Complete PYTHIA events

In a full-blown event generated with PYTHIA, the usage of PYJETS is more complicated, although the general principles survive. PYJETS is used extensively by many of the generation routines; indeed it provides the bridge between many of them. The PYTHIA event listing begins (optionally) with a few lines of event summary, specific to the hard process simulated and thus not described in the overview above. These specific parts are covered in the following.

In most instances, only the particles actually produced are of interest. For MSTP(125)=0, the event record starts off with the parton configuration existing after hard interaction, initial- and final-state radiation, multiple interactions and beam remnants have been considered. The partons are arranged in colour singlet clusters, ordered as required for string fragmentation. Also photons and leptons produced as part of the hard interaction (e.g. from $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{g}\gamma$ or $\u\overline{\mathrm{u}}\to \mathrm{Z}^0 \to \mathrm{e}^+\mathrm{e}^-$) appear in this part of the event record. These original entries appear with pointer K(I,3)=0, whereas the products of the subsequent fragmentation and decay have K(I,3) numbers pointing back to the line of the parent.

The standard documentation, obtained with MSTP(125)=1, includes a few lines at the beginning of the event record, which contain a brief summary of the process that has taken place. The number of lines used depends on the nature of the hard process and is stored in MSTI(4) for the current event. These lines all have K(I,1)=21. For all processes, lines 1 and 2 give the two incoming particles. When listed with PYLIST, these two lines will be separated from subsequent ones by a sequence of `======' signs, to improve readability. For diffractive and elastic events, the two outgoing states in lines 3 and 4 complete the list. Otherwise, lines 3 and 4 contain the two partons that initiate the two initial-state parton showers, and 5 and 6 the end products of these showers, i.e. the partons that enter the hard interaction. With initial-state radiation switched off, lines 3 and 5 and lines 4 and 6 are identical. For a simple $2 \to 2$ hard scattering, lines 7 and 8 give the two outgoing partons/particles from the hard interaction, before any final-state radiation. For $2 \to 2$ processes proceeding via an intermediate resonance such as $\gamma^* / \mathrm{Z}^0$, $\mathrm{W}^{\pm}$ or $\mathrm{h}^0$, the resonance is found in line 7 and the two outgoing partons/particles in 8 and 9. In some cases one of these may be a resonance in its own right, or both of them, so that further pairs of lines are added for subsequent decays. If the decay of a given resonance has been switched off, then no decay products are listed either in this initial summary or in the subsequent ordinary listing. Whenever partons are listed, they are assumed to be on the mass shell for simplicity. The fact that effective masses may be generated by initial- and final-state radiation is taken into account in the actual parton configuration that is allowed to fragment, however. The listing of the event documentation closes with another line made up of `======' signs.

A few examples may help clarify the picture. For a single diffractive event $\mathrm{p}\overline{\mathrm{p}}\to \mathrm{p}_{\mathrm{diffr}} \overline{\mathrm{p}}$, the event record will start with
I K(I,1) K(I,2) K(I,3) comment
1 21 2212 0 incoming $\mathrm{p}$
2 21 -2212 0 incoming $\overline{\mathrm{p}}$
========================= not part of record; appears in listings
3 21 9902210 1 outgoing $\mathrm{p}_{\mathrm{diffr}}$
4 21 -2212 2 outgoing $\overline{\mathrm{p}}$
========================= again not part of record

The typical QCD $2 \to 2$ process would be
I K(I,1) K(I,2) K(I,3) comment
1 21 2212 0 incoming $\mathrm{p}$
2 21 -2212 0 incoming $\overline{\mathrm{p}}$
=========================
3 21 2 1 $\u$ picked from incoming $\mathrm{p}$
4 21 -1 2 $\overline{\mathrm{d}}$ picked from incoming $\overline{\mathrm{p}}$
5 21 21 3 $\u$ evolved to $\mathrm{g}$ at hard scattering
6 21 -1 4 still $\overline{\mathrm{d}}$ at hard scattering
7 21 21 0 outgoing $\mathrm{g}$ from hard scattering
8 21 -1 0 outgoing $\overline{\mathrm{d}}$ from hard scattering
=========================

Note that, where well defined, the K(I,3) code does contain information as to which side the different partons come from, e.g. above the gluon in line 5 points back to the $\u$ in line 3, which points back to the proton in line 1. In the example above, it would have been possible to associate the scattered g in line 7 with the incoming one in line 5, but this is not possible in the general case, consider e.g. $\mathrm{g}\mathrm{g}\to \mathrm{g}\mathrm{g}$.

A special case is provided by $\mathrm{W}^+ \mathrm{W}^-$ or $\mathrm{Z}^0 \mathrm{Z}^0$ fusion to an $\mathrm{h}^0$. Then the virtual $\mathrm{W}$'s or $\mathrm{Z}$'s are shown in lines 7 and 8, the $\mathrm{h}^0$ in line 9, and the two recoiling quarks (that emitted the bosons) in 10 and 11, followed by the Higgs decay products. Since the $\mathrm{W}$'s and $\mathrm{Z}$'s are space-like, what is actually listed as the mass for them is $-\sqrt{-m^2}$. Thus $\mathrm{W}^+ \mathrm{W}^-$ fusion to an $\mathrm{h}^0$ in process 8 (not process 124, which is lengthier) might look like
I K(I,1) K(I,2) K(I,3) comment
1 21 2212 0 first incoming $\mathrm{p}$
2 21 2212 0 second incoming $\mathrm{p}$
=========================
3 21 2 1 $\u$ picked from first $\mathrm{p}$
4 21 21 2 $\mathrm{g}$ picked from second $\mathrm{p}$
5 21 2 3 still $\u$ after initial-state radiation
6 21 -4 4 $\mathrm{g}$ evolved to $\overline{\mathrm{c}}$
7 21 24 5 space-like $\mathrm{W}^+$ emitted by $\u$ quark
8 21 -24 6 space-like $\mathrm{W}^-$ emitted by $\overline{\mathrm{c}}$ quark
9 21 25 0 Higgs produced by $\mathrm{W}^+ \mathrm{W}^-$ fusion
10 21 1 5 $\u$ turned into $\d$ by emission of $\mathrm{W}^+$
11 21 -3 6 $\overline{\mathrm{c}}$ turned into $\overline{\mathrm{s}}$ by emission of $\mathrm{W}^-$
12 21 23 9 first $\mathrm{Z}^0$ coming from decay of $\mathrm{h}^0$
13 21 23 9 second $\mathrm{Z}^0$ coming from decay of $\mathrm{h}^0$
14 21 12 12 $\nu_{\mathrm{e}}$ from first $\mathrm{Z}^0$ decay
15 21 -12 12 $\overline{\nu}_{\mathrm{e}}$ from first $\mathrm{Z}^0$ decay
16 21 5 13 $\b$ quark from second $\mathrm{Z}^0$ decay
17 21 -5 13 $\overline{\mathrm{b}}$ antiquark from second $\mathrm{Z}^0$ decay
=========================

Another special case is when a spectrum of virtual photons are generated inside a lepton beam, i.e. when PYINIT is called with one or two 'gamma/lepton' arguments. (Where lepton could be either of e-, e+, mu-, mu+, tau- or tau+.) Then the documentation section is expanded to reflect the new layer of administration. Positions 1 and 2 contain the original beam particles, e.g. $\mathrm{e}$ and $\mathrm{p}$ (or $\mathrm{e}^+$ and $\mathrm{e}^-$). In position 3 (and 4 for $\mathrm{e}^+\mathrm{e}^-$) is (are) the scattered outgoing lepton(s). Thereafter comes the normal documentation, but starting from the photon rather than a lepton. For $\mathrm{e}\mathrm{p}$, this means 4 and 5 are the $\gamma^*$ and $\mathrm{p}$, 6 and 7 the shower initiators, 8 and 9 the incoming partons to the hard interaction, and 10 and 11 the outgoing ones. Thus the documentation is 3 lines longer (4 for $\mathrm{e}^+\mathrm{e}^-$) than normally.

The documentation lines are often helpful to understand in broad outline what happened in a given event. However, they only provide the main points of the process, with many intermediate layers of parton showers omitted. The documentation can therefore appear internally inconsistent, if the user does not remember what could have happened in between. For instance, the listing above would show the Higgs with the momentum it has before radiation off the two recoiling $\u$ and $\overline{\mathrm{c}}$ quarks is considered. When these showers are included, the Higgs momentum may shift by the changed recoil. However, this update is not visible in the initial summary, which thus still shows the Higgs before the showering. When the Higgs decays, on the other hand, it is the real Higgs momentum further down in the event record that is used, and that thus sets the momenta of the decay products that are also copied up to the summary. Such effects will persist in further decays; e.g. the $\b$ and $\overline{\mathrm{b}}$ shown at the end of the example above are before showers, and may deviate from the final parton momenta quite significantly. Similar shifts will also occur e.g. in a $\t\to \b\mathrm{W}^+ \to \b\mathrm{q}\overline{\mathrm{q}}'$ decays, when the gluon radiation off the $\b$ gives a recoil to the $\mathrm{W}$ that is not visible in the $\mathrm{W}$ itself but well in its decay products. In summary, the documentation section should never be mistaken for the physically observable state in the main section of the event record, and never be used as part of any realistic event analysis.

(An alternative approach would be in the spirit of the Les Houches `parton-level' event record, section , where the whole chain of decays normally is carried out before starting the parton showers. With this approach, one could have an internally consistent summary, but then in diverging disagreement with the "real" particles after each layer of shower evolution.)

After these lines with the initial information, the event record looks the same as for MSTP(125)=0, i.e. first comes the parton configuration to be fragmented and, after another separator line `======' in the output (but not the event record), the products of subsequent fragmentation and decay chains. This ordinary listing begins in position MSTI(4)+1. The K(I,3) pointers for the partons, as well as leptons and photons produced in the hard interaction, are now pointing towards the documentation lines above, however. In particular, beam remnants point to 1 or 2, depending on which side they belong to, and partons emitted in the initial-state parton showers point to 3 or 4. In the second example above, the partons produced by final-state radiation will be pointing back to 7 and 8; as usual, it should be remembered that a specific assignment to 7 or 8 need not be unique. For the third example, final-state radiation partons will come both from partons 10 and 11 and from partons 16 and 17, and additionally there will be a neutrino-antineutrino pair pointing to 14 and 15.

A hadronic event may contain several (semi)hard interactions, in the multiple interactions scenario. The hardest interaction of an event is shown in the initial section of the event record, while further ones are not. Therefore these extra partons, documented in the main section of the event, do not have a documentation copy to point back to, and so are assigned K(I,3)=0.

There exists a third documentation option, MSTP(125)=2. Here the history of initial- and final-state parton branchings may be traced, including all details on colour flow. This information has not been optimized for user-friendliness, and cannot be recommended for general usage. With this option, the initial documentation lines are the same. They are followed by blank lines, K(I,1)=0, up to line 100 (can be changed in MSTP(126)). From line 101 onwards each parton with K(I,1)= 3, 13 or 14 appears with special colour-flow information in the K(I,4) and K(I,5) positions. For an ordinary $2 \to 2$ scattering, the two incoming partons at the hard scattering are stored in lines 101 and 102, and the two outgoing in 103 and 104. The colour flow between these partons has to be chosen according to the proper relative probabilities in cases when many alternatives are possible, see section . If there is initial-state radiation, the two partons in lines 101 and 102 are copied down to lines 105 and 106, from which the initial-state showers are reconstructed backwards step by step. The branching history may be read by noting that, for a branching $a \to bc$, the K(I,3) codes of $b$ and $c$ point towards the line number of $a$. Since the showers are reconstructed backwards, this actually means that parton $b$ would appear in the listing before parton $a$ and $c$, and hence have a pointer to a position below itself in the list. Associated time-like partons $c$ may initiate time-like showers, as may the partons of the hard scattering. Again a showering parton or pair of partons will be copied down towards the end of the list and allowed to undergo successive branchings $c \to d e$, with $d$ and $e$ pointing towards $c$. The mass of time-like partons is properly stored in P(I,5); for space-like partons $-\sqrt{-m^2}$ is stored instead. After this section, containing all the branchings, comes the final parton configuration, properly arranged in colour, followed by all subsequent fragmentation and decay products, as usual.