
-
-<strong>double Thrust::oblateness() </strong> <br/>
-gives the thrust, major, minor and oblateness values, respectively,
-
-
-<a name="method12"></a>
-<p/><strong>Vec4 Thrust::eventAxis(int i) </strong> <br/>
-gives the matching normalized event-axis vectors, for <i>i</i> = 1, 2 or 3
-corresponding to thrust, major or minor, as a <code>Vec4</code> with
-vanishing time/energy component.
-
-
-<a name="method13"></a>
-<p/><strong>void Thrust::list(ostream& os = cout) </strong> <br/>
-provides a listing of the above information.
-
-
-<p/>
-There is also one method that returns information accumulated for all
-the events analyzed so far.
-
-<a name="method14"></a>
-<p/><strong>int Thrust::nError() </strong> <br/>
-tells the number of times <code>analyze(...)</code> failed to analyze
-events, i.e. returned <code>false</code>.
-
-
-<h3>ClusterJet</h3>
-
-<code>ClusterJet</code> (a.k.a. <code>LUCLUS</code> and
-<code>PYCLUS</code>) is a clustering algorithm of the type used for
-analyses of <i>e^+e^-</i> events, see the PYTHIA 6 manual. All
-visible particles in the events are clustered into jets. A few options
-are available for some well-known distance measures. Cutoff
-distances can either be given in terms of a scaled quadratic quantity
-like <i>y = pT^2/E^2</i> or an unscaled linear one like <i>pT</i>.
-
-<p/>
-Note that we have deliberately chosen not to include the <i>e^+e^-</i>
-equivalents of the Cambridge/Aachen and anti-<i>kRT</i> algorithms.
-These tend to be good at clustering the densely populated (in angle)
-cores of jets, but less successful for the sparsely populated transverse
-regions, where many jets may come to consist of a single low-momentum
-particle. In hadron collisions such jets could easily be disregarded,
-while in <i>e^+e^-</i> annihilation all particles derive back from the
-hard process.
-
-<p/>
-To do jet finding analyses you have to set up a <code>ClusterJet</code>
-instance, and then feed in events to it, one at a time. The results
-for the latest event are available as output from a few methods.
-
-<a name="method15"></a>
-<p/><strong>ClusterJet::ClusterJet(string measure = "Lund", int select = 2, int massSet = 2, bool precluster = false, bool reassign = false) </strong> <br/>
-create a <code>ClusterJet</code> instance, where
-<br/><code>argument</code><strong> measure </strong> (<code>default = <strong>"Lund"</strong></code>) : distance measure,
-to be provided as a character string (actually, only the first character
-is necessary)
-<br/><code>argumentoption </code><strong> "Lund"</strong> : the Lund <i>pT</i> distance,
-
-<br/><code>argumentoption </code><strong> "JADE"</strong> : the JADE mass distance, and
-
-<br/><code>argumentoption </code><strong> "Durham"</strong> : the Durham <i>kT</i> measure.
-
-
-<br/><code>argument</code><strong> select </strong> (<code>default = <strong>2</strong></code>) :
-tells which particles are analyzed,
-<br/><code>argumentoption </code><strong> 1</strong> : all final-state particles,
-<br/><code>argumentoption </code><strong> 2</strong> : all observable final-state particles,
-i.e. excluding neutrinos and other particles without strong or
-electromagnetic interactions (the <code>isVisible()</code> particle
-method), and
-
-<br/><code>argumentoption </code><strong> 3</strong> : only charged final-state particles.
-
-<br/><code>argument</code><strong> massSet </strong> (<code>default = <strong>2</strong></code>) : masses assumed for the particles
-used in the analysis
-<br/><code>argumentoption </code><strong> 0</strong> : all massless,
-<br/><code>argumentoption </code><strong> 1</strong> : photons are massless while all others are
-assigned the <i>pi+-</i> mass, and
-
-<br/><code>argumentoption </code><strong> 2</strong> : all given their correct masses.
-
-<br/><code>argument</code><strong> precluster </strong> (<code>default = <strong>false</strong></code>) :
-perform or not a early preclustering step, where nearby particles
-are lumped together so as to speed up the subsequent normal clustering.
-
-<br/><code>argument</code><strong> reassign </strong> (<code>default = <strong>false</strong></code>) :
-reassign all particles to the nearest jet each time after two jets
-have been joined.
-
-
-
-<a name="method16"></a>
-<p/><strong>ClusterJet::analyze( const Event& event, double yScale, double pTscale, int nJetMin = 1, int nJetMax = 0, ostream& os = cout) </strong> <br/>
-performs a jet finding analysis, where
-<br/><code>argument</code><strong> event </strong> : is an object of the <code>Event</code> class,
-most likely the <code>pythia.event</code> one.
-
-<br/><code>argument</code><strong> yScale </strong> :
-is the cutoff joining scale, below which jets are joined. Is given
-in quadratic dimensionless quantities. Either <code>yScale</code>
-or <code>pTscale</code> must be set nonvanishing, and the larger of
-the two dictates the actual value.
-
-<br/><code>argument</code><strong> pTscale </strong> :
-is the cutoff joining scale, below which jets are joined. Is given
-in linear quantities, such as <i>pT</i> or <i>m</i> depending on
-the measure used, but always in units of GeV. Either <code>yScale</code>
-or <code>pTscale</code> must be set nonvanishing, and the larger of
-the two dictates the actual value.
-
-<br/><code>argument</code><strong> nJetMin </strong> (<code>default = <strong>1</strong></code>) :
-the minimum number of jets to be reconstructed. If used, it can override
-the <code>yScale</code> and <code>pTscale</code> values.
-
-<br/><code>argument</code><strong> nJetMax </strong> (<code>default = <strong>0</strong></code>) :
-the maximum number of jets to be reconstructed. Is not used if below
-<code>nJetMin</code>. If used, it can override the <code>yScale</code>
-and <code>pTscale</code> values. Thus e.g.
-<code>nJetMin = nJetMax = 3</code> can be used to reconstruct exactly
-3 jets.
-
-<br/><code>argument</code><strong> os </strong> (<code>default = <strong>cout</strong></code>) : is the output stream for
-error messages. (The method does not rely on the <code>Info</code>
-mchinery for error messages.)
-
-<br/>If the routine returns <code>false</code> the analysis failed,
-e.g. because the number of particles was smaller than the minimum number
-of jets requested.
-
-
-<p/>
-After the analysis has been performed, a few <code>ClusterJet</code>
-class methods are available to return the result of the analysis:
-
-<a name="method17"></a>
-<p/><strong>int ClusterJet::size() </strong> <br/>
-gives the number of jets found, with jets numbered 0 through
-<code>size() - 1</code>.
-
-
-<a name="method18"></a>
-<p/><strong>Vec4 ClusterJet::p(int i) </strong> <br/>
-gives a <code>Vec4</code> corresponding to the four-momentum defined by
-the sum of all the contributing particles to the <i>i</i>'th jet.
-
-
-<a name="method19"></a>
-<p/><strong>int ClusterJet::mult(int i) </strong> <br/>
-the number of particles that have been clustered into the <i>i</i>'th jet.
-
-
-<a name="method20"></a>
-<p/><strong>int ClusterJet::jetAssignment(int i) </strong> <br/>
-gives the index of the jet that the particle <i>i</i> of the event
-record belongs to,
-
-
-<a name="method21"></a>
-<p/><strong>void ClusterJet::list(ostream& os = cout) </strong> <br/>
-provides a listing of the reconstructed jets.
-
-
-<a name="method22"></a>
-<p/><strong>int ClusterJet::distanceSize() </strong> <br/>
-the number of most recent clustering scales that have been stored
-for readout with the next method. Normally this would be five,
-but less if fewer clustering steps occured.
-
-
-<a name="method23"></a>
-<p/><strong>double ClusterJet::distance(int i) </strong> <br/>
-clustering scales, with <code>distance(0)</code> being the most
-recent one, i.e. normally the highest, up to <code>distance(4)</code>
-being the fifth most recent. That is, with <i>n</i> being the final
-number of jets, <code>ClusterJet::size()</code>, the scales at which
-<i>n+1</i> jets become <i>n</i>, <i>n+2</i> become <i>n+1</i>,
-and so on till <i>n+5</i> become <i>n+4</i>. Nonexisting clustering
-scales are returned as zero. The physical interpretation of a scale is
-as provided by the respective distance measure (Lund, JADE, Durham).
-
-
-<p/>
-There is also one method that returns information accumulated for all
-the events analyzed so far.
-
-<a name="method24"></a>
-<p/><strong>int ClusterJet::nError() </strong> <br/>
-tells the number of times <code>analyze(...)</code> failed to analyze
-events, i.e. returned <code>false</code>.
-
-
-<h3>CellJet</h3>
-
-<code>CellJet</code> (a.k.a. <code>PYCELL</code>) is a simple cone jet
-finder in the UA1 spirit, see the PYTHIA 6 manual. It works in an
-<i>(eta, phi, eT)</i> space, where <i>eta</i> is pseudorapidity,
-<i>phi</i> azimuthal angle and <i>eT</i> transverse energy.
-It will draw cones in <i>R = sqrt(Delta-eta^2 + Delta-phi^2)</i>
-around seed cells. If the total <i>eT</i> inside the cone exceeds
-the threshold, a jet is formed, and the cells are removed from further
-analysis. There are no split or merge procedures, so later-found jets
-may be missing some of the edge regions already used up by previous
-ones. Not all particles in the event are assigned to jets; leftovers
-may be viewed as belonging to beam remnants or the underlying event.
-It is not used by any experimental collaboration, but is closely
-related to the more recent and better theoretically motivated
-anti-<i>kT</i> algorithm [<a href="Bibliography.php" target="page">Cac08</a>].
-
-<p/>
-To do jet finding analyses you have to set up a <code>CellJet</code>
-instance, and then feed in events to it, one at a time. Especially note
-that, if you want to use the options where energies are smeared in
-order so emulate detector imperfections, you must hand in an external
-random number generator, preferably the one residing in the
-<code>Pythia</code> class. The results for the latest event are
-available as output from a few methods.
-
-<a name="method25"></a>
-<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) </strong> <br/>
-create a <code>CellJet</code> instance, where
-<br/><code>argument</code><strong> etaMax </strong> (<code>default = <strong>5.</strong></code>) :
-the maximum +-pseudorapidity that the detector is assumed to cover.
-
-<br/><code>argument</code><strong> nEta </strong> (<code>default = <strong>50</strong></code>) :
-the number of equal-sized bins that the <i>+-etaMax</i> range
-is assumed to be divided into.
-
-<br/><code>argument</code><strong> nPhi </strong> (<code>default = <strong>32</strong></code>) :
-the number of equal-sized bins that the <i>phi</i> range
-<i>+-pi</i> is assumed to be divided into.
-
-<br/><code>argument</code><strong> select </strong> (<code>default = <strong>2</strong></code>) :
-tells which particles are analyzed,
-<br/><code>argumentoption </code><strong> 1</strong> : all final-state particles,
-<br/><code>argumentoption </code><strong> 2</strong> : all observable final-state particles,
-i.e. excluding neutrinos and other particles without strong or
-electromagnetic interactions (the <code>isVisible()</code> particle
-method),
-and
-<br/><code>argumentoption </code><strong> 3</strong> : only charged final-state particles.
-
-<br/><code>argument</code><strong> smear </strong> (<code>default = <strong>0</strong></code>) :
-strategy to smear the actual <i>eT</i> bin by bin,
-<br/><code>argumentoption </code><strong> 0</strong> : no smearing,
-<br/><code>argumentoption </code><strong> 1</strong> : smear the <i>eT</i> according to a Gaussian
-with width <i>resolution * sqrt(eT)</i>, with the Gaussian truncated
-at 0 and <i>upperCut * eT</i>,
-<br/><code>argumentoption </code><strong> 2</strong> : smear the <i>e = eT * cosh(eta)</i> according
-to a Gaussian with width <i>resolution * sqrt(e)</i>, with the
-Gaussian truncated at 0 and <i>upperCut * e</i>.
-
-<br/><code>argument</code><strong> resolution </strong> (<code>default = <strong>0.5</strong></code>) :
-see above.
-
-<br/><code>argument</code><strong> upperCut </strong> (<code>default = <strong>2.</strong></code>) :
-see above.
-
-<br/><code>argument</code><strong> threshold </strong> (<code>default = <strong>0 GeV</strong></code>) :
-completely neglect all bins with an <i>eT < threshold</i>.
-
-<br/><code>argument</code><strong> rndmPtr </strong> (<code>default = <strong>0</strong></code>) :
-the random-number generator used to select the smearing described
-above. Must be handed in for smearing to be possible. If your
-<code>Pythia</code> class instance is named <code>pythia</code>,
-then <code>&pythia.rndm</code> would be the logical choice.
-
-
-
-<a name="method26"></a>
-<p/><strong>bool CellJet::analyze( const Event& event, double eTjetMin = 20., double coneRadius = 0.7, double eTseed = 1.5, ostream& os = cout) </strong> <br/>
-performs a jet finding analysis, where
-<br/><code>argument</code><strong> event </strong> : is an object of the <code>Event</code> class,
-most likely the <code>pythia.event</code> one.
-
-<br/><code>argument</code><strong> eTjetMin </strong> (<code>default = <strong>20. GeV</strong></code>) :
-is the minimum transverse energy inside a cone for this to be
-accepted as a jet.
-
-<br/><code>argument</code><strong> coneRadius </strong> (<code>default = <strong>0.7</strong></code>) :
- is the size of the cone in <i>(eta, phi)</i> space drawn around
-the geometric center of the jet.
-
-<br/><code>argument</code><strong> eTseed </strong> (<code>default = <strong>1.5 GeV</strong></code>) :
-the mimimum <i>eT</i> in a cell for this to be acceptable as
-the trial center of a jet.
-
-<br/><code>argument</code><strong> os </strong> (<code>default = <strong>cout</strong></code>) : is the output stream for
-error messages. (The method does not rely on the <code>Info</code>
-mchinery for error messages.)
-
-<br/>If the routine returns <code>false</code> the analysis failed,
-but currently this is not foreseen ever to happen.
-
-
-<p/>
-After the analysis has been performed, a few <code>CellJet</code>
-class methods are available to return the result of the analysis:
-
-<a name="method27"></a>
-<p/><strong>int CellJet::size() </strong> <br/>
-gives the number of jets found, with jets numbered 0 through
-<code>size() - 1</code>,
-
-
-<a name="method28"></a>
-<p/><strong>double CellJet::eT(i) </strong> <br/>
-gives the <i>eT</i> of the <i>i</i>'th jet, where jets have been
-ordered with decreasing <i>eT</i> values,
-
-
-<a name="method29"></a>
-<p/><strong>double CellJet::etaCenter(int i) </strong> <br/>
-
-<strong>double CellJet::phiCenter(int i) </strong> <br/>
-gives the <i>eta</i> and <i>phi</i> coordinates of the geometrical
-center of the <i>i</i>'th jet,
-
-
-<a name="method30"></a>
-<p/><strong>double CellJet::etaWeighted(int i) </strong> <br/>
-
-<strong>double CellJet::phiWeighted(int i) </strong> <br/>
-gives the <i>eta</i> and <i>phi</i> coordinates of the
-<i>eT</i>-weighted center of the <i>i</i>'th jet,
-
-
-<a name="method31"></a>
-<p/><strong>int CellJet::multiplicity(int i) </strong> <br/>
-gives the number of particles clustered into the <i>i</i>'th jet,
-
-
-<a name="method32"></a>
-<p/><strong>Vec4 CellJet::pMassless(int i) </strong> <br/>
-gives a <code>Vec4</code> corresponding to the four-momentum defined
-by the <i>eT</i> and the weighted center of the <i>i</i>'th jet,
-
-
-<a name="method33"></a>
-<p/><strong>Vec4 CellJet::pMassive(int i) </strong> <br/>
-gives a <code>Vec4</code> corresponding to the four-momentum defined by
-the sum of all the contributing cells to the <i>i</i>'th jet, where
-each cell contributes a four-momentum as if all the <i>eT</i> is
-deposited in the center of the cell,
-
-
-<a name="method34"></a>
-<p/><strong>double CellJet::m(int i) </strong> <br/>
-gives the invariant mass of the <i>i</i>'th jet, defined by the
-<code>pMassive</code> above,
-
-
-<a name="method35"></a>
-<p/><strong>void CellJet::list() </strong> <br/>
-provides a listing of the above information (except <code>pMassless</code>,
-for reasons of space).
-
-
-<p/>
-There is also one method that returns information accumulated for all
-the events analyzed so far.
-<a name="method36"></a>
-<p/><strong>int CellJet::nError() </strong> <br/>
-tells the number of times <code>analyze(...)</code> failed to analyze
-events, i.e. returned <code>false</code>.
-
-
-<h3>SlowJet</h3>
-
-<code>SlowJet</code> is a simple program for doing jet finding according
-to either of the <i>kT</i>, anti-<i>kT</i>, and Cambridge/Aachen
-algorithms, in a cylindrical coordinate frame. The name is obviously
-an homage to the <code>FastJet</code> program [<a href="Bibliography.php" target="page">Cac06</a>].
-That package contains many more algorithms, with many more options,
-and, above all, is <i>much</i> faster. Therefore <code>SlowJet</code>
-is not so much intended for massive processing of data or Monte Carlo
-files as for simple first tests. Nevertheless, within the advertised
-capabilities of <code>SlowJet</code>, it has been checked to find
-identically the same jets as <code>FastJet</code>. The time consumption
-typically is around or below that to generate an LHC <i>pp</i> event
-in the first place, so is not prohibitive. But the time rises rapidly
-for large multiplicities, so obviously <code>SlowJet</code> can not
-be used for tricks like distributing a dense grid of pseudoparticles
-to be able to define jet areas, like <code>FastJet</code> can, and also
-not for events with much pileup or other noise.
-
-<p/>
-The first step is to decide which particles should be included in the
-analysis, and with what four-momenta. The <code>SlowJet</code> constructor
-allows to pick a maximum pseudorapidity defined by the extent of the
-assumed detector, to pick among some standard options of which particles
-to analyze, and to allow for some standard mass assumptions, like that
-all charged particles have the pion mass. Obviously this is only a
-restricted set of possibilities.
-
-<p/>
-Full flexibility can be obtained by deriving from the base class
-<code>SlowJetHook</code> to write your own <code>include</code> method.
-This will be presented with one final-state particle at a time, and
-should return <code>true</code> for those particles that should be
-analyzed. It is also possible to return modified four-momenta and masses,
-to take into account detector smearing effects or particle identity
-misassignments, but you must respect <i>E^2 - p^2 = m^2</i>.
-
-<p/>
-Alternatively you can modify the event record itself, or a copy of it
-(if you want to keep the original intact). For instance, only final
-particles are considered in the analysis, i.e. particles with positive
-status code, so negative status code should then be assigned to those
-particles that you do not want to see analyzed. Again four-momenta and
-masses can be modified, subject to <i>E^2 - p^2 = m^2</i>.
-
-<p/>
-The jet reconstructions is then based on sequential recombination with
-progressive removal, using the <i>E</i> recombination scheme. To be
-more specific, the algorithm works as follows.
-<ol>
-<li>Each particle to be analyzed defines an original cluster. It has a
-well-defined four-momentum and mass at input. From this information the
-triplet <i>(pT, y, phi)</i> is calculated, i.e. the transverse momentum,
-rapidity and azimuthal angle of the cluster.</li>
-<li>Define distance measures of all clusters <i>i</i> to the beam
-<br/><i>d_iB = pT_i^2p</i><br/>
-and of all pairs <i>(i,j)</i> relative to each other
-<br/><i>d_ij = min( pT_i^2p, pT_j^2p) DeltaR_ij^2 / R^2 </i><br/>
-where
-<br/><i>DeltaR_ij^2 = (y_i - y_j)^2 + (phi_i - phi_j)^2.</i><br/>
-The jet algorithm is determined by the user-selected <i>p</i> value,
-where <i>p = -1</i> corresponds to the anti-<i>kT</i> one,
-<i>p = 0</i> to the Cambridge/Aachen one and <i>p = 1</i> to the
-<i>kT</i> one. Also <i>R</i> is chosen by the user, to give an
-approximate measure of the size of jets. However, note that jets need
-not have a circular shape in <i>(y, phi)</i> space, so <i>R</i>
-can not straight off be interpreted as a jet radius.</li>
-<li>Find the smallest of all <i>d_iB</i> and <i>d_ij</i>.</li>
-<li>If this is a <i>d_iB</i> then cluster <i>i</i> is removed from
-the clusters list and instead added to the jets list.
-Optionally, a <i>pTjetMin</i> requirement is imposed, where only
-clusters with <i>pT > pTjetMin</i> are added to the jets list.
-If so, some of the analyzed particles will not be part of any final
-jet.</li>
-<li>If instead te smallest measure is a <i>d_ij</i> then the
-four-momenta of the <i>i</i> and <i>j</i> clusters are added
-to define a single new cluster. Convert this four-momentum to a new
-<i>(pT, y, phi)</i> triplet and update the list of <i>d_iB</i>
-and <i>d_ij</i>.</li>
-<li>Return to step 3 until no clusters remain.</li>
-</ol>
-
-<p/>
-To do jet finding analyses you first have to set up a <code>SlowJet</code>
-instance, where the arguments of the constructor specifies the details
-of the subsequent analyses. Thereafter you can feed in events to it,
-one at a time, and have them analyzed by the <code>analyze</code> method.
-Information on the resulting jets can be extracted by a few different methods.
-The minimal procedure only requires one call per event to do the analysis.
-We will begin by presenting it, and only afterwards some extensions.
-
-<a name="method37"></a>
-<p/><strong>SlowJet::SlowJet(double power, double R, double pTjetMin = 0.,double etaMax = 25., int select = 2, int massSet = 2, SlowJetHook* sjHookPtr = 0) </strong> <br/>
-create a <code>SlowJet</code> instance, where
-<br/><code>argument</code><strong> power </strong> :
-tells (half) the power of the transverse-momentum dependence of the
-distance measure,
-<br/><code>argumentoption </code><strong> -1</strong> : the anti-<i>kT</i> algorithm,
-<br/><code>argumentoption </code><strong> 0</strong> : the Cambridge/Aachen algorithm, and
-<br/><code>argumentoption </code><strong> 1</strong> : the <i>kT</i> algorithm.
-
-<br/><code>argument</code><strong> R </strong> :
-the <i>R</i> size parameter, which is crudely related to the radius of
-the jet cone in <i>(y, phi)</i> space around the center of the jet.
-
-<br/><code>argument</code><strong> pTjetMin </strong> (<code>default = <strong>0.0 GeV</strong></code>) :
-the minimum transverse momentum required for a cluster
-to become a jet. By default all clusters become jets, and therefore
-all analyzed particles are assigned to a jet.
-For comparisons with perturbative QCD, however, it is only meaningful
-to consider jets with a significant <i>pT</i>.
-
-<br/><code>argument</code><strong> etaMax </strong> (<code>default = <strong>25.</strong></code>) :
-the maximum +-pseudorapidity that the detector is assumed to cover.
-If you pick a value above 20 there is assumed to be full coverage
-(obviously only meaningful for theoretical studies).
-
-<br/><code>argument</code><strong> select </strong> (<code>default = <strong>2</strong></code>) :
-tells which particles are analyzed,
-<br/><code>argumentoption </code><strong> 1</strong> : all final-state particles,
-<br/><code>argumentoption </code><strong> 2</strong> : all observable final-state particles,
-i.e. excluding neutrinos and other particles without strong or
-electromagnetic interactions (the <code>isVisible()</code> particle
-method),
-and
-<br/><code>argumentoption </code><strong> 3</strong> : only charged final-state particles.
-
-<br/><code>argument</code><strong> massSet </strong> (<code>default = <strong>2</strong></code>) : masses assumed for the particles
-used in the analysis
-<br/><code>argumentoption </code><strong> 0</strong> : all massless,
-<br/><code>argumentoption </code><strong> 1</strong> : photons are massless while all others are
-assigned the <i>pi+-</i> mass, and
-
-<br/><code>argumentoption </code><strong> 2</strong> : all given their correct masses.
-
-<br/><code>argument</code><strong> sjHookPtr </strong> (<code>default = <strong>0</strong></code>) :
-gives the possibility to send in your own selection routine for which
-particles should be part of the analysis; see further below on the
-<code>SlowJetHook</code> class. If this pointer is sent in nonzero,
-<code>etaMax</code> and <code>massSet</code> are disregarded,
-and <code>select</code> only gives the basic selection, to which
-the user can add further requirements.
-
-
-
-<a name="method38"></a>
-<p/><strong>bool SlowJet::analyze( const Event& event) </strong> <br/>
-performs a jet finding analysis, where
-<br/><code>argument</code><strong> event </strong> : is an object of the <code>Event</code> class,
-most likely the <code>pythia.event</code> one.
-
-<br/>If the routine returns <code>false</code> the analysis failed,
-but currently this is not foreseen ever to happen.
-
-
-<p/>
-After the analysis has been performed, a few <code>SlowJet</code>
-class methods are available to return the result of the analysis:
-
-<a name="method39"></a>
-<p/><strong>int SlowJet::sizeOrig() </strong> <br/>
-gives the original number of particles (and thus clusters) that the
-analysis starts with.
-
-
-<a name="method40"></a>
-<p/><strong>int SlowJet::sizeJet() </strong> <br/>
-gives the number of jets found, with jets numbered 0 through
-<code>sizeJet() - 1</code>, and ordered in terms of decreasing
-transverse momentum values w.r.t. the beam axis,
-
-
-<a name="method41"></a>
-<p/><strong>double SlowJet::pT(i) </strong> <br/>
-gives the transverse momentum <i>pT</i> of the <i>i</i>'th jet,
-
-
-<a name="method42"></a>
-<p/><strong>double SlowJet::y(int i) </strong> <br/>
-
-<strong>double SlowJet::phi(int i) </strong> <br/>
-gives the rapidity <i>y</i> and azimuthal angle <i>phi</i>
-of the center of the <i>i</i>'th jet (defined by the vector sum
-of constituent four-momenta),
-
-
-<a name="method43"></a>
-<p/><strong>Vec4 SlowJet::p(int i) </strong> <br/>
-
-<strong>double SlowJet::m(int i) </strong> <br/>
-gives a <code>Vec4</code> corresponding to the four-momentum
-sum of the particles assigned to the <i>i</i>'th jet, and
-the invariant mass of this four-vector,
-
-
-<a name="method44"></a>
-<p/><strong>int SlowJet::multiplicity(int i) </strong> <br/>
-gives the number of particles clustered into the <i>i</i>'th jet,
-
-
-<a name="method45"></a>
-<p/><strong>int SlowJet::jetAssignment(int i) </strong> <br/>
-gives the index of the jet that the particle <i>i</i> of the event
-record belongs to, or -1 if there is no jet containing particle
-<i>i</i>,
-
-
-<a name="method46"></a>
-<p/><strong>void SlowJet::removeJet(int i) </strong> <br/>
-removes the <i>i</i>'th jet,
-
-
-<a name="method47"></a>
-<p/><strong>void SlowJet::list() </strong> <br/>
-provides a listing of the above information.
-
-
-<p/>
-These are the basic methods. For more sophisticated usage
-it is possible to trace the clustering, one step at a time. If so, the
-<code>setup</code> method should be used to read in the event and find
-the initial smallest distance. Each subsequent <code>doStep</code>
-will then do one cluster joining and find the new smallest distance.
-You can therefore interrogate which clusters will be joined next
-before the joining actually is performed. Alternatively you can take
-several steps in one go, or take steps down to a predetermined number
-of jets plus remaining clusters.
-
-<a name="method48"></a>
-<p/><strong>bool SlowJet::setup( const Event& event) </strong> <br/>
-selects the particles to be analyzed, calculates initial distances,
-and finds the initial smallest distance.
-<br/><code>argument</code><strong> event </strong> : is an object of the <code>Event</code> class,
-most likely the <code>pythia.event</code> one.
-
-<br/>If the routine returns <code>false</code> the setup failed,
-but currently this is not foreseen ever to happen.
-
-
-<a name="method49"></a>
-<p/><strong>bool SlowJet::doStep() </strong> <br/>
-do the next step of the clustering. This can either be that two
-clusters are joined to one, or that a cluster is promoted to a jet
-(which is discarded if its <i>pT</i> value is below
-<code>pTjetMin</code>).
-<br/>The routine will only return <code>false</code> if there are no
-clusters left.
-
-
-<a name="method50"></a>
-<p/><strong>bool SlowJet::doNSteps(int nStep) </strong> <br/>
-calls the <code>doStep()</code> method <code>nStep</code> times,
-if possible. Will return <code>false</code> if the list of clusters
-is emptied before then. The stored jet information is still perfectly
-fine; it is only the number of steps that is wrong.
-
-
-<a name="method51"></a>
-<p/><strong>bool SlowJet::stopAtN(int nStop) </strong> <br/>
-calls the <code>doStep()</code> method until a total of <code>nStop</code>
-jet and cluster objects remain. Will return <code>false</code> if this
-is not possible, specifically if the number of objects already is smaller
-than <code>nStop</code> when the method is called. The stored jet and
-cluster information is still perfectly fine; it only does not have the
-expected multiplicity.
-
-
-<a name="method52"></a>
-<p/><strong>int SlowJet::sizeAll() </strong> <br/>
-gives the total current number of jets and clusters. The jets are
-numbered 0 through <code>sizeJet() - 1</code>, while the clusters
-are numbered <code>sizeJet()</code> through <code>sizeAll() - 1</code>.
-(Internally jets and clusters are represented by two separate arrays,
-but are here presented in one flat range.) Note that the jets are ordered
-in decreasing <i>pT</i>, while the clusters are not ordered.
-
-
-<p/>
-With this extension, the methods <code>double pT(int i)</code>,
-<code>double y(int i)</code>, <code>double phi(int i)</code>,
-<code>Vec4 p(int i)</code>, <code>double m(int i)</code> and
-<code>int multiplicity(int i)</code> can be used as before.
-Furthermore, <code>list()</code> generalizes
-
-<a name="method53"></a>
-<p/><strong>void SlowJet::list(bool listAll = false, ostream& os = cout) </strong> <br/>
-provides a listing of the above information.
-<br/><code>argument</code><strong> listAll </strong> : lists both jets and clusters if <code>true</code>,
-else only jets.
-
-
-
-<p/>
-Three further methods can be used to check what will happen next.
-
-<a name="method54"></a>
-<p/><strong>int SlowJet::iNext() </strong> <br/>
-
-<strong>int SlowJet::jNext() </strong> <br/>
-
-<strong>double SlowJet::dNext() </strong> <br/>
-if the next step is to join two clusters, then the methods give
-the <i>(i,j, d_ij)</i> values, if instead to promote
-a cluster to a jet then <i>(i, -1, d_iB)</i>.
-If no clusters remain then <i>(-1, -1, 0.)</i>. Note that
-the cluster numbers are offset as described above, i.e. they begin at
-<code>sizeJet()</code>, which of course easily could be subtracted off.
-Also note that the jet and cluster lists are (moderately) reshuffled
-in each new step.
-
-
-<p/>
-Finally, and separately, the <code>SlowJetHook</code> class can be used
-for a more smart selection of which particles to include in the analysis.
-For instance, isolated and/or high-<i>pT</i> muons, electrons and
-photons should presumably be identified separately at an early stage,
-and then not clustered to jets.
-
-<p/>
-Technically, it works like with <?php $filepath = $_GET["filepath"];
-echo "<a href='UserHooks.php?filepath=".$filepath."' target='page'>";?>User Hooks</a>.
-That is, PYTHIA contains the base class. You write a derived class.
-In the main program you create an instance of this class, and hand it
-in to <code>SlowJet</code>; in this case already as part of the
-constructor.
-
-<p/>
-The following methods should be defined in your derived class.
-
-<a name="method55"></a>
-<p/><strong>SlowJetHook::SlowJetHook() </strong> <br/>
-
-<strong>virtual SlowJetHook::~SlowJetHook() </strong> <br/>
-the constructor and destructor need not do anything, and if so you
-need not write your own destructor.
-
-
-<a name="method56"></a>
-<p/><strong>virtual bool SlowJetHook::include(int iSel, const Event& event, Vec4& pSel, double& mSel) </strong> <br/>
-is the main method that you will need to write. It will be called
-once for each final-state particle in an event, subject to the
-value of the <code>select</code> switch in the <code>SlowJet</code>
-constructor. The value <code>select = 2</code> may be convenient
-since then you do not need to remove e.g. neutrinos yourself, but
-use <code>select = 1</code> for full control. The method should then
-return <code>true</code> if you want to see particle included in the
-jet clustering, and <code>false</code> if not.
-<br/><code>argument</code><strong> iSel </strong> : is the index in the event record of the
-currently studied particle.
-
-<br/><code>argument</code><strong> event </strong> : is an object of the <code>Event</code> class,
-most likely the <code>pythia.event</code> one, where the currently
-studied particle is found.
-
-<br/><code>argument</code><strong> pSel </strong> : is at input the four-momentum of the
-currently studied particle. You can change the values, e.g. to take
-into account energy smearing in the detector, to define the initial
-cluster value, without corrupting the event record itself.
-
-<br/><code>argument</code><strong> mSel </strong> : is at input the mass of the currently studied
-particle. You can change the value, e.g. to take into account
-particle misidentification, to define the initial cluster value,
-without corrupting the event record itself. Note that the changes of
-<code>pSel</code> and <code>mSel</code> must be coordinated such that
-<i>E^2 - p^2 = m^2</i> holds.
-
-
-
-<p/>
-It is also possible to define further methods of your own.
-One such could e.g. be called directly in the main program before the
-<code>analyze</code> method is called, to identify and bookkeep
-some event properties you may not want to reanalyze for each
-individual particle.
-
-</body>
-</html>
-
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