Event Analysis
Introduction
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
Event format, and use a few basic facilities such
as four-vectors.
Sphericity
The standard sphericity tensor is
S^{ab} = (sum_i p_i^a p_i^b) / (sum_i p_i^2)
where the sum i runs over the particles in the event,
a, b = x, y, z, and p without such an index is
the absolute size of the three-momentum . This tensor can be
diagonalized to find eigenvalues and eigenvectors.
The above tensor can be generalized by introducing a power
r, such that
S^{ab} = (sum_i p_i^a p_i^b p_i^{r-2}) / (sum_i p_i^r)
In particular, r = 1 gives a linear dependence on momenta
and thus a collinear safe definition, unlike sphericity.
A sphericity analysis object is declared by
class Sphericity sph( power, select)
where
argument power (default = 2.) :
is the power r defined above, i.e.
argumentoption 2. : gives Spericity, and
argumentoption 1. : gives the linear form.
argument select (default = 2) :
tells which particles are analyzed,
argumentoption 1 : all final-state particles,
argumentoption 2 : all observable final-state particles,
i.e. excluding neutrinos and other particles without strong or
electromagnetic interactions (the isVisible()
particle method), and
argumentoption 3 : only charged final-state particles.
The analysis is performed by a call to the method
method analyze( event)
where
argument event : is an object of the Event class,
most likely the pythia.event one.
If the routine returns false the analysis failed,
e.g. if too few particles are present to analyze.
After the analysis has been performed, a few Sphericity
class methods are available to return the result of the analysis:
method sphericity()
gives the sphericity (or equivalent if r is not 2),
method aplanarity()
gives the aplanarity (with the same comment),
method eigenValue(i)
gives one of the three eigenvalues for i = 1, 2 or 3, in
descending order,
method EventAxis(i)
gives the matching eigenvector, as a Vec4 with vanishing
time/energy component.
method list()
provides a listing of the above information.
method nError()
tells the number of times analyze failed to analyze events.
Thrust
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.
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
n particles growing like n^3.
A thrust analysis object is declared by
class Thrust thr( select)
where
argument select (default = 2) :
tells which particles are analyzed,
argumentoption 1 : all final-state particles,
argumentoption 2 : all observable final-state particles,
i.e. excluding neutrinos and other particles without strong or
electromagnetic interactions (the isVisible()
particle method), and
argumentoption 3 : only charged final-state particles.
The analysis is performed by a call to the method
method analyze( event)
where
argument event : is an object of the Event class,
most likely the pythia.event one.
If the routine returns false the analysis failed,
e.g. if too few particles are present to analyze.
After the analysis has been performed, a few Thrust
class methods are available to return the result of the analysis:
method thrust(), tMajor(), tMinor(), oblateness()
gives the thrust, major, minor and oblateness values, respectively,
method EventAxis(i)
gives the matching event-axis vectors, for i = 1, 2 or 3
corresponding to thrust, major or minor, as a Vec4 with
vanishing time/energy component.
method list()
provides a listing of the above information.
method nError()
tells the number of times analyze failed to analyze events.
ClusterJet
ClusterJet (a.k.a. LUCLUS and
PYCLUS) is a clustering algorithm of the type used for
analyses of e^+e^- events, see the PYTHIA 6 manual. 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 y = pT^2/E^2 or an unscaled linear one like pT.
A cluster-jet analysis object is declared by
class ClusterJet clusterJet( measure, select, massSet,precluster, reassign)
where
argument measure (default = Lund) : distance measure, to be provided
as a character string (actually, only the first character is necessary)
argumentoption Lund : the Lund pT distance,
argumentoption JADE : the JADE mass distance, and
argumentoption Durham : the Durham kT measure.
argument select (default = 2) :
tells which particles are analyzed,
argumentoption 1 : all final-state particles,
argumentoption 2 : all observable final-state particles,
i.e. excluding neutrinos and other particles without strong or
electromagnetic interactions (the isVisible() particle
method), and
argumentoption 3 : only charged final-state particles.
argument massSet (default = 2) : masses assumed for the particles
used in the analysis
argumentoption 0 : all massless,
argumentoption 1 : photons are massless while all others are
assigned the pi+- mass, and
argumentoption 2 : all given their correct masses.
argument precluster (default = false) :
perform or not a early preclustering step, where nearby particles
are lumped together so as to speed up the subsequent normal clustering.
argument reassign (default = false) :
reassign all particles to the nearest jet each time after two jets
have been joined.
The analysis is performed by a
method analyze( event, yScale, pTscale, nJetMin, nJetMax)
where
argument event : is an object of the Event class,
most likely the pythia.event one.
argument yScale :
is the cutoff joining scale, below which jets are joined. Is given
in quadratic dimensionless quantities. Either yScale
or pTscale must be set nonvanishing, and the larger of
the two dictates the actual value.
argument pTscale :
is the cutoff joining scale, below which jets are joined. Is given
in linear quantities, such as pT or m depending on
the measure used, but always in units of GeV. Either yScale
or pTscale must be set nonvanishing, and the larger of
the two dictates the actual value.
argument nJetMin (default = 1) :
the minimum number of jets to be reconstructed. If used, it can override
the yScale and pTscale values.
argument nJetMax (default = 0) :
the maximum number of jets to be reconstructed. Is not used if below
nJetMin. If used, it can override the yScale
and pTscale values. Thus e.g.
nJetMin = nJetMax = 3 can be used to reconstruct exactly
3 jets.
If the routine returns false the analysis failed,
e.g. because the number of particles was smaller than the minimum number
of jets requested.
After the analysis has been performed, a few ClusterJet
class methods are available to return the result of the analysis:
method size()
gives the number of jets found, with jets numbered 0 through
size() - 1,
method p(i)
gives a Vec4 corresponding to the four-momentum defined by
the sum of all the contributing particles to the i'th jet,
method jetAssignment(i)
gives the index of the jet that the particle i of the event
record belongs to,
method list()
provides a listing of the reconstructed jets.
method nError()
tells the number of times analyze failed to analyze events.
CellJet
CellJet (a.k.a. PYCELL) is a simple cone jet
finder in the UA1 spirit, see the PYTHIA 6 manual. It works in an
(eta, phi, eT) space, where eta is pseudorapidity,
phi azimuthal angle and eT transverse energy.
It will draw cones in R = sqrt(Delta-eta^2 + Delta-phi^2)
around seed cells. If the total eT 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.
A cell-jet analysis object is declared by
class CellJet cellJet( etaMax, nEta, nPhi, select, smear, resolution, upperCut, threshold)
where
argument etaMax (default = 5.) :
the maximum +-pseudorapidity that the detector is assumed to cover.
argument nEta (default = 50) :
the number of equal-sized bins that the +-etaMax range
is assumed to be divided into.
argument nPhi (default = 32) :
the number of equal-sized bins that the phi range
+-pi is assumed to be divided into.
argument select (default = 2) :
tells which particles are analyzed,
argumentoption 1 : all final-state particles,
argumentoption 2 : all observable final-state particles,
i.e. excluding neutrinos and other particles without strong or
electromagnetic interactions (the isVisible() particle
method),
and
argumentoption 3 : only charged final-state particles.
argument smear (default = 0) :
strategy to smear the actual eT bin by bin,
argumentoption 0 : no smearing,
argumentoption 1 : smear the eT according to a Gaussian
with width resolution * sqrt(eT), with the Gaussian truncated
at 0 and upperCut * eT,
argumentoption 2 : smear the e = eT * cosh(eta) according
to a Gaussian with width resolution * sqrt(e), with the
Gaussian truncated at 0 and upperCut * e.
argument resolution (default = 0.5) :
see above
argument upperCut (default = 2.) :
see above
argument threshold (default = 0 GeV) :
completely neglect all bins with an eT < threshold.
The analysis is performed by a
method analyze( event, eTjetMin, coneRadius, eTseed)
where
argument event : is an object of the Event class,
most likely the pythia.event one.
argument eTjetMin (default = 20. GeV) :
is the minimum transverse energy inside a cone for this to be
accepted as a jet.
argument coneRadius (default = 0.7) :
is the size of the cone in (eta, phi) space drawn around
the geometric center of the jet.
argument eTseed (default = 1.5 GeV) :
the mimimum eT in a cell for this to be acceptable as
the trial center of a jet.
If the routine returns false the analysis failed,
but currently this is not foreseen ever to happen.
After the analysis has been performed, a few CellJet
class methods are available to return the result of the analysis:
method size()
gives the number of jets found, with jets numbered 0 through
size() - 1,
method eT(i)
gives the eT of the i'th jet, where jets have been
ordered with decreasing eT values,
method etaCenter(i), phiCenter(i)
gives the eta and phi coordinates of the geometrical
center of the i'th jet,
method etaWeighted(i), phiWeighted(i)
gives the eta and phi coordinates of the
eT-weighted center of the i'th jet,
method multiplicity(i)
gives the number of particles clustered into the i'th jet,
method pMassless(i)
gives a Vec4 corresponding to the four-momentum defined by the
eT and the weighted center of the i'th jet,
method pMassive(i)
gives a Vec4 corresponding to the four-momentum defined by
the sum of all the contributing cells to the i'th jet, where
each cell contributes a four-momentum as if all the eT is
deposited in the center of the cell,
method m(i)
gives the invariant mass of the i'th jet, defined by the
pMassive above,
method list()
provides a listing of the above information (except pMassless,
for reasons of space).
method nError()
tells the number of times analyze failed to analyze events.