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Common-Block Variables and Routines

Of the routines used to generate beam remnants, multiple interactions and pile-up events, none are intended to be called directly by the user. The only way to regulate these aspects is therefore via the variables in the PYPARS common block. Therefore most emphasis is put on the latter, while routines and additional commonblocks are listed more briefly.


\fbox{\texttt{COMMON/PYPARS/MSTP(200),PARP(200),MSTI(200),PARI(200)}}

Purpose:
to give access to a number of status codes and parameters which regulate the performance of PYTHIA. Most parameters are described in section [*]; here only those related to beam remnants, multiple interactions and pile-up events are described. If the default values, below denoted by (D = ...), are not satisfactory, they must in general be changed before the PYINIT call. Exceptions, i.e. variables which can be changed for each new event, are denoted by (C).

MSTP(81) :
(D = 1) master switch for multiple interactions (MI), and also for the associated treatment of initial- and final-state showers and beam remnants. Its meaning depends on whether PYEVNT (old and intermediate models) or PYEVNW (new model) are called.
= 0 :
MI off; old model (new model if PYEVNW called directly).
= 1 :
MI on; old model (new model if PYEVNW called directly).
= 10 :
MI off; intermediate model (new model if PYEVNW called directly).
= 11 :
MI on; intermediate model (new model if PYEVNW called directly).
= 20 :
MI off; new model for PYEVNT and PYEVNW alike.
= 21 :
MI on; new model for PYEVNT and PYEVNW alike.
Note:
when PYEVNT is called for the options = 20 and = 21, the one and only action this routine takes is to hand on execution to PYEVNW. Whenever, anywhere else in this manual, a distinction is made between PYEVNT and PYEVNW, for = 20 and = 21 it is the PYEVNW rules that apply. The only reason for hooking up PYEVNT and PYEVNW this way is to allow a uniform interface to some experimental setups, where the only way to steer program execution is by a cards file.
Warning:
many parameters have to be tuned differently for the old and new scenarios, such as PARP(81) - PARP(84), PARP(89) and PARP(90), and others are specific to each scenario. In addition, the optimal parameter values depend on the choice of parton densities and so on. Therefore you must pick a consistent set of values, rather than simply changing MSTP(81) by itself.
An example, for the old multiple interactions scenario, is R.D. Field's Tune A [Fie02] (which agrees with the current default, except for PARP(90)):
MSTP(81) = 1, MSTP(82) = 4, PARP(67) = 4.0, PARP(82) = 2.0,
PARP(83) = 0.5, PARP(84) = 0.4, PARP(85) = 0.9, PARP(86) = 0.95,
PARP(89) = 1800.0 and PARP(90) = 0.25, with CTEQ5L (default).
The same values cannot be used with the new scenario available with PYEVNW. Specifically, the fact that each multiple interaction here can radiate on its own, which only is the case for the first one in PYEVNT, means that each gives more activity. Thus fewer interactions, i.e. a higher $p_{\perp 0}$ scale, is required. Also other parameters are used in the new scenario. No tune of equivalent quality to Tune A is available so far. An example of a possible set is (where some are default values while others need to be set):
New model, smooth ISR, high FSR: MSTP(81) = 21, MSTP(70) = 2,
MSTP(72) = 2;
$p_{\perp 0}$ and reconnect: PARP(82) = 2.5D0, MSTP(95) = 1, PARP(78) = 1.3D0;
ExpOfPow(1.8) overlap profile: MSTP(82) = 5, PARP(83) = 1.8D0;
Reference energy and rescaling pace: PARP(89) = 1800D0,
PARP(90) = 0.25D0;
$\Lambda_{\mathrm{FSR}}$ scale: PARJ(81) = 0.14D0;
Beam remnants: MSTP(89) = 1, MSTP(88) = 0, PARP(79) = 2D0,
PARP(80) = 0.01D0.

MSTP(82) :
(D = 4) structure of multiple interactions. For QCD processes, used down to $p_{\perp}$ values below $p_{\perp\mathrm{min}}$, it also affects the choice of structure for the one hard/semi-hard interaction.
= 0 :
simple two-string model without any hard interactions. Toy model only!
= 1 :
multiple interactions assuming the same probability in all events, with an abrupt $p_{\perp\mathrm{min}}$ cut-off at PARP(81). (With a slow energy dependence given by PARP(89) and PARP(90).) This option has not been implemented for the new model in PYEVNW.
= 2 :
multiple interactions assuming the same probability in all events, with a continuous turn-off of the cross section at $p_{\perp 0}= $PARP(82). (With a slow energy dependence given by PARP(89) and PARP(90).)
= 3 :
multiple interactions assuming a varying impact parameter and a hadronic matter overlap consistent with a Gaussian matter distribution, with a continuous turn-off of the cross section at $p_{\perp 0}= $PARP(82). (With a slow energy dependence given by PARP(89) and PARP(90).)
= 4 :
multiple interactions assuming a varying impact parameter and a hadronic matter overlap consistent with a double Gaussian matter distribution given by PARP(83) and PARP(84), with a continuous turn-off of the cross section at $p_{\perp 0}= $PARP(82). (With a slow energy dependence given by PARP(89) and PARP(90).)
= 5 :
multiple interactions assuming a varying impact parameter and a hadronic matter overlap $\mathcal{O}(b) \propto exp(-b^d)$. This shape does not have to correspond to a simple functional form for the matter distributions themselves. The power $d = $PARP(83) (note changed meaning of this parameter relative to the MSTP(82) = 4 option) can be varied continuously, with a lower cutoff at 0.4 for technical reasons. The physically interersting range is between 1 and 2, i.e. between an exponential and a Gaussian. As above, there is a continuous turn-off of the cross section at $p_{\perp 0}= $PARP(82). (With a slow energy dependence given by PARP(89) and PARP(90).)
Note 1:
for MSTP(82) $\geq 2$ and CKIN(3) $>$ PARP(82) (modulo the slow energy dependence noted above), cross sections given with PYSTAT(1) may be somewhat too large, since (for reasons of efficiency) the probability factor that the hard interaction is indeed the hardest in the event is not included in the cross sections. It is included in the event selection, however, so the events generated are correctly distributed. For CKIN(3) values a couple of times larger than PARP(82) this ceases to be a problem.
Note 2:
the PARP(81) and PARP(82) values are sensitive to the choice of parton distributions, $\Lambda_{\mathrm{QCD}}$, etc., in the sense that a change in the latter variables leads to a net change in the multiple-interaction rate, which has to be compensated by a retuning of PARP(81) or PARP(82) if one wants to keep the net multiple-interaction structure the same. The default PARP(81) and PARP(82) values are consistent with the other default values give, i.e. parton distributions of the proton etc.
Note 3:
the multiple interactions combination of MSTP(81) = 0 (or = 10, = 20) and MSTP(82) $\geq 2$ is not so common, and certainly not intended to simulate realistic events, but it is an allowed way to obtain events with only the hardest interaction of those the events would contain with the corresponding MSTP(81) = 1 scenario. If also CKIN(3) is set larger than the respective $p_{\perp 0}$ scale (see PARP(82)), however, the program misbehaves. To avoid this, MSTP(82) is now set to 1 in such cases, in PYINIT. This may require some extra care if a run contains a loop over various MSTP(81) and MSTP(82) values.
Note 4:
for technical reasons, options 2 and above have not been implemented for $\gamma\mathrm{p}$ and $\gamma\gamma$ physics, i.e. there only the option 1 is available for multiple interactions. Furthermore (and partly related), it is not possible, at least not without some precautions, to run the MSTP(82) $\geq 2$ options with varying beam energies, see [*].

MSTP(83) :
(D = 100) number of Monte Carlo generated phase-space points per bin (whereof there are 20) in the initialization (in PYMULT) of multiple interactions for MSTP(82) $\geq 2$.

MSTP(84) :
(D = 1) switch for initial-state radiation in interactions after the first one in the intermediate and new models. (In the old model, no such radiation is implemented.)
= 0 :
off.
= 1 :
on, provided that MSTP(61) = 1.
Note :
initial-state radiation in the first (hardest) interaction is not affected by MSTP(84), but only by MSTP(61).

MSTP(85) :
(D = 1) switch for final-state radiation in interactions after the first one in the intermediate and new models. (In the old model, no such radiation is implemented.)
= 0 :
off.
= 1 :
on, provided that MSTP(71) = 1.
Note :
final-state radiation in the first (hardest) interaction is not affected by MSTP(85), but only by MSTP(71).

MSTP(86) :
(D = 2) requirements on multiple interactions based on the hardness scale of the main process.
= 1 :
the main collision is harder than all the subsequent ones. This is the old behaviour, preserved for reasons of backwards compatibility, and most of the time quite sensible, but with dangers as follows.
The traditional multiple interactions procedure is to let the main interaction set the upper $p_{\perp}$ scale for subsequent multiple interactions. For QCD, this is a matter of avoiding double-counting. Other processes normally are hard, so the procedure is then also sensible. However, for a soft main interaction, further softer interactions are hardly possible, i.e. multiple interactions are more or less killed. Such a behaviour could be motivated by the rejected events instead appearing as part of the interactions underneath a normal QCD hard interaction, but in practice the latter mechanism is not implemented. (And would have been very inefficient to work with, had it been.) For MSTP(82) $\geq 3$ it is even worse, since also the events themselves are likely to be rejected in the impact-parameter selection stage. Thus the spectrum of main events that survive is biased, with the low-$p_{\perp}$, soft tail suppressed. Furthermore, even when events are rejected by the impact-parameter procedure, this is not reflected in the cross section for the process, as it should have been. Results may thus be misleading.
= 2 :
when the main process is of the QCD jets type (the same as those in multiple interactions) subsequent interactions are requested to be softer, but for other processes no such requirement exists.
= 3 :
no requirements at all that multiple interactions have to be softer than the main interactions (of dubious use for QCD processes but intended for cross-checks).
Note:
process cross sections are unreliable whenever the main process does restrict subsequent interactions, and the main process can become soft. For QCD jet studies in this region it is then better to put CKIN(3) = 0 and get the `correct' total cross section.

MSTP(87) :
(D = 4) when a sea quark (antiquark) is picked from a hadron at some $x_{\mathrm{s}}$ value in the new model, there has to be a companion sea antiquark (quark) at some other $x_{\c }$ value. The $x_{\c }$ distribution is assumed given by a convolution of a mother gluon distribution $g(x = x_{\mathrm{s}} + x_{\c })$ with the perturbative $\mathrm{g}\to \mathrm{q}+ \overline{\mathrm{q}}$ DGLAP splitting kernel. The simple ansatz $g(x) = N (1-x)^n/x$ is used, where $N$ is a normalization constant and $n$ = MSTP(87). MSTP(87) thus controls the large-$x$ behaviour of the assumed gluon distribution. Only integers MSTP(87) = 0 - 4 are available; values below or above this range are set at the lower or upper limit, respectively.

MSTP(88) :
(D = 1) strategy for the collapse of a quark-quark-junction configuration to a diquark, or a quark-quark-junction-quark configuration to a baryon, in a beam remnant in the new model.
= 0 :
only allowed when valence quarks only are involved.
= 1 :
sea quarks can be used for diquark formation, but not for baryon formation.
= 2 :
sea quarks can be used also for baryon formation.

MSTP(89) :
(D = 1) Selection of method for colour connections in the initial state of the new model. Note that all options respect the suppression provided by PARP(80).
= 0 :
random.
= 1 :
the hard-scattering systems are ordered in rapidity. The initiators on each side are connected so as to minimize the rapidity difference between neighbouring systems.
= 2 :
each connection is chosen so as to minimize an estimate of the total string length resulting from it. (This is the most technically complicated, and hence a computationally slow approach.)

MSTP(90) :
(D = 0) strategy to compensate the `primordial $k_{\perp}$' assigned to a parton-shower initiator or beam-remnant parton in the new model.
= 0 :
all other such partons compensate uniformly.
= 1 :
compensation spread out across colour chain as $(1/2)^n$, where $n$ is number of steps the parton is removed in the chain.
= 2 :
nearest colour neighbours only compensate.

MSTP(91) :
(D = 1) (C) primordial $k_{\perp}$ distribution in hadron. See MSTP(93) for photon.
= 0 :
no primordial $k_{\perp}$.
= 1 :
Gaussian, width given in PARP(91), upper cut-off in PARP(93).
= 2 :
exponential, width given in PARP(92), upper cut-off in PARP(93). Not available in the new model.
= 3 :
distribution proportional to $1/(k_{\perp}^2+3\sigma^2/2)^3$, i.e. with $1/k_{\perp}^6$ tails. RMS width given in PARP(91) and upper cutoff in PARP(93). Not available in the old model.
= 4 :
flat distribution (on limited interval), RMS width given in PARP(91) and upper cutoff in PARP(93). Not available in the old model.
= 11 :
As 1, but width depends on the scale $Q$ of the hard interaction, being the maximum of the fragmentation width and $2.1 \times Q/(7.+Q)$. Not available in the old model.
= 13 :
As 3, but the width scales with Q as for 11.
= 14 :
As 4, but the width scales with Q as for 11.
Note:
when multiple interactions are switched on, the distribution used for the subsequent interactions vanishes in the old model, and has a RMS width forced equal to the fragmentation one in the new model, but the shape still follows the choice of MSTP(91).

MSTP(92) :
(D = 3) (C) energy partitioning in hadron or resolved-photon remnant, when this remnant is split into two jets in the old model. (For a splitting into a hadron plus a jet, see MSTP(94).) The energy fraction $\chi$ taken by one of the two objects, with conventions as described for PARP(94) and PARP(96), is chosen according to the different distributions below. Here $c_{\mathrm{min}} = 0.6~\mathrm{GeV}/E_{\mathrm{cm}} \approx %
2 \langle m_{\mathrm{q}} \rangle/E_{\mathrm{cm}}$.
= 1 :
1 for meson or resolved photon, $2(1-\chi)$ for baryon, i.e. simple counting rules.
= 2 :
$(k+1)(1-\chi)^k$, with $k$ given by PARP(94) or PARP(96).
= 3 :
proportional to $(1-\chi)^k/\sqrt[4]{\chi^2+c_{\mathrm{min}}^2}$, with $k$ given by PARP(94) or PARP(96).
= 4 :
proportional to $(1-\chi)^k/\sqrt{\chi^2+c_{\mathrm{min}}^2}$, with $k$ given by PARP(94) or PARP(96).
= 5 :
proportional to $(1-\chi)^k/(\chi^2+c_{\mathrm{min}}^2)^{b/2}$, with $k$ given by PARP(94) or PARP(96), and $b$ by PARP(98).

MSTP(93) :
(D = 1) (C) primordial $k_{\perp}$ distribution in photon, either it is one of the incoming particles or inside an electron.
= 0 :
no primordial $k_{\perp}$.
= 1 :
Gaussian, width given in PARP(99), upper cut-off in PARP(100).
= 2 :
exponential, width given in PARP(99), upper cut-off in PARP(100).
= 3 :
power-like of the type $\d k_{\perp}^2/(k_{\perp 0}^2 + k_{\perp}^2)^2$, with $k_{\perp 0}$ in PARP(99) and upper $k_{\perp}$ cut-off in PARP(100).
= 4 :
power-like of the type $\d k_{\perp}^2/(k_{\perp 0}^2 + k_{\perp}^2)$, with $k_{\perp 0}$ in PARP(99) and upper $k_{\perp}$ cut-off in PARP(100).
= 5 :
power-like of the type $\d k_{\perp}^2/(k_{\perp 0}^2 + k_{\perp}^2)$, with $k_{\perp 0}$ in PARP(99) and upper $k_{\perp}$ cut-off given by the $p_{\perp}$ of the hard process or by PARP(100), whichever is smaller.
Note:
for options 1 and 2 the PARP(100) value is of minor importance, once PARP(100)$\gg$PARP(99). However, options 3 and 4 correspond to distributions with infinite $\langle k_{\perp}^2 \rangle$ if the $k_{\perp}$ spectrum is not cut off, and therefore the PARP(100) value is as important for the overall distribution as is PARP(99).

MSTP(94) :
(D = 3) (C) energy partitioning in hadron or resolved-photon remnant, when this remnant is split into a hadron plus a remainder-jet in the old model. The energy fraction $\chi$ is taken by one of the two objects, with conventions as described below or for PARP(95) and PARP(97).
= 1 :
1 for meson or resolved photon, $2(1-\chi)$ for baryon, i.e. simple counting rules.
= 2 :
$(k+1)(1-\chi)^k$, with $k$ given by PARP(95) or PARP(97).
= 3 :
the $\chi$ of the hadron is selected according to the normal fragmentation function used for the hadron in jet fragmentation, see MSTJ(11). The possibility of a changed fragmentation function shape in diquark fragmentation (see PARJ(45)) is not included.
= 4 :
as = 3, but the shape is changed as allowed in diquark fragmentation (see PARJ(45)); this change is here also allowed for meson production. (This option is not so natural for mesons, but has been added to provide the same amount of freedom as for baryons).

MSTP(95) :
(D = 1) selection of method for colour reconnections in the final state in the new model. For MSTP(95) = 1, the amount of reconnections is controlled by PARP(78). For the remaining `colour annealing' options, the strength was not variable before version 6.402. In subsequent versions, the probability for a given string piece to retain its colour history and hence not participate in the annealing is
\begin{displaymath}
P_{\mathrm{keep}} = (1-\mbox{PARP(78)})^{n_{\mathrm{MI}}}~~~,
\end{displaymath} (232)

where $n_{\mathrm{MI}}$ is the number of interactions that occurred in the current event, making the reconnection probability for any given string piece larger in events with many interactions. Note that the meaning of this switch differs between events generated with the new model (in PYEVNW) and ones generated with the intermediate model (in PYEVNT). For the former case, the reconnections are performed after multiple interactions and the initial-state showers have been generated, but before the final-state showers, whereas in the latter case also the final-state showers are generated before reconnections are tried. (In the old model, instead PARP(85) and PARP(86) regulate colour connections, but in a different way.)
= 0 :
off.
= 1 :
on. (NB: reconnections are still only allowed if there was actually more than one interaction in the given event, (1) since the colour flow of 1 interaction should be defined entirely by the shower, and (2) since one otherwise obtains a (probably unwanted) component of diffractive topologies.)
= 2 :
on for hadron-hadron collisions simulated with PYEVNW, else off. Is based on the new approach described in section [*], where an attempt is made to minimize the total string length $\lambda$. In this variant, closed loops of colour-connected gluons are only accepted if all else fails. In PYTHIA 6.402 and later, strength of effect is controlled by PARP(78) as described above.
= 3 :
on for all collisions simulated with PYEVNW, else off. Same model as = 2.
= 4 :
same as = 2, but closed loops of colour-connected gluons are not suppressed.
= 5 :
same as = 3, but closed loops of colour-connected gluons are not suppressed.
= 6 :
same as = 2, but only free triplets (including also gluons with one string piece already attached) are allowed to initiate string pieces.
= 7 :
same as = 3, but only free triplets (including also gluons with one string piece already attached) are allowed to initiate string pieces.

MSTP(96) :
(D = 0) joined interactions (JI) on/off. JI is the possibility that partons entering different multiple interactions turn out to stem from a common mother when the initial-state showers are traced backwards.
= 0 :
no joinings allowed.
= 1 :
$p_{\perp}$ scales of joinings are found, but joinings are not actually performed.
= 2 :
(joinings allowed -- not yet implemented).
Note:
at present, only the splitting kernels have been implemented, allowing to estimate the overall rates and $p_{\perp}$ spectra of joinings, but the actual kinematics has not yet been worked out, so that only `trial joinings' can be generated. Even if switched on, joinings will therefore not at present occur physically in the generated events.

MSTP(131) :
(D = 0) master switch for pile-up events, i.e. several independent hadron-hadron interactions generated in the same bunch-bunch crossing, with the events following one after the other in the event record.
= 0 :
off, i.e. only one event is generated at a time.
= 1 :
on, i.e. several events are allowed in the same event record. Information on the processes generated may be found in MSTI(41) - MSTI(50).

MSTP(132) :
(D = 4) the processes that are switched on for pile-up events. The first event may be set up completely arbitrarily, using the switches in the PYSUBS common block, while all the subsequent events have to be of one of the `inclusive' processes which dominate the cross section, according to the options below. It is thus not possible to generate two rare events in the pile-up option.
= 1 :
low-$p_{\perp}$ processes (ISUB = 95) only. The low-$p_{\perp}$ model actually used, both in the hard event and in the pile-up events, is the one set by MSTP(81) etc. This means that implicitly also high-$p_{\perp}$ jets can be generated in the pile-up events.
= 2 :
low-$p_{\perp}$ + double diffractive processes (ISUB = 95 and 94).
= 3 :
low-$p_{\perp}$ + double diffractive + single diffractive processes (ISUB = 95, 94, 93 and 92).
= 4 :
low-$p_{\perp}$ + double diffractive + single diffractive + elastic processes, together corresponding to the full hadron-hadron cross section (ISUB = 95, 94, 93, 92 and 91).

MSTP(133) :
(D = 0) multiplicity distribution of pile-up events.
= 0 :
selected by you, before each PYEVNT call, by giving the MSTP(134) value.
= 1 :
a Poisson multiplicity distribution in the total number of pile-up events. This is the relevant distribution if the switches set for the first event in PYSUBS give the same subprocesses as are implied by MSTP(132). In that case the mean number of events per beam crossing is $\overline{n} = \sigma_{\mathrm{pile}} \times$PARP(131), where $\sigma_{\mathrm{pile}}$ is the sum of the cross section for allowed processes. Since bunch crossings which do not give any events at all (probability $\exp(-\overline{n})$) are not simulated, the actual average number per PYEVNT call is $\langle n \rangle = \overline{n}/(1-\exp(-\overline{n}))$.
= 2 :
a biased distribution, as is relevant when one of the events to be generated is assumed to belong to an event class with a cross section much smaller than the total hadronic cross section. If $\sigma_{\mathrm{rare}}$ is the cross section for this rare process (or the sum of the cross sections of several rare processes) and $\sigma_{\mathrm{pile}}$ the cross section for the processes allowed by MSTP(132), then define $\overline{n} = \sigma_{\mathrm{pile}} \times$PARP(131) and $f = \sigma_{\mathrm{rare}}/\sigma_{\mathrm{pile}}$. The probability that a bunch crossing will give $i$ events is then ${\cal P}_i = f \, i \, \exp(-\overline{n}) \, \overline{n}^i/i!$, i.e. the naïve Poisson is suppressed by a factor $f$ since one of the events will be rare rather than frequent, but enhanced by a factor $i$ since any of the $i$ events may be the rare one. Only beam crossings which give at least one event of the required rare type are simulated, and the distribution above normalized accordingly.
Note:
for practical reasons, it is required that $\overline{n} < 120$, i.e. that an average beam crossing does not contain more than 120 pile-up events. The multiplicity distribution is truncated above 200, or when the probability for a multiplicity has fallen below $10^{-6}$, whichever occurs sooner. Also low multiplicities with probabilities below $10^{-6}$ are truncated. See also PARI(91) - PARI(93).

MSTP(134) :
(D = 1) a user-selected multiplicity, i.e. total number of pile-up events, to be generated in the next PYEVNT call when MSTP(133) = 0. May be reset for each new event, but must be in the range $1 \leq $MSTP(134)$\leq 200$.


PARP(78) :
(D = 0.025) parameter controlling the amount of colour reconnection in the final state (the $F$ and $F'$ parameters in [Sjö04,Sjö04a]), when MSTP(95)=1. Since PYTHIA version 6.402 PARP(78) also controls the amount of colour reconnection for the `colour annealing' scenarios MSTP(95) > 1, but then has a different meaning than described here, see the MSTP(95) manual entry for details. For MSTP(95) = 1, try a fraction PARP(78) of the total number of possible reconnections. Perform all reconnections which reduce the total string length and which are consistent with the choice of strategy in MSTP(90). If at least one reconnection is successfully made, loop back and try again, else keep the final-state topology arrived to at this point. Note that a random colour reconnection is tested each time, so that the same reconnection may be tried twice and some not at all even when PARP(78) = 1D0. Thus, values somewhat larger than 1D0 are necessary if the `most extreme case' scenario is desired. Also note that the meaning of this parameter will most likely be changed in future updates. At present, it merely represents a crude way of turning up and down the amount of colour reconnections going on in the final state.

PARP(79) :
(D = 2.0) enhancement factor applied when assigning $x$ to composite systems (e.g. diquarks) in the beam remnant in the new model. Modulo a global rescaling (= normalization) of all the BR parton $x$ values, the $x$ of a composite system is PARP(79) times the trivial sum over $x$ values of its individual constituents.

PARP(80) :
(D = 0.1) when colours of partons kicked out from a beam remnant are to be attached to the remnant, PARP(80) gives a suppression for the probability of attaching those partons to the colour line between two partons which themselves both lie in the remnant. A smaller value thus corresponds to a smaller probability that several string pieces will go back and forth between the beam remnant and the hard-scattering systems.

PARP(81) :
(D = 1.9 GeV) effective minimum transverse momentum $p_{\perp\mathrm{min}}$ for multiple interactions with MSTP(82) = 1, at the reference energy scale PARP(89), with the degree of energy rescaling given by PARP(90). The optimal value depends on a number of other assumptions, especially which parton distributions are being used. The default is intended for CTEQ 5L.

PARP(82) :
(D = 2.0 GeV) regularization scale $p_{\perp 0}$ of the transverse-momentum spectrum for multiple interactions with MSTP(82) $\geq 2$, at the reference energy scale PARP(89), with the degree of energy rescaling given by PARP(90). (Current default based on the MSTP(82) = 4 option, without any change of MSTP(2) or MSTP(33).) The optimal value depends on a number of other assumptions, especially which parton distributions are being used. The default is intended for CTEQ 5L.

PARP(83), PARP(84) :
(D = 0.5, 0.4) parameters of the assumed matter overlap between the two colliding hadrons. For MSTP(82) = 4, a double Gaussian matter distribution of the form given in eq. ([*]) is used, i.e. with a core of radius PARP(84) of the main radius and containing a fraction PARP(83) of the total hadronic matter. For MSTP(82) = 5 the hadronic matter overlap (i.e. the convolution of the two colliding matter distributions) is $\mathcal{O}(b) \propto exp(-b^d)$, with power $d = $PARP(83) while PARP(84 is unused. The interesting range of PARP(83) values is different in the two cases, so this parameter should always be updated when MSTP(82) is changed.

PARP(85) :
(D = 0.9) probability that an additional interaction in the old multiple-interaction formalism gives two gluons, with colour connections to `nearest neighbours' in momentum space.

PARP(86) :
(D = 0.95) probability that an additional interaction in the old multiple-interaction formalism gives two gluons, either as described in PARP(85) or as a closed gluon loop. Remaining fraction is supposed to consist of quark-antiquark pairs.

PARP(87), PARP(88) :
(D = 0.7, 0.5) in order to account for an assumed dominance of valence quarks at low transverse momentum scales, a probability is introduced that a $\mathrm{g}\mathrm{g}$-scattering according to naïve cross section is replaced by a $\mathrm{q}\overline{\mathrm{q}}$ one; this is used only for MSTP(82) $\geq 2$. The probability is parameterized as ${\cal P} = a (1 - (p_{\perp}^2/(p_{\perp}^2 + b^2))^2)$, where $a =$PARP(87) and $b =$PARP(88)$\times$PARP(82) (including the slow energy rescaling of the $p_{\perp 0}$ parameter).

PARP(89) :
(D = 1800. GeV) reference energy scale, at which PARP(81) and PARP(82) give the $p_{\perp\mathrm{min}}$ and $p_{\perp 0}$ values directly. Has no physical meaning in itself, but is used for convenience only. (A form $p_{\perp\mathrm{min}}= \mathtt{PARP(81)} E_{\mathrm{cm}}^{\mathtt{PARP(90)}}$ would have been equally possible but then with a less transparent meaning of PARP(81).) For studies of the $p_{\perp\mathrm{min}}$ dependence at some specific energy it may be convenient to choose PARP(89) equal to this energy.

PARP(90) :
(D = 0.16) power of the energy-rescaling term of the $p_{\perp\mathrm{min}}$ and $p_{\perp 0}$ parameters, which are assumed proportional to $E_{\mathrm{cm}}^{\mathtt{PARP(90)}}$. The default value is inspired by the rise of the total cross section by the pomeron term, $s^{\epsilon} = E_{\mathrm{cm}}^{2\epsilon} = E_{\mathrm{cm}}^{2\times 0.08}$, which is not inconsistent with the small-$x$ behaviour. It is also reasonably consistent with the energy-dependence implied by a comparison with the UA5 multiplicity distributions at 200 and 900 GeV [UA584]. PARP(90) = 0 is an allowed value, i.e. it is possible to have energy-independent parameters.

PARP(91) :
(D = 2. GeV/$c$) (C) width of Gaussian primordial $k_{\perp}$ distribution inside hadron for MSTP(91) = 1, i.e. $\exp(-k_{\perp}^2/\sigma^2) \, k_{\perp} \, \d k_{\perp}$ with $\sigma =$PARP(91) and $\langle k_{\perp}^2 \rangle = $PARP(91)$^2$.
Warning:
the current default value is much larger than could be explained in purely nonperturbative terms. It is thus likely that the large value compensates for imperfections in the perturbative description and, as such, will have an energy and process dependence. It may therefore be necessary to vary this parameter for an optimal description.

PARP(92) :
(D = 0.40 GeV/$c$) (C) width parameter of exponential primordial $k_{\perp}$ distribution inside hadron for MSTP(91) = 2, i.e. $\exp(-k_{\perp}/\sigma) \, k_{\perp} \, \d k_{\perp}$ with $\sigma =$PARP(92) and $\langle k_{\perp}^2 \rangle = 6 \times$PARP(92)$^2$. Thus one should put PARP(92) $\approx$ PARP(91)$/\sqrt{6}$ to have continuity with the option above.

PARP(93) :
(D = 5. GeV/$c$) (C) upper cut-off for primordial $k_{\perp}$ distribution inside hadron.

PARP(94) :
(D = 1.) (C) for MSTP(92) $\geq 2$ this gives the value of the parameter $k$ for the case when a meson or resolved-photon remnant is split into two fragments (which is which is chosen at random).

PARP(95) :
(D = 0.) (C) for MSTP(94) = 2 this gives the value of the parameter $k$ for the case when a meson or resolved-photon remnant is split into a meson and a spectator fragment jet, with $\chi$ giving the energy fraction taken by the meson.

PARP(96) :
(D = 3.) (C) for MSTP(92) $\geq 2$ this gives the value of the parameter $k$ for the case when a nucleon remnant is split into a diquark and a quark fragment, with $\chi$ giving the energy fraction taken by the quark jet.

PARP(97) :
(D = 1.) (C) for MSTP(94) = 2 this gives the value of the parameter $k$ for the case when a nucleon remnant is split into a baryon and a quark jet or a meson and a diquark jet, with $\chi$ giving the energy fraction taken by the quark jet or meson, respectively.

PARP(98) :
(D = 0.75) (C) for MSTP(92) = 5 this gives the power of an assumed basic $1/\chi^b$ behaviour in the splitting distribution, with $b =$PARP(98).

PARP(99) :
(D = 1. GeV/$c$) (C) width parameter of primordial $k_{\perp}$ distribution inside photon; exact meaning depends on MSTP(93) value chosen (cf. PARP(91) and PARP(92) above).

PARP(100) :
(D = 5. GeV/$c$) (C) upper cut-off for primordial $k_{\perp}$ distribution inside photon.

PARP(131) :
(D = 0.01 mb$^{-1}$) in the pile-up events scenario, PARP(131) gives the assumed luminosity per bunch-bunch crossing, i.e. if a subprocess has a cross section $\sigma$, the average number of events of this type per bunch-bunch crossing is $\overline{n} = \sigma \times$PARP(131). PARP(131) may be obtained by dividing the integrated luminosity over a given time (1 s, say) by the number of bunch-bunch crossings that this corresponds to. Since the program will not generate more than 200 pile-up events, the initialization procedure will crash if $\overline{n}$ is above 120.

Further subroutines and commonblocks:

SUBROUTINE PYMULT(MMUL) :
to generate semi-hard interactions according to the old multiple-interaction formalism.

SUBROUTINE PYREMN(IPU1,IPU2) :
to add on target remnants and include primordial $k_{\perp}$ according to the old beam-remnant treatment.

SUBROUTINE PYMIGN(MMUL) :
initialises multiple interactions. Also generates multiple interaction kinematics and flavours in the `intermediate model' (equivalently to PYMULT in the `old model').

SUBROUTINE PYEVOL(MODE,PT2MAX,PT2MIN) :
initializes and evolves an event consisting of a single $2 \to 2$ hard scattering down in $p_{\perp}^2$ from some PT2MAX scale down to PT2MIN, with interleaved multiple interactions and initial-state radiation according to the new model.
MODE = -1 :
initialize interleaved MI/ISR/JI evolution first time for each event. Determine physical PT2MAX and PT2MIN scales.
MODE = 0 :
(re-)initialize ISR/MI/JI evolution: resets relevant parameters (saved during the first call). Is re-done every time an evolution must be restarted. (This only applies to a restart of the entire evolution, not to the case when PYEVOL is called multiple times for factorized evolution.)
MODE = 1 :
evolve ISR/MI/JI from PT2MAX to PT2MIN.
MODE = 2 :
finalize MI/ISR/JI evolution.
Note:
multiple calls to PYEVOL using MODE = 1 can be made, with the PT2MIN scale of one call being the PT2MAX scale of the next, producing a sequence of factorized evolution steps, if so desired. (Only relevant for some specialized applications like L-CKKW style PS/ME matching [Cat01].)

SUBROUTINE PYPTMI(MODE,PT2NOW,PT2CUT,PT2,IFAIL) :
initialises, generates, and accepts additional trial interactions in the new model. Also collapses the flavour wave function of newly created quarks (from interactions or ISR branchings) into valence, sea or companion quarks.
MODE = -1 :
initialize MI from scratch.
MODE = 0 :
generate trial interaction. Start at PT2NOW, solve Sudakov for PT2, abort if below PT2CUT.
MODE = 1 :
accept interaction at PT2NOW and store variables.
MODE = 2 :
decide sea/valence/companion for kicked-out quark at PT2NOW.
PT2NOW :
starting (max) $p_{\perp}^2$ scale for evolution.
PT2CUT :
lower limit for evolution.
PT2 :
result of evolution. Generated $p_{\perp}^2$ for trial interaction.
IFAIL :
status return code.
= 0: all is well.
< 0: phase space exhausted, generation to be terminated.
> 0: additional interaction vetoed, but continue evolution.

SUBROUTINE PYMIHK :
finds left-behind remnant flavour content and hooks up the colour flow between the hard scattering and remnants in the new model (part of PYREMN in the old scheme).

SUBROUTINE PYCTTR(I,KCS,IEND) :
auxiliary to PYMIHK. Traces the colour flow in the PYTHIA event record and translates it into a structure (/PYCTAG/) based on Les Houches Accord style colour tags.

SUBROUTINE PYMIHG(JCP1,JCG1,JCP2,JCG2) :
auxiliary routine to PYMIHK used to test initial-state colour connections. Keeps track of which colour tags have been collapsed with each other and tests whether a given new collapse will result in singlet gluons. Uses /PYCBLS/ to communicate with PYMIHK.

SUBROUTINE PYMIRM :
picks primordial $k_{\perp}$ and shares longitudinal momentum among beam remnants in the new model (part of PYREMN in the old scheme).

FUNCTION PYFCMP(XC,XS,NPOW) :
gives the approximate $xf(x; x_s)$ distribution of a companion quark.

FUNCTION PYPCMP(XS,NPOW) :
gives the approximate momentum integral of a companion-quark $xf(x)$ distribution.


\fbox{\begin{minipage}{150mm}\begin{tabbing}{\texttt{~COMMON/PYINTM/KFIVAL(2,3),...
...}}\\ {\texttt{\&XMI(2,240),Q2MI(240),IMISEP(0:240)}}\end{tabbing}\end{minipage}}

Purpose:
to carry information relevant for multiple interactions in the new model.

KFIVAL(JS,J) :
enumeration of the initial valence quark content on side JS. A baryon requires all three slots J, while a meson only requires the first two, so that KFIVAL(JS,3) = 0. The contents are initially zero for a $\gamma$, $\pi^0$, $\mathrm{K}_{\mathrm{S}}^0$ and $\mathrm{K}_{\mathrm{L}}$, and are only set once a valence quark is kicked out. (For instance, a $\pi^0$ can be either $\u\overline{\mathrm{u}}$ or $\d\overline{\mathrm{d}}$, only a scattering will tell.)

NMI(JS) :
total number of scattered and remnant partons on side JS, including hypothesized gluons that each branch to a sea (anti)quark and its companion.

IMI(JS,I,1) :
position in the /PYJETS/ event record of a scattered or remnant parton, or a hypothesized gluon that branches to a sea (anti)quark and its companion. Here JS gives the side and 1 $\le$ I $\le$ NMI(JS) enumerates the partons.

IMI(JS,I,2) :
nature of the partons described above.
= 0 :
a valence quark or a gluon.
> 0 :
parton is part of a sea quark-antiquark pair, and IMI(JS,I,2) gives the position in the event record of the companion.
< 0 :
flag that parton is a sea quark for which no companion has yet been defined; useful at intermediate stages but should not be found in the final event.

NVC(JS,IFL) :
total number of unmatched sea quarks on side JS of flavour IFL.

XASSOC(JS,IFL,I) :
the $x$ value of an unmatched sea quark, on side JS of flavour IFL and with $1 \le$ I $\le$ NVC(JS,IFL). When a companion quark is found then both XASSOC and NVC are updated.

XPSVC(IFL,J) :
subdivision of the parton density $xf(x)$ for flavour IFL obtained by a PYPDFU call (with MINT(30) = side JS).
J = -1 :
sea contribution.
J = 0 :
valence contribution.
1 $\le$ J $\le$ NVC(JS,IFL) :
sea companion contribution from each of the above unmatched sea quarks.

PVCTOT(JS,J) :
momentum fraction, i.e. integral of $xf(x)$, inside the remaining hadron on side JS.
J = -1 :
total carried originally by valence quarks.
J = 0 :
total carried by valence quarks that have been removed.
J = 1 :
total carried by unmatched sea companion quarks.

XMI(JS,I) :
$x$ value of incoming parton on side JS for interaction number I, 1 $\le$ I $\le$ MINT(31). When there is an initial-state shower, $x$ refers to the initiator of this shower rather than to the incoming parton at the hard interaction. The $x$ values are normalized to the full energy of the incoming hadron, i.e. are not rescaled by previous interactions.

Q2MI(I) :
the $Q^2$ scale of the hard interaction number I, 1 $\le$ I $\le$ MINT(31). This is the scale stored in VINT(54), i.e. the $Q^2$ used to evaluate parton densities at the hard scattering.

IMISEP(I) :
last line in the event record filled by partons belonging to the interaction number I, 1 $\le$ I $\le$ MINT(31). Thus interaction I is stored in lines IMISEP(I-1) + 1 through IMISEP(I), where IMISEP(0) has been set so that this holds also for I = 1.


\fbox{\texttt{~COMMON/PYCBLS/MCO(4000,2),NCC,JCCO(4000,2),JCCN(4000,2),MACCPT}}

Purpose:
to store temporary colour-tag information while hooking up initial state; used to communicate between PYMIHK and PYMIHG.

MCO(I,J) :
original colour tag J of parton I before initial-state connection procedure was started.

NCC :
number of colour tags that have so far been collapsed.

JCCO(I,J) :
colour tag collapse array, I $\le$ NCC. The I'th collapse is between colour tags JCCO(I,1) and JCCO(I,2).

JCCN(I,J) :
temporary storage for collapse being tested. If collapse is accepted, JCCO is set equal to JCCN.


\fbox{\texttt{~COMMON/PYCTAG/NCT, MCT(4000,2)}}

Purpose:
to carry Les Houches Accord style colour tag information for partons in the event record.

NCT :
number of colour lines in the event, from 1 to NCT.

MCT(I,1) :
colour tag of parton I in /PYJETS/.
MCT(I,2) :
anticolour tag of parton I in /PYJETS/.


\fbox{\begin{minipage}{150mm}\begin{tabbing}{\texttt{~COMMON/PYISMX/MIMX,JSMX,KF...
...}\\ {\texttt{\&PT2MX,PT2AMX,ZMX,RM2CMX,Q2BMX,PHIMX}}\end{tabbing}\end{minipage}}

Purpose:
to carry information on hardest initial-state radiation trial branching so far, during the interleaved generation with multiple interactions in PYEVOL. All quantities except NISGEN refer to this hardest trial branching so far.
MIMX :
interaction number.
JSMX :
side. JSMX determines which evolution step has `won' in the PYEVOL evolution. Its possible values are:
= -1 :
no evolution step was found above the current PT2MIN.
= 0 :
an additional interaction should be generated.
= 1 :
an ISR branching on side 1 (interaction number MIMX).
= 2 :
an ISR branching on side 2 (interaction number MIMX).
= 3 :
a joining on side 1 (interactions MJN1MX and MJN2MX).
= 4 :
a joining on side 2 (interactions MJN1MX and MJN2MX).
KFLAMX :
mother flavour.
KFLCMX :
time-like sister flavour.
KFBEAM(JS) :
KF code of beam on side JS.
NISGEN(JS,MI) :
number of already generated ISR branchings on interaction number MI, side JS.
PT2MX :
evolution $p_{\perp}^2$ scale.
PT2AMX :
physical $p_{\perp}^2$ value.
ZMX :
$z$ energy sharing fraction.
RM2CMX :
time-like sister mass-squared.
Q2BMX :
space-like virtuality.
PHIMX :
azimuthal ($\phi$) angle.


\fbox{\texttt{COMMON/PYISJN/MJN1MX,MJN2MX,MJOIND(2,240)}}

Purpose:
to carry information on possible joinings, i,e. when two separate showers are reconstructed to a common ancestor in the backwards evolution.


next up previous contents
Next: Fragmentation Up: Beam Remnants and Underlying Previous: Pile-up Events   Contents
Stephen Mrenna 2007-10-30