Common Block Variables

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.

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.

= 0 :

off.

= 1 :

on.

MSTP(82) :

(D=1) 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).)

= 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).)

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.

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(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 jets 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(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).

MSTP(92) :

(D=3) (C) energy partitioning in hadron or resolved photon remnant, when this remnant is split into two jets. (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. 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(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 Poissonian 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 crossing 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 Poissonian 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(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=1.9 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, 0.2) parameters of an assumed double Gaussian matter distribution inside the colliding hadrons for MSTP(82)=4, of the form given in eq. (), i.e. with a core of radius PARP(84) of the main radius and containing a fraction PARP(83) of the total hadronic matter.

PARP(85) :

(D=0.33) probability that an additional interaction in the multiple interaction formalism gives two gluons, with colour connections to `nearest neighbours' in momentum space.

PARP(86) :

(D=0.66) probability that an additional interaction in the 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=1000. 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, $s^{\epsilon} = E_{\mathrm{cm}}^{2\epsilon} = E_{\mathrm{cm}}^{2\cdot 0.08}$, 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=1. 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)$^2$.

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.