Routines and Common-Block Variables

The six routines `PYSPHE`, `PYTHRU`, `PYCLUS`,
`PYCELL`, `PYJMAS` and `PYFOWO` give you the possibility
to find some global event shape properties. The routine `PYTABU`
performs a statistical analysis of a number of different quantities
like particle content, factorial moments and the energy-energy
correlation.

Note that, by default, all remaining partons/particles except
neutrinos (and some other weakly interacting particles) are used in
the analysis. Neutrinos may be included with `MSTU(41) = 1`. Also
note that axes determined are stored in `PYJETS`, but are not
proper four-vectors and, as a general rule (with some exceptions),
should therefore not be rotated or boosted.

**Purpose:**- to diagonalize the momentum tensor, i.e. find the
eigenvalues
, with sum unity,
and the corresponding eigenvectors.

Momentum power dependence is given by`PARU(41)`; default corresponds to sphericity, while`PARU(41) = 1.`gives measures linear in momenta. Which particles (or partons) are used in the analysis is determined by the`MSTU(41)`value. `SPH :`-
, i.e. sphericity
(for
`PARU(41) = 2.`).`= -1. :`- analysis not performed because event contained less than two particles (or two exactly back-to-back particles, in which case the two transverse directions would be undefined).

`APL :`-
, i.e. aplanarity (for
`PARU(41) = 2.`).`= -1. :`- as
`SPH = -1.`

**Remark:**- the lines
`N + 1`through`N + 3`(`N - 2`through`N`for`MSTU(43) = 2`) in`PYJETS`will, after a call, contain the following information:`K(N+i,1) =`31;`K(N+i,2) =`95;`K(N+i,3) :`, the axis number, ;`K(N+i,4), K(N+i,5) =`0;`P(N+i,1) - P(N+i,3) :`the 'th eigenvector, , and components;`P(N+i,4) :`, the 'th eigenvalue;`P(N+i,5) =`0;`V(N+i,1) - V(N+i,5) =`0.

Also, the number of particles used in the analysis is given in`MSTU(62)`.

**Purpose:**- to find the thrust, major and minor axes and
corresponding projected momentum quantities, in particular thrust
and oblateness. The performance of the program is affected by
`MSTU(44)`,`MSTU(45)`,`PARU(42)`and`PARU(48)`. In particular,`PARU(42)`gives the momentum dependence, with the default value`= 1`corresponding to linear dependence. Which particles (or partons) are used in the analysis is determined by the`MSTU(41)`value. `THR :`- thrust (for
`PARU(42) = 1.`).`= -1. :`- analysis not performed because event contained less than two particles.
`= -2. :`- remaining space in
`PYJETS`(partly used as working area) not large enough to allow analysis.

`OBL :`- oblateness (for
`PARU(42) = 1.`).`= -1., -2. :`- as for
`THR`.

**Remark:**- the lines
`N + 1`through`N + 3`(`N - 2`through`N`for`MSTU(43) = 2`) in`PYJETS`will, after a call, contain the following information:`K(N+i,1) =`31;`K(N+i,2) =`96;`K(N+i,3) :`, the axis number, ;`K(N+i,4), K(N+i,5) =`0;`P(N+i,1) - P(N+i,3) :`the thrust, major and minor axis, respectively, for and 3;`P(N+i,4) :`corresponding thrust, major and minor value;`P(N+i,5) =`0;`V(N+i,1) - V(N+i,5) =`0.

Also, the number of particles used in the analysis is given in`MSTU(62)`.

**Purpose:**- to reconstruct an arbitrary number of jets using a
cluster analysis method based on particle momenta.

Three different distance measures are available, see section . The choice is controlled by`MSTU(46)`. The distance scale , above which two clusters may not be joined, is normally given by`PARU(44)`. In general, may be varied to describe different `jet-resolution powers'; the default value, 2.5 GeV, is fairly well suited for physics at 30-40 GeV. With the alternative mass distance measure,`PARU(44)`can be used to set the absolute maximum cluster mass, or`PARU(45)`to set the scaled one, i.e. in , where is the total invariant mass of the particles being considered.

It is possible to continue the cluster search from the configuration already found, with a new higher scale, by selecting`MSTU(48)`properly. In`MSTU(47)`one can also require a minimum number of jets to be reconstructed; combined with an artificially large this can be used to reconstruct a predetermined number of jets.

Which particles (or partons) are used in the analysis is determined by the`MSTU(41)`value, whereas assumptions about particle masses is given by`MSTU(42)`. The parameters`PARU(43)`and`PARU(48)`regulate more technical details (for events at high energies and large multiplicities, however, the choice of a larger`PARU(43)`may be necessary to obtain reasonable reconstruction times). `NJET :`- the number of clusters reconstructed.
`= -1 :`- analysis not performed because event contained less than
`MSTU(47)`(normally 1) particles, or analysis failed to reconstruct the requested number of jets. `= -2 :`- remaining space in
`PYJETS`(partly used as working area) not large enough to allow analysis.

**Remark:**- if the analysis does not fail, further information is
found in
`MSTU(61) - MSTU(63)`and`PARU(61) - PARU(63)`. In particular,`PARU(61)`contains the invariant mass for the system analysed, i.e. the number used in determining the denominator of .`PARU(62)`gives the generalized thrust, i.e. the sum of (absolute values of) cluster momenta divided by the sum of particle momenta (roughly the same as multicity [Bra79]).`PARU(63)`gives the minimum distance (in or ) between two clusters in the final cluster configuration, 0 in case of only one cluster.

Further, the lines`N + 1`through`N + NJET`(`N - NJET + 1`through`N`for`MSTU(43) = 2`) in`PYJETS`will, after a call, contain the following information:`K(N+i,1) =`31;`K(N+i,2) =`97;`K(N+i,3) :`, the jet number, with the jets arranged in falling order of absolute momentum;`K(N+i,4) :`the number of particles assigned to jet ;`K(N+i,5) =`0;`P(N+i,1) - P(N+i,5) :`momentum, energy and invariant mass of jet ;`V(N+i,1) - V(N+i,5) =`0.

Also, for a particle which was used in the analysis,`K(I,4)`, where`I`is the particle number and the number of the jet it has been assigned to. Undecayed particles not used then have`K(I,4) = 0`. An exception is made for lines with`K(I,1) = 3`(which anyhow are not normally interesting for cluster search), where the colour-flow information stored in`K(I,4)`is left intact.`MSTU(3)`is only set equal to the number of jets for positive`NJET`and`MSTU(43) = 1`.

**Purpose:**- to provide a simpler cluster routine more in line
with what is currently used in the study of high- collider
events.

A detector is assumed to stretch in pseudorapidity between`-PARU(51)`and`+PARU(51)`and be segmented in`MSTU(51)`equally large (pseudorapidity) bins and`MSTU(52)`(azimuthal) bins. Transverse energy for undecayed entries are summed up in each bin. For`MSTU(53)`non-zero, the energy is smeared by calorimetric resolution effects, cell by cell. This is done according to a Gaussian distribution; if`MSTU(53) = 1`the standard deviation for the is`PARU(55)`, if`MSTU(53) = 2`the standard deviation for the is`PARU(55)`, and expressed in GeV. The Gaussian is cut off at 0 and at a factor`PARU(56)`times the correct or . Cells with an below a given threshold`PARU(58)`are removed from further consideration; by default`PARU(58) = 0.`and thus all cells are kept.

All bins with`PARU(52)`are taken to be possible initiators of jets, and are tried in falling sequence to check whether the total summed over cells no more distant than`PARU(54)`in exceeds`PARU(53)`. If so, these cells define one jet, and are removed from further consideration. Contrary to`PYCLUS`, not all particles need be assigned to jets. Which particles (or partons) are used in the analysis is determined by the`MSTU(41)`value. `NJET :`- the number of jets reconstructed (may be 0).
`= -2 :`- remaining space in
`PYJETS`(partly used as working area) not large enough to allow analysis.

**Remark:**- the lines
`N + 1`through`N + NJET`(`N - NJET + 1`through`N`for`MSTU(43) = 2`) in`PYJETS`will, after a call, contain the following information:`K(N+i,1) =`31;`K(N+i,2) =`98;`K(N+i,3) :`, the jet number, with the jets arranged in falling order in ;`K(N+i,4) :`the number of particles assigned to jet ;`K(N+i,5) =`0;`V(N+i,1) - V(N+i,5) =`0.

Further, for`MSTU(54) = 1``P(N+i,1), P(N+i,2) =`position in and of the center of the jet initiator cell, i.e. geometrical center of jet;`P(N+i,3), P(N+i,4) =`position in and of the -weighted center of the jet, i.e. the center of gravity of the jet;`P(N+i,5) =`sum of the jet;

while for`MSTU(54) = 2``P(N+i,1) - P(N+i,5) :`the jet momentum vector, constructed from the summed and the and of the -weighted center of the jet as

;

and for`MSTU(54) = 3``P(N+i,1) - P(N+i,5) :`the jet momentum vector, constructed by adding vectorially the momentum of each cell assigned to the jet, assuming that all the was deposited at the center of the cell, and with the jet mass in`P(N+i,5)`calculated from the summed and as .

Also, the number of particles used in the analysis is given in`MSTU(62)`, and the number of cells hit in`MSTU(63)`.`MSTU(3)`is only set equal to the number of jets for positive`NJET`and`MSTU(43) = 1`.

**Purpose:**- to reconstruct high and low jet mass of an event.
A simplified algorithm is used, wherein a preliminary division of
the event into two hemispheres is done transversely to the sphericity
axis. Then one particle at a time is reassigned to the other
hemisphere if that reduces the sum of squares of the two jet masses,
. The procedure is stopped when no
further significant change (see
`PARU(48)`) is obtained. Often, the original assignment is retained as it is. Which particles (or partons) are used in the analysis is determined by the`MSTU(41)`value, whereas assumptions about particle masses is given by`MSTU(42)`. `PMH :`- heavy jet mass (in GeV).
`= -2. :`- remaining space in
`PYJETS`(partly used as working area) not large enough to allow analysis.

`PML :`- light jet mass (in GeV).
`= -2. :`- as for
`PMH = -2.`

**Remark:**- After a successful call,
`MSTU(62)`contains the number of particles used in the analysis, and`PARU(61)`the invariant mass of the system analysed. The latter number is helpful in constructing scaled jet masses.

**Purpose:**- to do an event analysis in terms of the Fox-Wolfram
moments. The moments are normalized to the lowest one, .
Which particles (or partons) are used in the analysis is determined
by the
`MSTU(41)`value. `H10 :`- . Is if momentum is balanced.
`H20 :`- .
`H30 :`- .
`H40 :`- .
**Remark:**- the number of particles used in the analysis is given
in
`MSTU(62)`.

**Purpose:**- to provide a number of event-analysis options which
can be be used on each new event, with accumulated statistics to be
written out on request. When errors are quoted, these refer to
the uncertainty in the average value for the event sample as a
whole, rather than to the spread of the individual events, i.e. errors decrease like one over the square root of the number of
events analysed. For a correct use of
`PYTABU`, it is not permissible to freely mix generation and analysis of different classes of events, since only one set of statistics counters exists. A single run may still contain sequential `subruns', between which statistics is reset. Whenever an event is analysed, the number of particles/partons used is given in`MSTU(62)`. `MTABU :`- determines which action is to be taken. Generally, a
last digit equal to 0 indicates that the statistics counters for this
option is to be reset; since the counters are reset (by
`DATA`statements) at the beginning of a run, this is not used normally. Last digit 1 leads to an analysis of current event with respect to the desired properties. Note that the resulting action may depend on how the event generated has been rotated, boosted or edited before this call. The statistics accumulated is output in tabular form with last digit 2, while it is dumped in the`PYJETS`common block for last digit 3. The latter option may be useful for interfacing to graphics output. **Warning:**- this routine cannot be used on weighted events,
i.e. in the statistics calculation all events are assumed to come
with the same weight.
`= 10 :`- statistics on parton multiplicity is reset.
`= 11 :`- the parton content of the current event is analysed,
classified according to the flavour content of the hard
interaction and the total number of partons. The flavour
content is assumed given in
`MSTU(161)`and`MSTU(162)`; these are automatically set e.g. in`PYEEVT`and`PYEVNT`calls. Main application is for annihilation events. `= 12 :`- gives a table on parton multiplicity distribution.
`= 13 :`- stores the parton multiplicity distribution of events
in
`PYJETS`, using the following format:`N =`total number of different channels found;`K(I,1) =`32;`K(I,2) =`99;`K(I,3), K(I,4) =`the two flavours of the flavour content;`K(I,5) =`total number of events found with flavour content of`K(I,3)`and`K(I,4)`;`P(I,1) - P(I,5) =`relative probability to find given flavour content and a total of 1, 2, 3, 4 or 5 partons, respectively;`V(I,1) - V(I,5) =`relative probability to find given flavour content and a total of 6-7, 8-10, 11-15, 16-25 or above 25 partons, respectively.

In addition,`MSTU(3) = 1`and`K(N+1,1) =`32;`K(N+1,2) =`99;`K(N+1,5) =`number of events analysed. `= 20 :`- statistics on particle content is reset.
`= 21 :`- the particle/parton content of the current event is
analysed, also for particles which have subsequently decayed and
partons which have fragmented (unless this has been made impossible
by a preceding
`PYEDIT`call). Particles are subdivided into primary and secondary ones, the main principle being that primary particles are those produced in the fragmentation of a string, while secondary come from decay of other particles. `= 22 :`- gives a table of particle content in events.
`= 23 :`- stores particle content in events in
`PYJETS`, using the following format:`N =`number of different particle species found;`K(I,1) =`32;`K(I,2) =`99;`K(I,3) =`particle`KF`code;`K(I,5) =`total number of particles and antiparticles of this species;`P(I,1) =`average number of primary particles per event;`P(I,2) =`average number of secondary particles per event;`P(I,3) =`average number of primary antiparticles per event;`P(I,4) =`average number of secondary antiparticles per event;`P(I,5) =`average total number of particles or antiparticles per event.

In addition,`MSTU(3) = 1`and`K(N+1,1) =`32;`K(N+1,2) =`99;`K(N+1,5) =`number of events analysed;`P(N+1,1) =`average primary multiplicity per event;`P(N+1,2) =`average final multiplicity per event;`P(N+1,3) =`average charged multiplicity per event. `= 30 :`- statistics on factorial moments is reset.
`= 31 :`- analyses the factorial moments of the multiplicity
distribution in different bins of rapidity and azimuth.
Which particles (or partons) are used in the analysis is
determined by the
`MSTU(41)`value. The selection between usage of true rapidity, pion rapidity or pseudorapidity is regulated by`MSTU(42)`. The axis is assumed to be event axis; if this is not desirable find an event axis e.g. with`PYSPHE`or`PYTHRU`and use`PYEDIT(31)`. Maximum (pion-, pseudo-) rapidity, which sets the limit for the rapidity plateau or the experimental acceptance, is given by`PARU(57)`. `= 32 :`- prints a table of the first four factorial moments for various bins of pseudorapidity and azimuth. The moments are properly normalized so that they would be unity (up to statistical fluctuations) for uniform and uncorrelated particle production according to Poisson statistics, but increasing for decreasing bin size in case of `intermittent' behaviour. The error on the average value is based on the actual statistical sample (i.e. does not use any assumptions on the distribution to relate errors to the average values of higher moments). Note that for small bin sizes, where the average multiplicity is small and the factorial moment therefore only very rarely is non-vanishing, moment values may fluctuate wildly and the errors given may be too low.
`= 33 :`- stores the factorial moments in
`PYJETS`, using the format:`N =`30, with`I =`-10 corresponding to results for slicing the rapidity range in bins,`I =`-20 to slicing the azimuth in bins, and`I =`-30 to slicing both rapidity and azimuth, each in bins;`K(I,1) =`32;`K(I,2) =`99;`K(I,3) =`number of bins in rapidity;`K(I,4) =`number of bins in azimuth;`P(I,1) =`rapidity bin size;`P(I,2) - P(I,5) =`- , i.e. mean of second, third, fourth and fifth factorial moment;`V(I,1) =`azimuthal bin size;`V(I,2) - V(I,5) =`statistical errors on - .

In addition,`MSTU(3) =`1 and`K(31,1) =`32;`K(31,2) =`99;`K(31,5) =`number of events analysed. `= 40 :`- statistics on energy-energy correlation is reset.
`= 41 :`- the energy-energy correlation of the
current
event is analysed. Which particles (or partons) are used in the
analysis is determined by the
`MSTU(41)`value. Events are assumed given in their c.m. frame. The weight assigned to a pair and is , where is the sum of energies of all analysed particles in the event. Energies are determined from the momenta of particles, with mass determined according to the`MSTU(42)`value. Statistics is accumulated for the relative angle , ranging between 0 and 180 degrees, subdivided into 50 bins. `= 42 :`- prints a table of the energy-energy correlation and its asymmetry , with errors. The definition of errors is not unique. In our approach each event is viewed as one observation, i.e. an and distribution is obtained by summing over all particle pairs of an event, and then the average and spread of this event-distribution is calculated in the standard fashion. The quoted error is therefore inversely proportional to the square root of the number of events. It could have been possible to view each single particle pair as one observation, which would have given somewhat lower errors, but then one would also be forced to do a complicated correction procedure to account for the pairs in an event not being uncorrelated (two hard jets separated by a given angle typically corresponds to several pairs at about that angle). Note, however, that in our approach the squared error on an bin is smaller than the sum of the squares of the errors on the corresponding bins (as it should be). Also note that it is not possible to combine the errors of two nearby bins by hand from the information given, since nearby bins are correlated (again a trivial consequence of the presence of jets).
`= 43 :`- stores the and in
`PYJETS`, using the format:`N =`25;`K(I,1) =`32;`K(I,2) =`99;`P(I,1) =`for angles between`I-1`and`I`, in units of ;`P(I,2) =`for angles between`50-I`and`51-I`, in units of ;`P(I,3) =`for angles between`I-1`and`I`, in units of ;`P(I,4), P(I,5) :`lower and upper edge of angular range of bin`I`, expressed in radians;`V(I,1) - V(I,3) :`errors on the and values stored in`P(I,1) - P(I,3)`(see`= 42`for comments);`V(I,4), V(I,5) :`lower and upper edge of angular range of bin`I`, expressed in degrees.

In addition,`MSTU(3) = 1`and`K(26,1) =`32;`K(26,2) =`99;`K(26,5) =`number of events analysed. `= 50 :`- statistics on complete final states is reset.
`= 51 :`- analyses the particle content of the final state of
the current event record. During the course of the run, statistics
is thus accumulated on how often different final states appear.
Only final states with up to 8 particles are analysed, and there
is only reserved space for up to 200 different final states.
Most high-energy events have multiplicities far above 8, so the
main use for this tool is to study the effective branching
ratios obtained with a given decay model for e.g. charm or bottom
hadrons. Then
`PY1ENT`may be used to generate one decaying particle at a time, with a subsequent analysis by`PYTABU`. Depending on at what level this studied is to be carried out, some particle decays may be switched off, like . `= 52 :`- gives a list of the (at most 200) channels with up
to 8 particles in the final state, with their relative branching
ratio. The ordering is according to multiplicity, and within
each multiplicity according to an ascending order of
`KF`codes. The`KF`codes of the particles belonging to a given channel are given in descending order. `= 53 :`- stores the final states and branching ratios found in
`PYJETS`, using the format:`N =`number of different explicit final states found (at most 200);`K(I,1) =`32;`K(I,2) =`99;`K(I,5) =`multiplicity of given final state, a number between 1 and 8;`P(I,1) - P(I,5), V(I,1) - V(I,3) :`the`KF`codes of the up to 8 particles of the given final state, converted to real numbers, with trailing zeroes for positions not used;`V(I,5) :`effective branching ratio for the given final state.

In addition,`MSTU(3) = 1`and`K(N+1,1) =`32;`K(N+1,2) =`99;`K(N+1,5) =`number of events analysed;`V(N+1,5) =`summed branching ratio for finals states not given above, either because they contained more than 8 particles or because all 200 channels have been used up.

**Purpose:**- to give access to a number of status codes and
parameters which regulate the performance of fragmentation and event
analysis routines. Most parameters are described in section
; here only those related to the event-analysis
routines are described.

`MSTU(41) :`- (D = 2) partons/particles used in
the event-analysis routines
`PYSPHE`,`PYTHRU`,`PYCLUS`,`PYCELL`,`PYJMAS`,`PYFOWO`and`PYTABU`(`PYTABU(11)`excepted).`= 1 :`- all partons/particles that have not fragmented/decayed.
`= 2 :`- ditto, with the exception of neutrinos and unknown
particles. Also the lowest-lying neutralino (code 1000022),
the graviton (39) and the gravitino (1000039) are treated on an equal
footing with neutrinos. Other similar but not foreseen particles would
not be disregarded automatically, but would have to be put to
`K(I,1) > 10`by hand. `= 3 :`- only charged, stable particles, plus any partons still not fragmented.

`MSTU(42) :`- (D = 2) assumed particle masses, used in
calculating energies
, as subsequently
used in
`PYCLUS`,`PYJMAS`and`PYTABU`(in the latter also for pseudorapidity, pion rapidity or true rapidity selection).`= 0 :`- all particles are assumed massless.
`= 1 :`- all particles, except the photon, are assumed to have the charged pion mass.
`= 2 :`- the true masses are used.

`MSTU(43) :`- (D = 1) storing of event-analysis information (mainly
jet axes), in
`PYSPHE`,`PYTHRU`,`PYCLUS`and`PYCELL`.`= 1 :`- stored after the event proper, in positions
`N + 1`through`N + MSTU(3)`. If several of the routines are used in succession, all but the latest information is overwritten. `= 2 :`- stored with the event proper, i.e. at the end of the
event listing, with
`N`updated accordingly. If several of the routines are used in succession, all the axes determined are available.

`MSTU(44) :`- (D = 4) is the number of the fastest (i.e. with
largest momentum) particles used to construct the (at most) 10 most
promising starting configurations for the thrust axis determination.
`MSTU(45) :`- (D = 2) is the number of different starting
configurations above, which have to converge to the same (best) value
before this is accepted as the correct thrust axis.
`MSTU(46) :`- (D = 1) distance measure used for the joining of
clusters in
`PYCLUS`.`= 1 :`- , i.e. approximately relative transverse
momentum. Anytime two clusters have been joined, particles are
reassigned to the cluster they now are closest to. The distance
cut-off
is stored in
`PARU(44)`. `= 2 :`- distance measure as in
`= 1`, but particles are never reassigned to new jets. `= 3 :`- JADE distance measure , but with dimensions
to correspond approximately to total invariant mass. Particles may
never be reassigned between clusters. The distance cut-off
is stored in
`PARU(44)`. `= 4 :`- as
`= 3`, but a scaled JADE distance is used instead of . The distance cut-off is stored in`PARU(45)`. `= 5 :`- Durham distance measure
, but with
dimensions to correspond approximately to transverse momentum. Particles
may never be reassigned between clusters. The distance cut-off
is stored in
`PARU(44)`. `= 6 :`- as
`= 5`, but a scaled Durham distance is used instead of . The distance cut-off is stored in`PARU(45)`.

`MSTU(47) :`- (D = 1) the minimum number of clusters to be
reconstructed by
`PYCLUS`. `MSTU(48) :`- (D = 0) mode of operation of the
`PYCLUS`routine.`= 0 :`- the cluster search is started from scratch.
`= 1 :`- the clusters obtained in a previous cluster search on the
same event (with
`MSTU(48) = 0`) are to be taken as the starting point for subsequent cluster joining. For this call to have any effect, the joining scale in`PARU(44)`or`PARU(45)`must have been changed. If the event record has been modified after the last`PYCLUS`call, or if any other cluster search parameter setting has been changed, the subsequent result is unpredictable.

`MSTU(51) :`- (D = 25) number of pseudorapidity bins that the range
between
`-PARU(51)`and`+PARU(51)`is divided into to define cell size for`PYCELL`. `MSTU(52) :`- (D = 24) number of azimuthal bins, used to define the
cell size for
`PYCELL`. `MSTU(53) :`- (D = 0) smearing of correct energy, imposed
cell-by-cell in
`PYCELL`, to simulate calorimeter resolution effects.`= 0 :`- no smearing.
`= 1 :`- the transverse energy in a cell, , is smeared
according to a Gaussian distribution with standard deviation
`PARU(55)`, where is given in GeV. The Gaussian is cut off so that`PARU(56)`. `= 2 :`- as
`= 1`, but it is the energy rather than the transverse energy that is smeared.

`MSTU(54) :`- (D = 1) form for presentation of information about
reconstructed clusters in
`PYCELL`, as stored in`PYJETS`according to the`MSTU(43)`value.`= 1 :`- the
`P`vector in each line contains and for the geometric origin of the jet, and for the weighted center of the jet, and jet , respectively. `= 2 :`- the
`P`vector in each line contains a massless four-vector giving the direction of the jet, obtained as

,

where and give the weighted center of a jet and its transverse energy. `= 3 :`- the
`P`vector in each line contains a massive four-vector, obtained by adding the massless four-vectors of all cells that form part of the jet, and calculating the jet mass from . For each cell, the total is summed up, and then translated into a massless four-vector assuming that all the was deposited in the center of the cell.

`MSTU(61) :`- (I) first entry for storage of event-analysis
information in last event analysed with
`PYSPHE`,`PYTHRU`,`PYCLUS`or`PYCELL`. `MSTU(62) :`- (R) number of particles/partons used in the last
event analysis with
`PYSPHE`,`PYTHRU`,`PYCLUS`,`PYCELL`,`PYJMAS`,`PYFOWO`or`PYTABU`. `MSTU(63) :`- (R) in a
`PYCLUS`call, the number of preclusters constructed in order to speed up analysis (should be equal to`MSTU(62)`if`PARU(43) = 0.`). In a`PYCELL`call, the number of cells hit. `MSTU(161), MSTU(162) :`- hard flavours involved
in current event,
as used in an analysis with
`PYTABU(11)`. Either or both may be set 0, to indicate the presence of one or none hard flavours in event. Is normally set by high-level routines, like`PYEEVT`or`PYEVNT`, but can also be set by you.

`PARU(41) :`- (D = 2.) power of momentum-dependence
in
`PYSPHE`, default corresponds to sphericity,`= 1.`to linear event measures. `PARU(42) :`- (D = 1.) power of momentum-dependence in
`PYTHRU`, default corresponds to thrust. `PARU(43) :`- (D = 0.25 GeV) maximum distance
allowed in
`PYCLUS`when forming starting clusters used to speed up reconstruction. The meaning of the parameter is in for`MSTU(46)`or and in else. If`= 0.`, no preclustering is obtained. If chosen too large, more joining may be generated at this stage than is desirable. The main application is at high energies, where some speedup is imperative, and the small details are not so important anyway. `PARU(44) :`- (D = 2.5 GeV) maximum distance
,
below which it is allowed to join two clusters into one in
`PYCLUS`. Is used for`MSTU(46)`and`= 5`, i.e. both for and mass distance measure. `PARU(45) :`- (D = 0.05) maximum distance
or ditto with
,
below which it is allowed to join two clusters into one in
`PYCLUS`for`MSTU(46) =`4 or 6. `PARU(48) :`- (D = 0.0001) convergence criterion for thrust (in
`PYTHRU`) or generalized thrust (in`PYCLUS`), or relative change of (in`PYJMAS`), i.e. when the value changes by less than this amount between two iterations the process is stopped. `PARU(51) :`- (D = 2.5) defines maximum absolute pseudorapidity
used for detector assumed in
`PYCELL`. `PARU(52) :`- (D = 1.5 GeV) gives minimum for a cell
to be considered as a potential jet initiator by
`PYCELL`. `PARU(53) :`- (D = 7.0 GeV) gives minimum summed for
a collection of cells to be accepted as a jet.
`PARU(54) :`- (D = 1.) gives the maximum distance in
from cell initiator
when grouping cells to check whether they qualify as a jet.
`PARU(55) :`- (D = 0.5) when smearing the transverse energy
(or energy, see
`MSTU(53)`) in`PYCELL`, the calorimeter cell resolution is taken to be`PARU(55)`(or`PARU(55)`) for (or ) in GeV. `PARU(56) :`- (D = 2.) maximum factor of upward fluctuation in
transverse energy or energy in a given cell when calorimeter
resolution is included in
`PYCELL`(see`MSTU(53)`). `PARU(57) :`- (D = 3.2) maximum rapidity (or pseudorapidity or
pion rapidity, depending on
`MSTU(42)`) used in the factorial moments analysis in`PYTABU`. `PARU(58) :`- (D = 0. GeV) in a
`PYCELL`call, cells with a transverse energy below`PARP(58)`are removed from further consideration. This may be used to represent a threshold in an actual calorimeter, or may be chosen just to speed up the algorithm in a high-multiplicity environment. `PARU(61) :`- (I) invariant mass of a system analysed with
`PYCLUS`or`PYJMAS`, with energies calculated according to the`MSTU(42)`value. `PARU(62) :`- (R) the generalized thrust obtained after a
successful
`PYCLUS`call, i.e. ratio of summed cluster momenta and summed particle momenta. `PARU(63) :`- (R) the minimum distance between two clusters
in the final cluster configuration after a successful
`PYCLUS`call; is 0 if only one cluster left.