Common block variables

The status codes and parameters relevant for the $\mathrm{e}^+\mathrm{e}^-$ routines are found in the common block PYDAT1. This common block also contains more general status codes and parameters, described elsewhere.

Purpose:

to give access to a number of status codes and parameters regulating the performance of the $\mathrm{e}^+\mathrm{e}^-$ event generation routines.

MSTJ(101) :

(D=5) gives the type of QCD corrections used for continuum events.

= 0 :

only $\mathrm{q}\overline{\mathrm{q}}$ events are generated.

= 1 :

$\mathrm{q}\overline{\mathrm{q}}+ \mathrm{q}\overline{\mathrm{q}}\mathrm{g}$ events are generated according to first-order QCD.

= 2 :

$\mathrm{q}\overline{\mathrm{q}}+ \mathrm{q}\overline{\mathrm{q}}\mathrm{g}+ \ma... ...{g}\mathrm{g}+ \mathrm{q}\overline{\mathrm{q}}\mathrm{q}'\overline{\mathrm{q}}'$ events are generated according to second-order QCD.

= 3 :

$\mathrm{q}\overline{\mathrm{q}}+ \mathrm{q}\overline{\mathrm{q}}\mathrm{g}+ \ma... ...{g}\mathrm{g}+ \mathrm{q}\overline{\mathrm{q}}\mathrm{q}'\overline{\mathrm{q}}'$ events are generated, but without second-order corrections to the 3-jet rate.

= 5 :

a parton shower is allowed to develop from an original $\mathrm{q}\overline{\mathrm{q}}$ pair, see MSTJ(38) - MSTJ(50) for details.

= -1 :

only $\mathrm{q}\overline{\mathrm{q}}\mathrm{g}$ events are generated (within same matrix-element cuts as for =1). Since the change in flavour composition from mass cuts or radiative corrections is not taken into account, this option is not intended for quantitative studies.

= -2 :

only $\mathrm{q}\overline{\mathrm{q}}\mathrm{g}\mathrm{g}$ and $\mathrm{q}\overline{\mathrm{q}}\mathrm{q}' \overline{\mathrm{q}}'$ events are generated (as for =2). The same warning as for =-1 applies.

= -3 :

only $\mathrm{q}\overline{\mathrm{q}}\mathrm{g}\mathrm{g}$ events are generated (as for =2). The same warning as for =-1 applies.

= -4 :

only $\mathrm{q}\overline{\mathrm{q}}\mathrm{q}' \overline{\mathrm{q}}'$ events are generated (as for =2). The same warning as for =-1 applies.

Note 1:

MSTJ(101) is also used in PYONIA, with

$\leq$ 4 :

$\mathrm{g}\mathrm{g}\mathrm{g}+ \gamma\mathrm{g}\mathrm{g}$ events are generated according to lowest-order matrix elements.

$\geq$ 5 :

a parton shower is allowed to develop from the original $\mathrm{g}\mathrm{g}\mathrm{g}$ or $\mathrm{g}\mathrm{g}\gamma$ configuration, see MSTJ(38) - MSTJ(50) for details.

Note 2:

The default values of fragmentation parameters have been chosen to work well with the default parton-shower approach above. If any of the other options are used, or if the parton shower is used in non-default mode, it is normally necessary to retune fragmentation parameters. As an example, we note that the second-order matrix-element approach (MSTJ(101)=2) at PETRA/PEP energies gives a better description when the $a$ and $b$ parameters of the symmetric fragmentation function are set to $a =$PARJ(41)=1, $b =$PARJ(42)=0.7, and the width of the transverse momentum distribution to $\sigma =$PARJ(21)=0.40. In principle, one also ought to change the joining parameter to PARJ(33)=PARJ(35)=1.1 to preserve a flat rapidity plateau, but if this should be forgotten, it does not make too much difference. For applications at TRISTAN or LEP, one has to change the matrix-element approach parameters even more, to make up for additional soft gluon effects not covered in this approach.

MSTJ(102) :

(D=2) inclusion of weak effects ($\mathrm{Z}^0$ exchange) for flavour production, angular orientation, cross sections and initial-state photon radiation in continuum events.

= 1 :

QED, i.e. no weak effects are included.

= 2 :

QFD, i.e. including weak effects.

= 3 :

as =2, but at initialization in PYXTEE the $\mathrm{Z}^0$ width is calculated from $\sin^2 \! \theta_W$, $\alpha_{\mathrm{em}}$ and $\mathrm{Z}^0$ and quark masses (including bottom and top threshold factors for MSTJ(103) odd), assuming three full generations, and the result is stored in PARJ(124).

MSTJ(103) :

(D=7) mass effects in continuum matrix elements, in the form MSTJ(103) $= M_1 + 2M_2 + 4M_3$, where $M_i = 0$ if no mass effects and $M_i = 1$ if mass effects should be included. Here;

$M_1$ :

threshold factor for new flavour production according to QFD result;

$M_2$ :

gluon emission probability (only applies for |MSTJ(101)|$\leq 1$, otherwise no mass effects anyhow);

$M_3$ :

angular orientation of event (only applies for |MSTJ(101)|$\leq 1$ and MSTJ(102)=1, otherwise no mass effects anyhow).

MSTJ(104) :

(D=5) number of allowed flavours, i.e. flavours that can be produced in a continuum event if the energy is enough. A change to 6 makes top production allowed above the threshold, etc. Note that in $\mathrm{q}\overline{\mathrm{q}}\mathrm{q}' \overline{\mathrm{q}}'$ events only the first five flavours are allowed in the secondary pair, produced by a gluon breakup.

MSTJ(105) :

(D=1) fragmentation and decay in PYEEVT and PYONIA calls.

= 0 :

no PYEXEC calls, i.e. only matrix-element and/or parton-shower treatment, and collapse of small jet systems into one or two particles (in PYPREP).

= 1 :

PYEXEC calls are made to generate fragmentation and decay chain.

= -1 :

no PYEXEC calls and no collapse of small jet systems into one or two particles (in PYPREP).

MSTJ(106) :

(D=1) angular orientation in PYEEVT and PYONIA.

= 0 :

standard orientation of events, i.e. $\mathrm{q}$ along $+z$ axis and $\overline{\mathrm{q}}$ along $-z$ axis or in $xz$ plane with $p_x > 0$ for continuum events, and $\g_1\g_2\g_3$ or $\gamma\g_2\g_3$ in $xz$ plane with $\g_1$ or $\gamma$ along the $+z$ axis for onium events.

= 1 :

random orientation according to matrix elements.

MSTJ(107) :

(D=0) radiative corrections to continuum events.

= 0 :

no radiative corrections.

= 1 :

initial-state radiative corrections (including weak effects for MSTJ(102)= 2 or 3).

MSTJ(108) :

(D=2) calculation of $\alpha_{\mathrm{s}}$ for matrix-element alternatives. The MSTU(111) and PARU(112) values are automatically overwritten in PYEEVT or PYONIA calls accordingly.

= 0 :

fixed $\alpha_{\mathrm{s}}$ value as given in PARU(111).

= 1 :

first-order formula is always used, with $\Lambda_{\mathrm{QCD}}$ given by PARJ(121).

= 2 :

first- or second-order formula is used, depending on value of MSTJ(101), with $\Lambda_{\mathrm{QCD}}$ given by PARJ(121) or PARJ(122).

MSTJ(109) :

(D=0) gives a possibility to switch from QCD matrix elements to some alternative toy models. Is not relevant for shower evolution, MSTJ(101)=5, where one can use MSTJ(49) instead.

= 0 :

standard QCD scenario.

= 1 :

a scalar gluon model. Since no second-order corrections are available in this scenario, one can only use this with MSTJ(101) = 1 or -1. Also note that the event-as-a-whole angular distribution is for photon exchange only (i.e. no weak effects), and that no higher-order corrections to the total cross section are included.

= 2 :

an Abelian vector gluon theory, with the colour factors $C_F = 1$ ($= 4/3$ in QCD), $N_C = 0$ ($= 3$ in QCD) and $T_R = 3 n_f$ ($= n_f/2$ in QCD). If one selects $\alpha_{\mathrm{Abelian}} = (4/3) \alpha_{\mathrm{QCD}}$, the 3-jet cross section will agree with the QCD one, and differences are to be found only in 4-jets. The MSTJ(109)=2 option has to be run with MSTJ(110)=1 and MSTJ(111)=0; if need be, the latter variables will be overwritten by the program.
Warning: second-order corrections give a large negative contribution to the 3-jet cross section, so large that the whole scenario is of doubtful use. In order to make the second-order options work at all, the 3-jet cross section is here by hand set exactly equal to zero for MSTJ(101)=2. It is here probably better to use the option MSTJ(101)=3, although this is not a consistent procedure either.

MSTJ(110) :

(D=2) choice of second-order contributions to the 3-jet rate.

= 1 :

the GKS second-order matrix elements.

= 2 :

the Zhu parameterization of the ERT matrix elements, based on the program of Kunszt and Ali, i.e. in historical sequence ERT/Kunszt/Ali/Zhu. The parameterization is available for $y =$ 0.01, 0.02, 0.03, 0.04 and 0.05. Values outside this range are put at the nearest border, while those inside it are given by a linear interpolation between the two nearest points. Since this procedure is rather primitive, one should try to work at one of the values given above. Note that no Abelian QCD parameterization is available for this option.

MSTJ(111) :

(D=0) use of optimized perturbation theory for second-order matrix elements (it can also be used for first-order matrix elements, but here it only corresponds to a trivial rescaling of the $\alpha_{\mathrm{s}}$ argument).

= 0 :

no optimization procedure; i.e. $Q^2 = E_{\mathrm{cm}}^2$.

= 1 :

an optimized $Q^2$ scale is chosen as $Q^2 = f E_{\mathrm{cm}}^2$, where $f =$PARJ(128) for the total cross section $R$ factor, while $f =$PARJ(129) for the 3- and 4-jet rates. This $f$ value enters via the $\alpha_{\mathrm{s}}$, and also via a term proportional to $\alpha_{\mathrm{s}}^2 \ln f$. Some constraints are imposed; thus the optimized `3-jet' contribution to $R$ is assumed to be positive (for PARJ(128)), the total 3-jet rate is not allowed to be negative (for PARJ(129)), etc. However, there is no guarantee that the differential 3-jet cross section is not negative (and truncated to 0) somewhere (this can also happen with $f = 1$, but is then less frequent). The actually obtained $f$ values are stored in PARJ(168) and PARJ(169), respectively. If an optimized $Q^2$ scale is used, then the $\Lambda_{\mathrm{QCD}}$ (and $\alpha_{\mathrm{s}}$) should also be changed. With the value $f=0.002$, it has been shown [Bet89] that a $\Lambda_{\mathrm{QCD}} = 0.100$ GeV gives a reasonable agreement; the parameter to be changed is PARJ(122) for a second-order running $\alpha_{\mathrm{s}}$. Note that, since the optimized $Q^2$ scale is sometimes below the charm threshold, the effective number of flavours used in $\alpha_{\mathrm{s}}$ may well be 4 only. If one feels that it is still appropriate to use 5 flavours (one choice might be as good as the other), it is necessary to put MSTU(113)=5.

MSTJ(115) :

(D=1) documentation of continuum or onium events, in increasing order of completeness.

= 0 :

only the parton shower, the fragmenting partons and the generated hadronic system are stored in the PYJETS common block.

= 1 :

also a radiative photon is stored (for continuum events).

= 2 :

also the original $\mathrm{e}^+\mathrm{e}^-$ are stored (with K(I,1)=21).

= 3 :

also the $\gamma$ or $\gamma^* / \mathrm{Z}^0$ exchanged for continuum events, the onium state for resonance events is stored (with K(I,1)=21).

MSTJ(116) :

(D=1) initialization of total cross section and radiative photon spectrum in PYEEVT calls.

= 0 :

never; cannot be used together with radiative corrections.

= 1 :

calculated at first call and then whenever KFL or MSTJ(102) is changed or ECM is changed by more than PARJ(139).

= 2 :

calculated at each call.

= 3 :

everything is re-initialized in the next call, but MSTJ(116) is afterwards automatically put =1 for use in subsequent calls.

MSTJ(119) :

(I) check on need to re-initialize PYXTEE.

MSTJ(120) :

(R) type of continuum event generated with the matrix-element option (with the shower one, the result is always =1).

= 1 :

$\mathrm{q}\overline{\mathrm{q}}$.

= 2 :

$\mathrm{q}\overline{\mathrm{q}}\mathrm{g}$.

= 3 :

$\mathrm{q}\overline{\mathrm{q}}\mathrm{g}\mathrm{g}$ from Abelian (QED-like) graphs in matrix element.

= 4 :

$\mathrm{q}\overline{\mathrm{q}}\mathrm{g}\mathrm{g}$ from non-Abelian (i.e. containing triple-gluon coupling) graphs in matrix element.

= 5 :

$\mathrm{q}\overline{\mathrm{q}}\mathrm{q}' \overline{\mathrm{q}}'$.

MSTJ(121) :

(R) flag set if a negative differential cross section was encountered in the latest PYX3JT call. Events are still generated, but maybe not quite according to the distribution one would like (the rate is set to zero in the regions of negative cross section, and the differential rate in the regions of positive cross section is rescaled to give the `correct' total 3-jet rate).

PARJ(121) :

(D=1.0 GeV) $\Lambda$ value used in first-order calculation of $\alpha_{\mathrm{s}}$ in the matrix-element alternative.

PARJ(122) :

(D=0.25 GeV) $\Lambda$ values used in second-order calculation of $\alpha_{\mathrm{s}}$ in the matrix-element alternative.

PARJ(123) :

(D=91.187 GeV) mass of $\mathrm{Z}^0$ as used in propagators for the QFD case.

PARJ(124) :

(D=2.489 GeV) width of $\mathrm{Z}^0$ as used in propagators for the QFD case. Overwritten at initialization if MSTJ(102)=3.

PARJ(125) :

(D=0.01) $y_{\mathrm{cut}}$, minimum squared scaled invariant mass of any two partons in 3- or 4-jet events; the main user-controlled matrix-element cut. PARJ(126) provides an additional constraint. For each new event, it is additionally checked that the total 3- plus 4-jet fraction does not exceed unity; if so the effective $y$ cut will be dynamically increased. The actual $y$-cut value is stored in PARJ(150), event by event.

PARJ(126) :

(D=2. GeV) minimum invariant mass of any two partons in 3- or 4-jet events; a cut in addition to the one above, mainly for the case of a radiative photon lowering the hadronic c.m. energy significantly.

PARJ(127) :

(D=1. GeV) is used as a safety margin for small colour-singlet jet systems, cf. PARJ(32), specifically $\mathrm{q}\overline{\mathrm{q}}'$ masses in $\mathrm{q}\overline{\mathrm{q}}\mathrm{q}' \overline{\mathrm{q}}'$ 4-jet events and $\mathrm{g}\mathrm{g}$ mass in onium $\gamma \mathrm{g}\mathrm{g}$ events.

PARJ(128) :

(D=0.25) optimized $Q^2$ scale for the QCD $R$ (total rate) factor for the MSTJ(111)=1 option is given by $Q^2 = f E_{\mathrm{cm}}^2$, where $f =$PARJ(128). For various reasons the actually used $f$ value may be increased compared with the nominal one; while PARJ(128) gives the nominal value, PARJ(168) gives the actual one for the current event.

PARJ(129) :

(D=0.002) optimized $Q^2$ scale for the 3- and 4-jet rate for the MSTJ(111)=1 option is given by $Q^2 = f E_{\mathrm{cm}}^2$, where $f =$PARJ(129). For various reasons the actually used $f$ value may be increased compared with the nominal one; while PARJ(129) gives the nominal value, PARJ(169) gives the actual one for the current event. The default value is in agreement with the studies of Bethke [Bet89].

PARJ(131), PARJ(132) :

(D=2*0.) longitudinal polarizations $P_{\mathrm{L}}^+$ and $P_{\mathrm{L}}^-$ of incoming $\mathrm{e}^+$ and $\mathrm{e}^-$.

PARJ(133) :

(D=0.) transverse polarization $P_{\mathrm{T}} = \sqrt{P_{\mathrm{T}}^+ P_{\mathrm{T}}^-}$, with $P_{\mathrm{T}}^+$ and $P_{\mathrm{T}}^-$ transverse polarizations of incoming $\mathrm{e}^+$ and $\mathrm{e}^-$.

PARJ(134) :

(D=0.) mean of transverse polarization directions of incoming $\mathrm{e}^+$ and $\mathrm{e}^-$, $\Delta \varphi = (\varphi^+ + \varphi^-) /2$, with $\varphi$ the azimuthal angle of polarization, leading to a shift in the $\varphi$ distribution of jets by $\Delta \varphi$.

PARJ(135) :

(D=0.01) minimum photon energy fraction (of beam energy) in initial-state radiation; should normally never be changed (if lowered too much, the fraction of events containing a radiative photon will exceed unity, leading to problems).

PARJ(136) :

(D=0.99) maximum photon energy fraction (of beam energy) in initial-state radiation; may be changed to reflect actual trigger conditions of a detector (but must always be larger than PARJ(135)).

PARJ(139) :

(D=0.2 GeV) maximum deviation of $E_{\mathrm{cm}}$ from the corresponding value at last PYXTEE call, above which a new call is made if MSTJ(116)=1.

PARJ(141) :

(R) value of $R$, the ratio of continuum cross section to the lowest-order muon pair production cross section, as given in massless QED (i.e. three times the sum of active quark squared charges, possibly modified for polarization).

PARJ(142) :

(R) value of $R$ including quark-mass effects (for MSTJ(102)=1) and/or weak propagator effects (for MSTJ(102)=2).

PARJ(143) :

(R) value of $R$ as PARJ(142), but including QCD corrections as given by MSTJ(101).

PARJ(144) :

(R) value of $R$ as PARJ(143), but additionally including corrections from initial-state photon radiation (if MSTJ(107)=1). Since the effects of heavy flavour thresholds are not simply integrable, the initial value of PARJ(144) is updated during the course of the run to improve accuracy.

PARJ(145) - PARJ(148) :

(R) absolute cross sections in nb as for the cases PARJ(141) - PARJ(144) above.

PARJ(150) :

(R) current effective matrix element cut-off $y_{\mathrm{cut}}$, as given by PARJ(125), PARJ(126) and the requirements of having non-negative cross sections for 2-, 3- and 4-jet events. Not used in parton showers.

PARJ(151) :

(R) value of c.m. energy ECM at last PYXTEE call.

PARJ(152) :

(R) current first-order contribution to the 3-jet fraction; modified by mass effects. Not used in parton showers.

PARJ(153) :

(R) current second-order contribution to the 3-jet fraction; modified by mass effects. Not used in parton showers.

PARJ(154) :

(R) current second-order contribution to the 4-jet fraction; modified by mass effects. Not used in parton showers.

PARJ(155) :

(R) current fraction of 4-jet rate attributable to $\mathrm{q}\overline{\mathrm{q}}\mathrm{q}' \overline{\mathrm{q}}'$ events rather than $\mathrm{q}\overline{\mathrm{q}}\mathrm{g}\mathrm{g}$ ones; modified by mass effects. Not used in parton showers.

PARJ(156) :

(R) has two functions when using second-order QCD. For a 3-jet event, it gives the ratio of the second-order to the total 3-jet cross section in the given kinematical point. For a 4-jet event, it gives the ratio of the modified 4-jet cross section, obtained when neglecting interference terms whose colour flow is not well defined, to the full unmodified one, all evaluated in the given kinematical point. Not used in parton showers.

PARJ(157) - PARJ(159) :

(I) used for cross-section calculations to include mass threshold effects to radiative photon cross section. What is stored is basic cross section, number of events generated and number that passed cuts.

PARJ(160) :

(R) nominal fraction of events that should contain a radiative photon.

PARJ(161) - PARJ(164) :

(I) give shape of radiative photon spectrum including weak effects.

PARJ(168) :

(R) actual $f$ value of current event in optimized perturbation theory for $R$; see MSTJ(111) and PARJ(128).

PARJ(169) :

(R) actual $f$ value of current event in optimized perturbation theory for 3- and 4-jet rate; see MSTJ(111) and PARJ(129).

PARJ(171) :

(R) fraction of cross section corresponding to the axial coupling of quark pair to the intermediate $\gamma^* / \mathrm{Z}^0$ state; needed for the Abelian gluon model 3-jet matrix element.