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 name="Sphericity sph( power, select)"
where
argument name="power" default="2.":
is the power r defined above, i.e.
argoption value="2.": gives Spericity, and
argoption value="1.": gives the linear form.
argument name="select" default="2":
tells which particles are analyzed,
argoption value="1": all final-state particles,
argoption value="2": all observable final-state particles,
i.e. excluding neutrinos and other particles without strong or
electromagnetic interactions (the isVisible()
particle method), and
argoption value="3": only charged final-state particles.
The analysis is performed by a call to the method
method name="analyze( event)"
where
argument name="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 name="sphericity()"
gives the sphericity (or equivalent if r is not 2),
method name="aplanarity()"
gives the aplanarity (with the same comment),
method name="eigenValue(i)"
gives one of the three eigenvalues for i = 1, 2 or 3, in
descending order,
method name="EventAxis(i)"
gives the matching eigenvector, as a Vec4 with vanishing
time/energy component.
method name="list()"
provides a listing of the above information.
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 Pythia6 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 name="Thrust thr( select)"
where
argument name="select" default="2":
tells which particles are analyzed,
argoption value="1": all final-state particles,
argoption value="2": all observable final-state particles,
i.e. excluding neutrinos and other particles without strong or
electromagnetic interactions (the isVisible()
particle method), and
argoption value="3": only charged final-state particles.
The analysis is performed by a call to the method
method name="analyze( event)"
where
argument name="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 name="thrust(), tMajor(), tMinor(), oblateness()"
gives the thrust, major, minor and oblateness values, respectively,
method name="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 name="list()"
provides a listing of the above information.
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 name="ClusterJet clusterJet( measure, select, massSet,
precluster, reassign)"
where
argument name="measure" default="Lund": distance measure, to be provided
as a character string (actually, only the first character is necessary)
argoption value="Lund": the Lund pT distance,
argoption value="JADE": the JADE mass distance, and
argoption value="Durham": the Durham kT measure.
argument name="select" default="2":
tells which particles are analyzed,
argoption value="1": all final-state particles,
argoption value="2": all observable final-state particles,
i.e. excluding neutrinos and other particles without strong or
electromagnetic interactions (the isVisible() particle
method), and
argoption value="3": only charged final-state particles.
argument name="massSet" default="2": masses assumed for the particles
used in the analysis
argoption value="0": all massless,
argoption value="1": photons are massless while all others are
assigned the pi+- mass, and
argoption value="2": all given their correct masses.
argument name="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 name="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 name="analyze( event, yScale, pTscale, nJetMin, nJetMax)"
where
argument name="event": is an object of the Event class,
most likely the pythia.event one.
argument name="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 name="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 name="nJetMin" default="1":
the mimimum number of jets to be reconstructed. If used, it can override
the yScale and pTscale values.
argument name="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 name="size()"
gives the number of jets found,
method name="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 name="jetAssignment(i)"
gives the index of the jet that the particle i of the event
record belongs to,
method name="list()"
provides a listing of the reconstructed jets.
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 jet
may be missing some of the edge regions already used up by previous
ones.
A cell-jet analysis object is declared by
class name="CellJet cellJet( etaMax, nEta, nPhi, select, smear,
resolution, upperCut, threshold)"
where
argument name="etaMax" default="5.":
the maximum +-pseudorapidity that the detector is assumed to cover.
argument name="nEta" default="50":
the number of equal-sized bins that the +-etaMax range
is assumed to be divided into.
argument name="nPhi" default="32":
the number of equal-sized bins that the phi range
+-pi is assumed to be divided into.
argument name="select" default="2":
tells which particles are analyzed,
argoption value="1": all final-state particles,
argoption value="2": all observable final-state particles,
i.e. excluding neutrinos and other particles without strong or
electromagnetic interactions (the isVisible() particle
method),
and
argoption value="3": only charged final-state particles.
argument name="smear" default="0":
strategy to smear the actual eT bin by bin,
argoption value="0": no smearing,
argoption value="1": smear the eT according to a Gaussian
with width resolution * sqrt(eT), with the Gaussian truncated
at 0 and upperCut * eT,
argoption value="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 name="resolution" default="0.5":
see above
argument name="upperCut" default="2.":
see above
argument name="threshold" default="0 GeV":
completely neglect all bins with an eT < threshold.
The analysis is performed by a
method name="analyze( event, eTjetMin, coneRadius, eTseed)"
where
argument name="event": is an object of the Event class,
most likely the pythia.event one.
argument name="eTjetMin" default="20. GeV":
is the minimum transverse energy inside a cone for this to be
accepted as a jet.
argument name="coneRadius" default="0.7":
is the size of the cone in (eta, phi) space drawn around
the geometric center of the jet.
argument name="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 name="size()"
gives the number of jets found,
method name="eT(i)"
gives the eT of the i'th jet, where jets have been
ordered with decreasing eT values,
method name="etaCenter(i), phiCenter(i)"
gives the eta and phi coordinates of the geometrical
center of the i'th jet,
method name="etaWeighted(i), phiWeighted(i)"
gives the eta and phi coordinates of the
eT-weighted center of the i'th jet,
method name="multiplicity(i)"
gives the number of particles clustered into the i'th jet,
method name="pMassless(i)"
gives a Vec4 corresponding to the four-momentum defined by the
eT and the weighted center of the i'th jet,
method name="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 name="m(i)"
gives the invariant mass of the i'th jet, defined by the
pMassive above,
method name="list()"
provides a listing of the above information (except pMassless,
for reasons of space).