The General Switches and Parameters

The common block PYDAT1 contains the main switches and parameters for the fragmentation and decay treatment, but also for some other aspects. Here one may control in detail what the program is to do, if the default mode of operation is not satisfactory.

Purpose:

to give access to a number of status codes and parameters which regulate the performance of the program as a whole. Here MSTU and PARU are related to utility functions, as well as a few parameters of the Standard Model, while MSTJ and PARJ affect the underlying physics assumptions. Some of the variables in PYDAT1 are described elsewhere, and are therefore here only reproduced as references to the relevant sections. This in particular applies to many coupling constants, which are found in section , and switches of the older dedicated $\mathrm{e}^+\mathrm{e}^-$ machinery, section .

MSTU(1) - MSTU(3) :

variables used by the event study routines, section .

MSTU(4) :

(D=4000) number of lines available in the common block PYJETS. Should always be changed if the dimensions of the K and P arrays are changed by you, but should otherwise never be touched. Maximum allowed value is 10000, unless MSTU(5) is also changed.

MSTU(5) :

(D=10000) is used in building up the special colour-flow information stored in K(I,4) and K(I,5) for K(I,3)= 3, 13 or 14. The generic form for j= 4 or 5 is
K(I,j)$= 2 \times$MSTU(5)$^2 \times$MCFR$+$MSTU(5)$^2 \times$MCTO$+$MSTU(5)$\times$ICFR$+$ICTO,
with notation as in section . One should always have MSTU(5)$\geq$MSTU(4). On a 32 bit machine, values MSTU(5)$> 20000$ may lead to overflow problems, and should be avoided.

MSTU(6) :

(D=500) number of KC codes available in the KCHG, PMAS, MDCY, and CHAF arrays; should be changed if these dimensions are changed.

MSTU(7) :

(D=8000) number of decay channels available in the MDME, BRAT and KFDP arrays; should be changed if these dimensions are changed.

MSTU(10) :

(D=2) use of parton/particle masses in filling routines (PY1ENT, PY2ENT, PY3ENT, PY4ENT).

= 0 :

assume the mass to be zero.

= 1 :

keep the mass value stored in P(I,5), whatever it is. (This may be used e.g. to describe kinematics with off-mass-shell partons).

= 2 :

find masses according to mass tables as usual.

MSTU(11) - MSTU(12) :

variables used by the event study routines, section .

MSTU(13) :

(D=1) writing of information on variable values changed by a PYGIVE call.

= 0 :

no information is provided.

= 1 :

information is written to standard output.

MSTU(14) :

variable used by the event study routines, section .

MSTU(15) :

(D=0) decides how PYLIST shows empty lines, which are interspersed among ordinary particles in the event record.

= 0 :

do not print lines with K(I,1)$\leq 0$.

= 1 :

do not print lines with K(I,1)$< 0$.

= 2 :

print all lines.

MSTU(16) :

(D=1) choice of mother pointers for the particles produced by a fragmenting parton system.

= 1 :

all primary particles of a system point to a line with KF = 92 or 93, for string or independent fragmentation, respectively, or to a line with KF = 91 if a parton system has so small a mass that it is forced to decay into one or two particles. The two (or more) shower initiators of a showering parton system point to a line with KF = 94. The entries with KF = 91-94 in their turn point back to the predecessor partons, so that the KF = 91-94 entries form a part of the event history proper.

= 2 :

although the lines with KF = 91-94 are present, and contain the correct mother and daughter pointers, they are not part of the event history proper, in that particles produced in string fragmentation point directly to either of the two endpoint partons of the string (depending on the side they were generated from), particles produced in independent fragmentation point to the respective parton they were generated from, particles in small mass systems point to either endpoint parton, and shower initiators point to the original on-mass-shell counterparts. Also the daughter pointers bypass the KF = 91-94 entries. In independent fragmentation, a parton need not produce any particles at all, and then have daughter pointers 0.
When junctions are present, the related primary baryon points back to the junction around which it is produced. More generally, consider a system stored as $\mathrm{q}_1\mathrm{q}_2\mathrm{J}\mathrm{q}_3$. In the listing of primary hadrons coming from this system, the first ones will have K(I,3) pointers back to $\mathrm{q}_1$, either they come from the hadronization of the $\mathrm{q}_1$ or $\mathrm{q}_2$ string pieces. (In principle the hadrons could be classified further, but this has not been done.) Then comes the junction baryon, which may be followed by hadrons again pointing back to $\mathrm{q}_1$. This is because the final string piece, between the junction and $\mathrm{q}_3$, is fragmented from both ends with a joining to conserve overall energy and momentum. (Typically the two shortest strings are put ahead of the junction.) More properly these hadrons also could have pointed back to the junction, but then the special status of the junction baryon would have been lost. The final hadrons point to $\mathrm{q}_3$, and have fragmented off this end of the string piece in to the junction. The above example generalizes easily to topologies with two junctions, e.g. $\mathrm{q}_1\mathrm{q}_2\mathrm{J}\mathrm{J}\overline{\mathrm{q}}_3\overline{\mathrm{q}}_4$, where now particles in the central $\mathrm{J}\mathrm{J}$ string would point either to $\mathrm{q}_1$ or $\overline{\mathrm{q}}_4$ depending on production side.

Note :

MSTU(16) should not be changed between the generation of an event and the translation of this event record with a PYHEPC call, since this may give an erroneous translation of the event history.

MSTU(17) :

(D=0) storage option for MSTU(90) and associated information on $z$ values for heavy-flavour production.

= 0 :

MSTU(90) is reset to zero at each PYEXEC call. This is the appropriate course if PYEXEC is only called once per event, as is normally the case when you do not yourself call PYEXEC.

= 1 :

you have to reset MSTU(90) to zero yourself before each new event. This is the appropriate course if several PYEXEC calls may appear for one event, i.e. if you call PYEXEC directly.

MSTU(19) :

(D=0) advisory warning for unphysical flavour setups in PY2ENT, PY3ENT or PY4ENT calls.

= 0 :

yes.

= 1 :

no; MSTU(19) is reset to 0 in such a call.

MSTU(20) :

(D=0) flag for the initialization status of the PYCOMP routine. A value 0 indicates that tables should be (re)initialized, after which it is set 1. In case you change the KCHG(KC,4) array you should reset MSTU(20)=0 to force a re-initialization at the next PYCOMP call.

MSTU(21) :

(D=2) check on possible errors during program execution. Obviously no guarantee is given that all errors will be caught, but some of the most trivial user-caused errors may be found.

= 0 :

errors do not cause any immediate action, rather the program will try to cope, which may mean e.g. that it runs into an infinite loop.

= 1 :

parton/particle configurations are checked for possible errors. In case of problem, an exit is made from the misbehaving subprogram, but the generation of the event is continued from there on. For the first MSTU(22) errors a message is printed; after that no messages appear.

= 2 :

parton/particle configurations are checked for possible errors. In case of problem, an exit is made from the misbehaving subprogram, and subsequently from PYEXEC. You may then choose to correct the error, and continue the execution by another PYEXEC call. For the first MSTU(22) errors a message is printed, after that the last event is printed and execution is stopped.

MSTU(22) :

(D=10) maximum number of errors that are printed.

MSTU(23) :

(I) count of number of errors experienced to date. Is not updated for errors in a string system containing junctions. (Since errors occasionally do happen there, and are difficult to eliminate altogether.)

MSTU(24) :

(R) type of latest error experienced; reason that event was not generated in full. Is reset at each PYEXEC call.

= 0 :

no error experienced.

= 1 :

program has reached end of or is writing outside PYJETS memory.

= 2 :

unknown flavour code or unphysical combination of codes; may also be caused by erroneous string connection information.

= 3 :

energy or mass too small or unphysical kinematical variable setup.

= 4 :

program is caught in an infinite loop.

= 5 :

momentum, energy or charge was not conserved (even allowing for machine precision errors, see PARU(11)); is evaluated only after event has been generated in full, and does not apply when independent fragmentation without momentum conservation was used.

= 6 :

error call from outside the fragmentation/decay package (e.g. the $\mathrm{e}^+\mathrm{e}^-$ routines).

= 7 :

inconsistent particle data input in PYUPDA (MUPDA = 2,3) or other PYUPDA-related problem.

= 8 :

problems in more peripheral service routines.

= 9 :

various other problems.

MSTU(25) :

(D=1) printing of warning messages.

= 0 :

no warnings are written.

= 1 :

first MSTU(26) warnings are printed, thereafter no warnings appear.

MSTU(26) :

(D=10) maximum number of warnings that are printed.

MSTU(27) :

(I) count of number of warnings experienced to date.

MSTU(28) :

(R) type of latest warning given, with codes parallelling those for MSTU(24), but of a less serious nature.

MSTU(29) :

(I) denotes the presence (1) or not (0) of a junction in the latest system studied. Used to decide whether to update the MSTU(23) counter in case of errors.

MSTU(30) :

(I) count of number of errors experienced to date, equivalent to MSTU(23) except that it is also updated for errors in a string system containing junctions.

MSTU(31) :

(I) number of PYEXEC calls in present run.

MSTU(32) - MSTU(33) :

variables used by the event study routines, section .

MSTU(41) - MSTU(63) :

switches for event-analysis routines, see section .

MSTU(70) - MSTU(80) :

variables used by the event study routines, section .

MSTU(90) :

number of heavy-flavour hadrons (i.e. hadrons containing charm or bottom) produced in the fragmentation stage of the current event, for which the positions in the event record are stored in MSTU(91) - MSTU(98) and the $z$ values in the fragmentation in PARU(91) - PARU(98). At most eight values will be stored (normally this is no problem). No $z$ values can be stored for those heavy hadrons produced when a string has so small mass that it collapses to one or two particles, nor for those produced as one of the final two particles in the fragmentation of a string. If MSTU(17)=1, MSTU(90) should be reset to zero by you before each new event, else this is done automatically.

MSTU(91) - MSTU(98) :

the first MSTU(90) positions will be filled with the line numbers of the heavy-flavour hadrons produced in the current event. See MSTU(90) for additional comments. Note that the information is corrupted by calls to PYEDIT with options 0-5 and 21-23; calls with options 11-15 work, however.

MSTU(101) - MSTU(118) :

switches related to couplings, see section .

MSTU(121) - MSTU(125) :

internally used in the advanced popcorn code, see subsection .

MSTU(131) - MSTU(140) :

internally used in the advanced popcorn code, see subsection .

MSTU(161), MSTU(162) :

information used by event-analysis routines, see section .

PARU(1) :

(R) $\pi \approx 3.141592653589793$.

PARU(2) :

(R) $2\pi \approx 6.283185307179586$.

PARU(3) :

(D=0.197327) conversion factor for GeV$^{-1} \to$ fm or fm$^{-1} \to$ GeV.

PARU(4) :

(D=5.06773) conversion factor for fm $\to$ GeV$^{-1}$ or GeV $\to$ fm$^{-1}$.

PARU(5) :

(D=0.389380) conversion factor for GeV$^{-2} \to$ mb or mb$^{-1} \to$ GeV$^2$.

PARU(6) :

(D=2.56819) conversion factor for mb $\to$ GeV$^{-2}$ or GeV$^2 \to$ mb$^{-1}$.

PARU(11) :

(D=0.001) relative error, i.e. non-conservation of momentum and energy divided by total energy, that may be attributable to machine precision problems before a physics error is suspected (see MSTU(24)=5).

PARU(12) :

(D=0.09 GeV$^2$) effective cut-off in squared mass, below which partons may be recombined to simplify (machine precision limited) kinematics of string fragmentation. (Default chosen to be of the order of a light quark mass, or half a typical light meson mass.)

PARU(13) :

(D=0.01) effective angular cut-off in radians for recombination of partons, used in conjunction with PARU(12).

PARU(21) :

(I) contains the total energy $W$ of all first generation partons/particles after a PYEXEC call; to be used by the PYP function for I>0, J= 20-25.

PARU(41) - PARU(63) :

parameters for event-analysis routines, see section .

PARU(91) - PARU(98) :

the first MSTU(90) positions will be filled with the fragmentation $z$ values used internally in the generation of heavy-flavour hadrons -- how these are translated into the actual energies and momenta of the observed hadrons is a complicated function of the string configuration. The particle with $z$ value stored in PARU(i) is to be found in line MSTU(i) of the event record. See MSTU(90) and MSTU(91) - MSTU(98) for additional comments.

PARU(101) - PARU(195) :

various coupling constants and parameters related to couplings, see section .

MSTJ(1) :

(D=1) choice of fragmentation scheme.

= 0 :

no jet fragmentation at all.

= 1 :

string fragmentation according to the Lund model.

= 2 :

independent fragmentation, according to specification in MSTJ(2) and MSTJ(3).

MSTJ(2) :

(D=3) gluon jet fragmentation scheme in independent fragmentation.

= 1 :

a gluon is assumed to fragment like a random $\d$, $\u$ or $\mathrm{s}$ quark or antiquark.

= 2 :

as =1, but longitudinal (see PARJ(43), PARJ(44) and PARJ(59)) and transverse (see PARJ(22)) momentum properties of quark or antiquark substituting for gluon may be separately specified.

= 3 :

a gluon is assumed to fragment like a pair of a $\d$, $\u$ or $\mathrm{s}$ quark and its antiquark, sharing the gluon energy according to the Altarelli-Parisi splitting function.

= 4 :

as =3, but longitudinal (see PARJ(43), PARJ(44) and PARJ(59)) and transverse (see PARJ(22)) momentum properties of quark and antiquark substituting for gluon may be separately specified.

MSTJ(3) :

(D=0) energy, momentum and flavour conservation options in independent fragmentation. Whenever momentum conservation is described below, energy and flavour conservation is also implicitly assumed.

= 0 :

no explicit conservation of any kind.

= 1 :

particles share momentum imbalance compensation according to their energy (roughly equivalent to boosting event to c.m. frame). This is similar to the approach in the Ali et al. program [Ali80].

= 2 :

particles share momentum imbalance compensation according to their longitudinal mass with respect to the imbalance direction.

= 3 :

particles share momentum imbalance compensation equally.

= 4 :

transverse momenta are compensated separately within each jet, longitudinal momenta are rescaled so that ratio of final jet to initial parton momentum is the same for all the jets of the event. This is similar to the approach in the Hoyer et al. program [Hoy79].

= 5 :

only flavour is explicitly conserved.

= 6 - 10 :

as =1 - 5, except that above several colour singlet systems that followed immediately after each other in the event listing (e.g. $\mathrm{q}\overline{\mathrm{q}}\mathrm{q}\overline{\mathrm{q}}$) were treated as one single system, whereas here they are treated as separate systems.

= -1 :

independent fragmentation, where also particles moving backwards with respect to the jet direction are kept, and thus the amount of energy and momentum mismatch may be large.

MSTJ(11) :

(D=4) choice of longitudinal fragmentation function, i.e. how large a fraction of the energy available a newly-created hadron takes.

= 1 :

the Lund symmetric fragmentation function, see PARJ(41) - PARJ(45).

= 2 :

choice of some different forms for each flavour separately, see PARJ(51) - PARJ(59).

= 3 :

hybrid scheme, where light flavours are treated with symmetric Lund (=1), but charm and heavier can be separately chosen, e.g. according to the Peterson/SLAC function (=2).

= 4 :

the Lund symmetric fragmentation function (=1), for heavy endpoint quarks modified according to the Bowler (Artru-Mennessier, Morris) space-time picture of string evolution, see PARJ(46).

= 5 :

as =4, but with possibility to interpolate between Bowler and Lund separately for $\c$ and $\b$; see PARJ(46) and PARJ(47).

MSTJ(12) :

(D=2) choice of baryon production model.

= 0 :

no baryon-antibaryon pair production at all; initial diquark treated as a unit.

= 1 :

diquark-antidiquark pair production allowed; diquark treated as a unit.

= 2 :

diquark-antidiquark pair production allowed, with possibility for diquark to be split according to the `popcorn' scheme.

= 3 :

as =2, but additionally the production of first rank baryons may be suppressed by a factor PARJ(19).

= 4 :

as =2, but diquark vertices suffer an extra suppression of the form $1-\exp(\rho\Gamma)$, where $\rho\approx0.7\mathrm{GeV}^{-2}$ is stored in PARF(192).

= 5 :

Advanced version of the popcorn model. Independent of PARJ(3-7). Instead depending on PARJ(8-10). When using this option PARJ(1) needs to enhanced by approx. a factor 2 (i.e. it losses a bit of its normal meaning), and PARJ(18) is suggested to be set to 0.19. See section for further details.

MSTJ(13) :

(D=0) generation of transverse momentum for endpoint quark(s) of single quark jet or $\mathrm{q}\overline{\mathrm{q}}$ jet system (in multijet events no endpoint transverse momentum is ever allowed for).

= 0 :

no transverse momentum for endpoint quarks.

= 1 :

endpoint quarks obtain transverse momenta like ordinary $\mathrm{q}\overline{\mathrm{q}}$ pairs produced in the field (see PARJ(21)); for 2-jet systems the endpoints obtain balancing transverse momenta.

MSTJ(14) :

(D=1) treatment of a colour-singlet parton system with a low invariant mass.

= 0 :

no precautions are taken, meaning that problems may occur in PYSTRF (or PYINDF) later on. Warning messages are issued when low masses are encountered, however, or when the flavour or colour configuration appears to be unphysical.

= 1 :

small parton systems are allowed to collapse into two particles or, failing that, one single particle. Normally all small systems are treated this way, starting with the smallest one, but some systems would require more work and are left untreated; they include diquark-antidiquark pairs below the two-particle threshold. See further MSTJ(16) and MSTJ(17).

= -1 :

special option for PYPREP calls, where no precautions are taken (as for =0), but, in addition, no checks are made on the presence of small-mass systems or unphysical flavour or colour configurations; i.e. PYPREP only rearranges colour strings.

MSTJ(15) :

(D=0) production probability for new flavours.

= 0 :

according to standard Lund parameterization, as given by PARJ(1) - PARJ(20).

= 1 :

according to probabilities stored in PARF(201) - PARF(1960); note that no default values exist here, i.e. PARF must be set by you. The MSTJ(12) switch can still be used to set baryon production mode, with the modification that MSTJ(12)=2 here allows an arbitrary number of mesons to be produced between a baryon and an antibaryon (since the probability for diquark $\to$ meson $+$ new diquark is assumed independent of prehistory).

MSTJ(16) :

(D=2) mode of cluster treatment (where a cluster is a low-mass string that can fragment to two particles at the most).

= 0 :

old scheme. Cluster decays (to two hadrons) are isotropic. In cluster collapses (to one hadron), energy-momentum compensation is to/from the parton or hadron furthest away in mass.

= 1 :

intermediate scheme. Cluster decays are anisotropic in a way that is intended to mimic the Gaussian $p_{\perp}$ suppression and string `area law' of suppressed rapidity orderings of ordinary string fragmentation. In cluster collapses, energy-momentum compensation is to/from the string piece most closely moving in the same direction as the cluster. Excess energy is put as an extra gluon on this string piece, while a deficit is taken from both endpoints of this string piece as a common fraction of their original momentum.

= 2 :

new default scheme. Essentially as =1 above, except that an energy deficit is preferentially taken from the endpoint of the string piece that is moving closest in direction to the cluster.

MSTJ(17) :

(D=2) number of attempts made to find two hadrons that have a combined mass below the cluster mass, and thus allow a cluster to decay to two hadrons rather than collapse to one. Thus the larger MSTJ(17), the smaller the fraction of collapses. At least one attempt is always made, and this was the old default behaviour.

MSTJ(18) :

(D=10) maximum number of times the junction rest frame is evaluated with improved knowledge of the proper energies. When the boost in an iteration corresponds to a $\gamma < 1.01$ the iteration would be stopped sooner. An iterative solution is required since the rest frame of the junction is defined by a vector sum of energies (see PARP(48)) that are assumed already known in this rest frame. (In practice, this iteration is normally a minor effect, of more conceptual than practical impact.)

MSTJ(19) :

(D=0) in a string system containing two junctions (or, more properly, a junction and an antijunction), there is a possibility for these two to disappear, by an `annihilation' that gives two separate strings [Sjö03]. That is, a configuration like $\mathrm{q}_1\mathrm{q}_2\mathrm{J}\mathrm{J}\overline{\mathrm{q}}_3\overline{\mathrm{q}}_4$ can collapse to $\mathrm{q}_1 \overline{\mathrm{q}}_3$ plus $\mathrm{q}_2 \overline{\mathrm{q}}_4$.

= 0 :

the selection between the two alternatives is made dynamically, so as to pick the string configuration with the smallest length.

= 1 :

the two-junction topology always remains.

= 2 :

the two-junction topology always collapses to two separate strings.

Note:

the above also applies, suitably generalized, when parton-shower activity is included in the event. If the shower in between the two junctions comes to contain a $\mathrm{g}\to \mathrm{q}\overline{\mathrm{q}}$ branching, however, the system inevitable is split into two separate junction systems $\mathrm{q}_1 \mathrm{q}_2 \mathrm{J}\mathrm{q}$ plus $\overline{\mathrm{q}}\mathrm{J} \overline{\mathrm{q}}_3 \overline{\mathrm{q}}_4$

MSTJ(21) :

(D=2) form of particle decays.

= 0 :

all particle decays are inhibited.

= 1 :

a particle declared unstable in the MDCY vector, and with decay channels defined, may decay within the region given by MSTJ(22). A particle may decay into partons, which then fragment further according to the MSTJ(1) value.

= 2 :

as =1, except that a $\mathrm{q}\overline{\mathrm{q}}$ parton system produced in a decay (e.g. of a $\mathrm{B}$ meson) is always allowed to fragment according to string fragmentation, rather than according to the MSTJ(1) value (this means that momentum, energy and charge are conserved in the decay).

MSTJ(22) :

(D=1) cut-off on decay length for a particle that is allowed to decay according to MSTJ(21) and the MDCY value.

= 1 :

a particle declared unstable is also forced to decay.

= 2 :

a particle is decayed only if its average proper lifetime is smaller than PARJ(71).

= 3 :

a particle is decayed only if the decay vertex is within a distance PARJ(72) of the origin.

= 4 :

a particle is decayed only if the decay vertex is within a cylindrical volume with radius PARJ(73) in the $xy$-plane and extent to $\pm$PARJ(74) in the $z$ direction.

MSTJ(23) :

(D=1) possibility of having a shower evolving from a $\mathrm{q}\overline{\mathrm{q}}$ pair created as decay products. This switch only applies to decays handled by PYDECY rather than PYRESD, and so is of less relevance today.

= 0 :

never.

= 1 :

whenever the decay channel matrix-element code is MDME(IDC,2)= 4, 32, 33, 44 or 46, the two first decay products (if they are partons) are allowed to shower, like a colour-singlet subsystem, with maximum virtuality given by the invariant mass of the pair.

MSTJ(24) :

(D=2) particle masses.

= 0 :

discrete mass values are used.

= 1 :

particles registered as having a mass width in the PMAS vector are given a mass according to a truncated Breit-Wigner shape, linear in $m$, eq. ().

= 2 :

as =1, but gauge bosons (actually all particles with $\vert$KF$\vert \leq 100$) are distributed according to a Breit-Wigner quadratic in $m$, as obtained from propagators.

= 3 :

as =1, but Breit-Wigner shape is always quadratic in $m$, eq. ().

MSTJ(26) :

(D=2) inclusion of $\mathrm{B}$- $\overline{\mathrm{B}}$ mixing in decays.

= 0 :

no.

= 1 :

yes, with mixing parameters given by PARJ(76) and PARJ(77). Mixing decays are not specially marked.

= 2 :

yes, as =1, but a $\mathrm{B}$ ( $\overline{\mathrm{B}}$) that decays as a $\overline{\mathrm{B}}$ ($\mathrm{B}$) is marked as K(I,1)=12 rather than the normal K(I,1)=11.

MSTJ(28) :

(D=0) call to an external $\tau$ decay library like TAUOLA. For this option to be meaningful, it is up to you to write the appropriate interface and include that in the routine PYTAUD, as explained in section .

= 0 :

not done, i.e. the internal PYDECY treatment is used.

= 1 :

done whenever the $\tau$ mother particle species can be identified, else the internal PYDECY treatment is used. Normally the mother particle should always be identified, but it is possible for you to remove event history information or to add extra $\tau$'s directly to the event record, and then the mother is not known.

= 2 :

always done.

MSTJ(38) - MSTJ(50) :

switches for time-like parton showers, see section .

MSTJ(51) :

(D=0) inclusion of Bose-Einstein effects.

= 0 :

no effects included.

= 1 :

effects included according to an exponential parameterization $f_2(Q) = 1 +$PARJ(92) $\times \exp(-Q/$PARJ(93)$)$, where $f_2(Q)$ represents the ratio of particle production at $Q$ with Bose-Einstein effects to that without, and the relative momentum $Q$ is defined by $Q^2(p_1,p_2) = -(p_1 - p_2)^2 = (p_1 + p_2)^2 - 4m^2$. Particles with width broader than PARJ(91) are assumed to have time to decay before Bose-Einstein effects are to be considered.

= 2 :

effects included according to a Gaussian parameterization $f_2(Q) = 1 +$PARJ(92) $\times \exp(- (Q/$PARJ(93)$)^2 )$, with notation and comments as above.

MSTJ(52) :

(D=3) number of particle species for which Bose-Einstein correlations are to be included, ranged along the chain $\pi^+$, $\pi^-$, $\pi^0$, $\mathrm{K}^+$, $\mathrm{K}^-$, $\mathrm{K}^0_{\mathrm{L}}$, $\mathrm{K}^0_{\mathrm{S}}$, $\eta$ and $\eta'$. Default corresponds to including all pions ($\pi^+$, $\pi^-$, $\pi^0$), 7 to including all Kaons as well, and 9 is maximum.

MSTJ(53) :

(D=0) In $\mathrm{e}^+ \mathrm{e}^- \to \mathrm{W}^+ \mathrm{W}^-$, $\mathrm{e}^+\mathrm{e}^-\to \mathrm{Z}^0 \mathrm{Z}^0$, or if PARJ(94)$>0$ and there are several strings in the event, apply BE algorithm

= 0 :

on all pion pairs.

= 1 :

only on pairs were both pions come from the same $\mathrm{W}/\mathrm{Z}/$string.

= 2 :

only on pairs were the pions come from different $\mathrm{W}/\mathrm{Z}/$strings.

= -2 :

when calculating balancing shifts for pions from same $\mathrm{W}/\mathrm{Z}/$string, only consider pairs from this $\mathrm{W}/\mathrm{Z}/$string.

Note:

if colour reconnections has occurred in an event, the distinction between pions coming from different $\mathrm{W}/ \mathrm{Z}$'s is lost.

MSTJ(54) :

(D=2) Alternative local energy compensation. (Notation in brackets refer to the one used in [Lön95].)

= 0 :

global energy compensation ($\mathrm{BE}_0$).

= 1 :

compensate with identical pairs by negative BE enhancement with a third of the radius ($\mathrm{BE}_3$).

= 2 :

ditto, but with the compensation constrained to vanish at $Q=0$, by an additional $1 - \exp(-Q^2R^2/4)$ factor ( $\mathrm{BE}_{32}$).

= -1 :

compensate with pair giving the smallest invariant mass ($BE_m$).

= -2 :

compensate with pair giving the smallest string length ($BE_{\lambda}$).

MSTJ(55) :

(D=0) Calculation of difference vector.

= 0 :

in the lab frame.

= 1 :

in the c.m. of the given pair.

MSTJ(56) :

(D=0) In $\mathrm{e}^+ \mathrm{e}^- \to \mathrm{W}^+ \mathrm{W}^-$ or $\mathrm{e}^+\mathrm{e}^-\to \mathrm{Z}^0 \mathrm{Z}^0$ include distance between $\mathrm{W}/ \mathrm{Z}$'s.

= 0 :

radius is the same for all pairs.

= 1 :

radius for pairs from different $\mathrm{W}/ \mathrm{Z}$'s is $R+\delta R_{\mathrm{W}\mathrm{W}}$ ( $R+\delta R_{\mathrm{Z}\mathrm{Z}}$), where $\delta R$ is the generated distance between the decay vertices. (When considering $\mathrm{W}$ or $\mathrm{Z}$ pairs with an energy well above threshold, this should give more realistic results.)

MSTJ(57) :

(D=1) Penalty for shifting particles with close-by identical neighbours in local energy compensation, MSTJ(54) < 0.

= 0 :

no penalty.

= 1 :

penalty.

MSTJ(91) :

(I) flag when generating gluon jet with options MSTJ(2)= 2 or 4 (then =1, else =0).

MSTJ(92) :

(I) flag that a $\mathrm{q}\overline{\mathrm{q}}$ or $\mathrm{g}\mathrm{g}$ pair or a $\mathrm{g}\mathrm{g}\mathrm{g}$ triplet created in PYDECY should be allowed to shower, is 0 if no pair or triplet, is the entry number of the first parton if a pair indeed exists, is the entry number of the first parton, with a $-$ sign, if a triplet indeed exists.

MSTJ(93) :

(I) switch for PYMASS action. Is reset to 0 in PYMASS call.

= 0 :

ordinary action.

= 1 :

light ($\d$, $\u$, $\mathrm{s}$, $\c$, $\b$) quark masses are taken from PARF(101) - PARF(105) rather than PMAS(1,1) - PMAS(5,1). Diquark masses are given as sum of quark masses, without spin splitting term.

= 2 :

as =1. Additionally the constant terms PARF(121) and PARF(122) are subtracted from quark and diquark masses, respectively.

MSTJ(101) - MSTJ(121) :

switches for $\mathrm{e}^+\mathrm{e}^-$ event generation, see section .

PARJ(1) :

(D=0.10) is ${\cal P}(\mathrm{q}\mathrm{q})/{\cal P}(\mathrm{q})$, the suppression of diquark-antidiquark pair production in the colour field, compared with quark-antiquark production.

PARJ(2) :

(D=0.30) is ${\cal P}(\mathrm{s})/{\cal P}(u)$, the suppression of $\mathrm{s}$ quark pair production in the field compared with $\u$ or $\d$ pair production.

PARJ(3) :

(D=0.4) is $({\cal P}(\u\mathrm{s})/{\cal P}(\u\d ))/({\cal P}(\mathrm{s})/{\cal P}(\d ))$, the extra suppression of strange diquark production compared with the normal suppression of strange quarks.

PARJ(4) :

(D=0.05) is $(1/3){\cal P}(\u\d _1)/{\cal P}(\u\d _0)$, the suppression of spin 1 diquarks compared with spin 0 ones (excluding the factor 3 coming from spin counting).

PARJ(5) :

(D=0.5) parameter determining relative occurrence of baryon production by $BM\overline{B}$ and by $B\overline{B}$ configurations in the simple popcorn baryon production model, roughly ${\cal P}(BM\overline{B})/({\cal P}(B\overline{B})+{\cal P}(BM\overline{B})) =$ PARJ(5)$/(0.5+$PARJ(5)$)$. This and subsequent baryon parameters are modified in the advanced popcorn scenario, see subsection .

PARJ(6) :

(D=0.5) extra suppression for having a $\mathrm{s}\overline{\mathrm{s}}$ pair shared by the $B$ and $\overline{B}$ of a $BM\overline{B}$ situation.

PARJ(7) :

(D=0.5) extra suppression for having a strange meson $M$ in a $BM\overline{B}$ configuration.

PARJ(8) - PARJ(10) :

used in the advanced popcorn scenario, see subsection .

PARJ(11) - PARJ(17) :

parameters that determine the spin of mesons when formed in fragmentation or decays.

PARJ(11) :

(D=0.5) is the probability that a light meson (containing $\u$ and $\d$ quarks only) has spin 1 (with 1-PARJ(11) the probability for spin 0).

PARJ(12) :

(D=0.6) is the probability that a strange meson has spin 1.

PARJ(13) :

(D=0.75) is the probability that a charm or heavier meson has spin 1.

PARJ(14) :

(D=0.) is the probability that a spin = 0 meson is produced with an orbital angular momentum 1, for a total spin = 1.

PARJ(15) :

(D=0.) is the probability that a spin = 1 meson is produced with an orbital angular momentum 1, for a total spin = 0.

PARJ(16) :

(D=0.) is the probability that a spin = 1 meson is produced with an orbital angular momentum 1, for a total spin = 1.

PARJ(17) :

(D=0.) is the probability that a spin = 1 meson is produced with an orbital angular momentum 1, for a total spin = 2.

Note :

the end result of the numbers above is that, with i = 11, 12 or 13, depending on flavour content,
${\cal P}(S = 0, L = 0, J = 0) = (1 - \mathtt{PARJ(i)}) \times (1 - \mathtt{PARJ(14)})$,
${\cal P}(S = 0, L = 1, J = 1) = (1 - \mathtt{PARJ(i)}) \times \mathtt{PARJ(14)}$,
${\cal P}(S = 1, L = 0, J = 1) =$
  $\mathtt{PARJ(i)} \times (1 - \mathtt{PARJ(15)} - \mathtt{PARJ(16)} - \mathtt{PARJ(17)})$,
${\cal P}(S = 1, L = 1, J = 0) = \mathtt{PARJ(i)} \times \mathtt{PARJ(15)}$,
${\cal P}(S = 1, L = 1, J = 1) = \mathtt{PARJ(i)} \times \mathtt{PARJ(16)}$,
${\cal P}(S = 1, L = 1, J = 2) = \mathtt{PARJ(i)} \times \mathtt{PARJ(17)}$,
where $S$ is the quark `true' spin and $J$ is the total spin, usually called the spin $s$ of the meson.

PARJ(18) :

(D=1.) is an extra suppression factor multiplying the ordinary SU(6) weight for spin $3$/2 baryons, and hence a means to break SU(6) in addition to the dynamic breaking implied by PARJ(2), PARJ(3), PARJ(4), PARJ(6) and PARJ(7).

PARJ(19) :

(D=1.) extra baryon suppression factor, which multiplies the ordinary diquark-antidiquark production probability for the breakup closest to the endpoint of a string, but leaves other breaks unaffected. Is only used for MSTJ(12)=3.

PARJ(21) :

(D=0.36 GeV) corresponds to the width $\sigma$ in the Gaussian $p_x$ and $p_y$ transverse momentum distributions for primary hadrons. See also PARJ(22) - PARJ(24).

PARJ(22) :

(D=1.) relative increase in transverse momentum in a gluon jet generated with MSTJ(2)= 2 or 4.

PARJ(23), PARJ(24) :

(D=0.01, 2.) a fraction PARJ(23) of the Gaussian transverse momentum distribution is taken to be a factor PARJ(24) larger than input in PARJ(21). This gives a simple parameterization of non-Gaussian tails to the Gaussian shape assumed above.

PARJ(25) :

(D=1.) extra suppression factor for $\eta$ production in fragmentation; if an $\eta$ is rejected a new flavour pair is generated and a new hadron formed.

PARJ(26) :

(D=0.4) extra suppression factor for $\eta'$ production in fragmentation; if an $\eta'$ is rejected a new flavour pair is generated and a new hadron formed.

PARJ(31) :

(D=0.1 GeV) gives the remaining $W_+$ below which the generation of a single jet is stopped. (It is chosen smaller than a pion mass, so that no hadrons moving in the forward direction are missed.)

PARJ(32) :

(D=1. GeV) is, with quark masses added, used to define the minimum allowable energy of a colour-singlet parton system.

PARJ(33) - PARJ(34) :

(D=0.8 GeV, 1.5 GeV) are, together with quark masses, used to define the remaining energy below which the fragmentation of a parton system is stopped and two final hadrons formed. PARJ(33) is normally used, except for MSTJ(11)=2, when PARJ(34) is used.

PARJ(36) :

(D=2.) represents the dependence on the mass of the final quark pair for defining the stopping point of the fragmentation. Is strongly correlated to the choice of PARJ(33) - PARJ(35).

PARJ(37) :

(D=0.2) relative width of the smearing of the stopping point energy.

PARJ(39) :

(D=0.08 GeV$^{-2}$) refers to the probability for reverse rapidity ordering of the final two hadrons, according to eq. (), for MSTJ(11)=2 (for other MSTJ(11) values PARJ(42) is used).

PARJ(40):

(D=1.) possibility to modify the probability for reverse rapidity ordering of the final two hadrons in the fragmentation of a string with PYSTRF, or from the only two hadrons of a low-mass string considered in PYPREP. Modifies eq. () to ${\cal P}_{\mathrm{reverse}} = 1/(1 + \exp(\mathtt{PARJ(40)}b\Delta))$.

PARJ(41), PARJ(42) :

(D=0.3, 0.58 GeV$^{-2}$) give the $a$ and $b$ parameters of the symmetric Lund fragmentation function for MSTJ(11)=1, 4 and 5 (and MSTJ(11)=3 for ordinary hadrons).

PARJ(43), PARJ(44) :

(D=0.5, 0.9 GeV$^{-2}$) give the $a$ and $b$ parameters as above for the special case of a gluon jet generated with IF and MSTJ(2)= 2 or 4.

PARJ(45) :

(D=0.5) the amount by which the effective $a$ parameter in the Lund flavour dependent symmetric fragmentation function is assumed to be larger than the normal $a$ when diquarks are produced. More specifically, referring to eq. (), $a_{\alpha} =$PARJ(41) when considering the fragmentation of a quark and = PARJ(41) + PARJ(45) for the fragmentation of a diquark, with corresponding expression for $a_{\beta}$ depending on whether the newly created object is a quark or diquark (for an independent gluon jet generated with MSTJ(2)= 2 or 4, replace PARJ(41) by PARJ(43)). In the popcorn model, a meson created in between the baryon and antibaryon has $a_{\alpha} = a_{\beta} =$PARJ(41) + PARJ(45).

PARJ(46), PARJ(47) :

(D=2*1.) modification of the Lund symmetric fragmentation for heavy endpoint quarks according to the recipe by Bowler, available when MSTJ(11)= 4 or 5 is selected. The shape is given by eq. (). If MSTJ(11)=4 then $r_{\mathrm{Q}} =$PARJ(46) for both $\c$ and $\b$, while if MSTJ(11)=5 then $r_{\c } =$PARJ(46) and $r_{\b } =$PARJ(47). PARJ(46) and PARJ(47) thus provide a possibility to interpolate between the `pure' Bowler shape, $r = 1$, and the normal Lund one, $r=0$. The additional modifications made in PARJ(43) - PARJ(45) are automatically taken into account, if necessary.

PARJ(48) :

(D=1.5 GeV) in defining the junction rest frame, the effective pull direction of a chain of partons is defined by the vector sum of their momenta, multiplied by a factor $\exp (- \sum E / \mathtt{PARJ(48)})$, where the energy sum runs over all partons on the string between (but excluding) the given one and the junction itself. The energies should be defined in the junction rest frame, which requires an iterative approximation, see MSTJ(18).

PARJ(49) :

(D=1. GeV) retry (up to 10 times) when both strings, to be joined in a junction to form a new string endpoint, have a remaining energy above PARJ(49) (evaluated in the junction rest frame) after having been fragmented.

PARJ(50) :

(D=10. GeV) retry as above when either of the strings have a remaining energy above a random energy evenly distributed between PARJ(49) and PARJ(49) + PARJ(50) (drawn anew for each test).

PARJ(51) - PARJ(55) :

(D=3*0.77, $-0.05$, $-0.005$) give a choice of four possible ways to parameterize the fragmentation function for MSTJ(11)=2 (and MSTJ(11)=3 for charm and heavier). The fragmentation of each flavour KF may be chosen separately; for a diquark the flavour of the heaviest quark is used. With $c =$PARJ(50+KF), the parameterizations are:
$0 \leq c \leq 1$ : Field-Feynman, $f(z) = 1 - c + 3c(1-z)^2$;
$-1 \leq c < 0$ : Peterson/SLAC, $f(z) = 1/(z(1-1/z-(-c)/(1-z))^2)$;
$c > 1$ : power peaked at $z = 0$, $f(z) = (1-z)^{c-1}$;
$c < -1$ : power peaked at $z=1$, $f(z) = z^{-c-1}$.

PARJ(59) :

(D=1.) replaces PARJ(51) - PARJ(53) for gluon jet generated with MSTJ(2)= 2 or 4.

PARJ(61) - PARJ(63) :

(D=4.5, 0.7, 0.) parameterizes the energy dependence of the primary multiplicity distribution in phase-space decays. The former two correspond to $c_1$ and $c_2$ of eq. (), while the latter allows a further additive term in the multiplicity specifically for onium decays.

PARJ(64) :

(0.003 GeV) minimum kinetic energy in decays (safety margin for numerical precision errors). When violated, typically new masses would be selected if particles have a Breit-Wigner width, or a new decay channel where that is relevant.

PARJ(65) :

(D=0.5 GeV) mass which, in addition to the spectator quark or diquark mass, is not assumed to partake in the weak decay of a heavy quark in a hadron. This parameter was mainly intended for top decay and is currently not in use.

PARJ(66) :

(D=0.5) relative probability that colour is rearranged when two singlets are to be formed from decay products. Only applies for MDME(IDC,2)= 11-30, i.e. low-mass phase-space decays.

PARJ(71) :

(D=10 mm) maximum average proper lifetime $c\tau$ for particles allowed to decay in the MSTJ(22)=2 option. With the default value, $\mathrm{K}_{\mathrm{S}}^0$, $\Lambda$, $\Sigma^-$, $\Sigma^+$, $\Xi^-$, $\Xi^0$ and $\Omega^-$ are stable (in addition to those normally taken to be stable), but charm and bottom do still decay.

PARJ(72) :

(D=1000 mm) maximum distance from the origin at which a decay is allowed to take place in the MSTJ(22)=3 option.

PARJ(73) :

(D=100 mm) maximum cylindrical distance $\rho = \sqrt{x^2 + y^2}$ from the origin at which a decay is allowed to take place in the MSTJ(22)=4 option.

PARJ(74) :

(D=1000 mm) maximum z distance from the origin at which a decay is allowed to take place in the MSTJ(22)=4 option.

PARJ(76) :

(D=0.7) mixing parameter $x_d = \Delta M/\Gamma$ in $\mathrm{B}^0$- $\overline{\mathrm{B}}^0$ system.

PARJ(77) :

(D=10.) mixing parameter $x_s = \Delta M/\Gamma$ in $\mathrm{B}_s^0$- $\overline{\mathrm{B}}_s^0$ system.

PARJ(80) - PARJ(90) :

parameters for time-like parton showers, see section .

PARJ(91) :

(D=0.020 GeV) minimum particle width in PMAS(KC,2), above which particle decays are assumed to take place before the stage where Bose-Einstein effects are introduced.

PARJ(92) :

(D=1.) nominal strength of Bose-Einstein effects for $Q=0$, see MSTJ(51). This parameter, often denoted $\lambda$, expresses the amount of incoherence in particle production. Due to the simplified picture used for the Bose-Einstein effects, in particular for effects from three nearby identical particles, the actual $\lambda$ of the simulated events may be larger than the input value.

PARJ(93) :

(D=0.20 GeV) size of the Bose-Einstein effect region in terms of the $Q$ variable, see MSTJ(51). The more conventional measure, in terms of the radius $R$ of the production volume, is given by $R = \hbar/$PARJ(93)$\approx 0.2$ fm$\times$GeV/PARJ(93)$=$PARU(3)/PARJ(93).

PARJ(94) :

(D=0.0 GeV) Increase radius for pairs from different $\mathrm{W}/\mathrm{Z}/$strings.

< 0 :

if MSTJ(56) = 1, the radius for pairs from different $\mathrm{W}/ \mathrm{Z}$'s is increased to $R+\delta R_{\mathrm{W}\mathrm{W}}+\mbox{\texttt{PARU(3)}}/\mathrm{abs}(\mbox{\texttt{PARJ(94)}})$.

> 0 :

the radius for pairs from different strings is increased to
$R+\mbox{\texttt{PARU(3)}}/\mbox{\texttt{PARJ(94)}}$.

PARJ(95) :

(R) Set to the energy imbalance after the BE algorithm, before rescaling of momenta.

PARJ(96) :

(R) Set to the $\alpha$ needed to retain energy-momentum conservation in each event for relevant models.

PARJ(121) - PARJ(171) :

parameters for $\mathrm{e}^+\mathrm{e}^-$ event generation, see section .

PARJ(180) - PARJ(195) :

various coupling constants and parameters related to couplings, see section .