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2\section{Higher Order Processes\label{HIGHER}}
3
4 Higher order processes can be generated either by the QCD
5evolution or by supplying partons from an external generator.
6
7 Frequently it is interesting to generate higher-order processes
8with a particular branching in the QCD evolution or with a particular
9particle or group of particles being produced from the fragmentation.
10Examples include
11\begin{enumerate}
12\item Branching of jets into heavy quarks (e.g., $g \to b + \bar b$);
13\item Decay of such a heavy quark into a lepton or neutrino;
14\item Radiation of a photon, $W$, or $Z$ from a jet.
15\end{enumerate}
16It is important to realize that all of the cross sections and the QCD
17evolution in ISAJET are based on leading-log QCD, so generating such
18processes does not give the correct higher order QCD cross sections or
19K factors'', even though it may produce better agreement with them in
20some cases.
21
22 ISAJET does produce events with particular topologies which
23in many cases are the most important effect of higher order processes.
24In the heavy quark example, the lowest order process
25$$26g + g \to Q + \bar Q 27$$
28produces back-to-back heavy quark pairs, whereas the splitting process
29$$30g + g \to g + g, \quad g \to Q + \bar Q 31$$
32produces collinear pairs. Such collinear pairs are essential to obtain
33agreement with experimental data on $b \bar b$ production, and they
34often are the dominant background for processes of interest.
35
36 Branchings such as the emission of a heavy quark pair, a photon,
37or a $W^\pm$ or $Z^0$ are rare, and since they may occur at any step
38in the evolution, one cannot force them to occur. Therefore,
39generation of such events is very slow. M. Della Negra (UA1) suggested
40first doing $n_1$ QCD evolutions for each hard scattering and
41rejecting events without the desired partons, then doing $n_2$
42fragmentations for each successful evolution. This generates the
43equivalent of $n_1 n_2$ events for each hard scattering, so the cross
44section must be divided by $n_1 n_2$. This algorithm can speed up the
45generation of $g \to b + \bar b$ splitting by a factor of ten for $n_1 46= n_2 = 10$.
47
48 Since the evolution and fragmentation steps are executed $n_1n_2$
49times even if good events are found, a single hard scattering can lead
50to multiple events. This does not change the inclusive cross sections,
51but it does mean that the fluctuations may be larger than expected.
52Hence it is important to choose the numbers $n_1$ and $n_2$ carefully.
53
54 The following entities are used in ISAJET for generating events
55with multiple evolution and fragmentation:
56
57 \verb|NEVENT|: The number of primary hard scatterings to be
58generated. Set as usual on the input line with the energy.
59
60 \verb|SIGF|: The cross section for the selected hard
61scatterings divided by $n_1 \times n_2$. Hence the correct weight is
62SIGF/NEVENT, just as for normal running. (The cross section printed at
63the end of a run does not contain this factor.)
64
65 \verb|NEVOLVE|: The number $n_1$ of evolutions per hard
66scattering. This should never be set unless you supply a REJJET
67function. Do not confuse this with NOEVOLVE.
68
69 \verb|NHADRON|: The number $n_2$ of fragmentations for a given
70evolution. This should never be set unless you supply a REJFRG
71function. Do not confuse this with NOHADRON.
72
73 \verb|REJJET|: A logical function which if true causes the
74evolution to be rejected. The user must supply one to make the
75selections which he wants. The default always .FALSE. but includes an
76example as a comment.
77
78 \verb|REJFRG|: A logical function which if true causes the
79fragmentation to be rejected. The user must supply one to make the
80selections which he wants. The default always .FALSE. but includes an
81example as a comment.
82
83\noindent Note that one can also use function EDIT to make a final
84selection of the events. Of course ISAJET must be relinked if EDIT,
85REJJET or REJFRG is modified.
86
87 At the end of a run, the jet cross section, the cross section for
88the selected events, and the number and fraction of events selected are
89printed. The cross section SIGF stored internally is divided by $n_1 90\times n_2$ so that if the events are used to make histograms, then
91the correct weight per event is
92\begin{verbatim}
93 SIGF/NEVENT
94\end{verbatim}
95just as for normal events. Of course NEVENT now has a different meaning;
96it is in general larger than the number of events in the file but might
98
99 NEVOLVE and NHADRON are set as parameters in the input. One wants
100to choose them to give better acceptance of the primary hard scatterings
101but not to give multiple events for one hard scattering. For lepton
102production from heavy quarks the values
103\begin{verbatim}
104NEVOLVE
10510/
10710/
108\end{verbatim}
109seem appropriate, giving reasonable efficiency. For radiation of photons
110from jets, NEVOLVE can be somewhat larger but NHADRON should be one, and
111REJFRG should always return .FALSE., since the selection is just on the
112parton process, not on the hadronization.
113
114 The loops over evolutions and fragmentations are done inside of
115subroutine ISAEVT and are always executed the same number of times even
116though ISAEVT returns after each generated event. Logical flag OK
117signals a good event, and logical flag DONE signals that the run is
118finished. If you control the event generation loop yourself, you should
119make use of these flags as in the following extract from subroutine
120ISAJET:
121\begin{verbatim}
122 ILOOP=0
123 101 CONTINUE
124 ILOOP=ILOOP+1
125 CALL ISAEVT(ILOOP,OK,DONE)
126 IF(OK) CALL ISAWEV
127 IF(.NOT.DONE) GO TO 101
128\end{verbatim}
129Otherwise you may get the wrong weights.
130
131 It is possible to supply to ISAJET events with partons generated
132by some other program that may have more accurate matrix elements for
133higher order processes. Because any such calculation must involve
134cutoffs ISAJET assumes that the partons were generated imposing some
135$R$ cutoff, where $R=\sqrt{\phi^2+\eta^2}$, and some $E_t$ cutoff.
136Given that information ISAJET will generate initial state radiation
137partons only below the Et cutoff and final state radiation inside the
138$R$ cutoff. The external partons can be supplied to ISAJET by calls to
1392 subroutines. To initialize ISAJET for externally supplied partons,
140use
141\begin{verbatim}
142 CALL INISAP(CMSE,REACTION,BEAMS,WZ,NDCAYS,DCAYS,ETMIN,RCONE,OK)
143\end{verbatim}
144where the inputs are
145
146\smallskip\noindent
147\begin{tabular}{lcl}
148 CMSE &=& center of mass energy\\
149 REACTION &=& reaction (only TWOJET and DRELLYAN are \\
150 && implemented so far)\\
151 BEAMS(2) &=& chose 'P ' or 'AP'\\
152 ETMIN &=& minimum ET of supplied partons\\
153 RCONE &=& minimum cone (R) between supplied partons\\
154 WZ &=& option 'W', 'Z', or ' ' no $W$'s or $Z$'s\\
155 NDCAYS &=& number of decay options (if 0, assume decay has\\
157 DCAYS &=& list of particles W or Z can decay into\\
158\end{tabular}
159\smallskip
160
161\noindent and the output is
162
163\smallskip\noindent
164\begin{tabular}{lcl}
165 OK &=& TRUE if initialization is possible\\
166\end{tabular}
167\smallskip
168
169\noindent Then for each event use
170\begin{verbatim}
171 CALL IPARTNS(NPRTNS,IDS,PRTNS,IDQ,WEIGHT,WZDK)
172\end{verbatim}
173where the inputs are
174
175\smallskip\noindent
176\begin{tabular}{lcl}
177 NPRTNS &=& number of partons, $\le10$\\
178 IDS(NPRTNS) &=& ids of final partons\\
179 PRTNS(4,NPRTNS) &=& parton 4 vectors\\
180 IDQ(2) &=& ids of initial partons\\
181 WEIGHT &=& weight\\
182 WZDK &=& if true last 2 partons are from W,Z decay\\
183\end{tabular}
184\smallskip
185
186 Further QCD radiation is then generated consistent with
187ETMIN and RCONE, and the partons are fragmented into hadrons as usual.
188If RCONE is set to a value greater than 1.5 no cone restriction is
189applied during parton evolution.