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Manuscript Title: Two-photon physics with GALUGA 2.0.
Authors: G.A. Schuler
Program title: GALUGA
Catalogue identifier: ADHE_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 108(1998)279
Programming language: Fortran.
Computer: IBM RS/6000.
Operating system: UNIX.
Keywords: Particle physics, Elementary, Event simulation, Monte Carlo, Two-photon, e+e Azimuthal dependence.
Classification: 11.2.

Nature of problem:
Hadronic two-photon reactions in a new energy domain are becoming accessible with LEP2. Unlike purely electroweak processes, hadronic processes contain dominant non-perturbative components parametrized by suitable structure functions, which are functions of the two-photon invariant mass W and the photon virtualities Q1 and Q2. It is hence advantageous to have a Monte Carlo program that can generate events with the possibility to keep W and, optionally, Qi at fixed, user-defined values. Moreover, at least one program with an exact treatment of both the kinematics and the dynamics over the whole range m**2 >> m**2(W/sqrt(s))**4 ~< s (m is the electron mass and sqrt(s) the e+e- c.m. energy) is needed, (i) to check the various approximations used in other programs, and (ii) to be able to explore additional information on the hadronic physics, e.g. coded in azimuthal dependences.

Solution method:
The differential cross section for e+e- -> e+e-X at given two-photon invariant mass W is rewritten in terms of four invariants with the photon virtualities Qi as the two outermost integration variables (next to W), in order to simultaneously cope with antitagged and tagged electron modes. Due care is taken of numerically stable expressions while keeping all electron-mass and Qi dependences. Special attention is devoted to the azimuthal dependences of the cross section. Cuts on the scattered electrons are to a large extent incorporated analytically and suitable mappings introduced to deal with the peaking structure of the differential cross section. The event generation yields either weighted events or unweighted ones (i.e. equally weighted events with weight 1), the latter based on the hit-or-miss technique. Optionally, VEGAS [1] can be invoked to (i) obtain an accurate estimate of the integrated cross section and (ii) improve the event generation efficiency through additional variable mappings provided by the grid information of VEGAS. The program is set up so that additional hadronic (or leptonic) reactions can easily be added.
Other subprograms used: VEGAS, RANLUX [2], HBOOK [3] and DATIME [4].

Summary of revisions:
Differences with earlier version [5]
  1. The W-integrated total e+e- cross section sigma can now be calculated besides dsigma/dW**2 and d2sigma/dW**2dQ22.
  2. The program can be used to calculate sigma for a total, Regge-like hadronic cross section as well as the effective two-photon luminosity function L defined by sigma = integral(dtau L(tau) sigmagammagamma (tau s)), where sigmagammagamma is the real-photon cross section. In both cases four different ansatze for the Qi dependence of the hadronic form factors is provided.
  3. The total two-photon cross section at large Qi**2 calculated in perturbative QCD, in terms of the BFKL Pomeron, is incorporated.
  4. Structure functions for the formation of resonances in two-photon collisions are included for 30 mesons, light or heavy. One can choose between two models: in one, the full, non-trivial Q1**2, Q2**2 correlations as given in the constituent quark model are kept. The alternative model is based on a factorized VMD-inspired ansatz.

Running time:
The integration time depends on the required cross section accuracy and the applied cuts. For instance, 13 seconds on an IBM RS/6000 yields an accuracy of the VEGAS integration of about 0.1 per cent for the antitag mode or of about 0.2 per cent for a typical single-tag mode; within the same time the error of the simple Monte Carlo integration is about 0.5 per cent for either mode. Event generation with or without VEGAS improvement and for either tag mode takes about 4x10**-4 (2x10**-3) seconds per event for weighted (unweighted) events.

References:
[1] G.P. Lepage, J. Comp. Phys. 27 (1978) 192.
[2] F. James, "RANLUX: a Fortran implementation of the high-quality pseudorandom number generator of Luscher", CERN Program Library V115, Comput. Phys. Commun. 79 (1994) 111; M. Luscher, Comput. Phys. Commun. 79 (1994) 100.
[3] R. Brun and D. Lienart, "HBOOK User Guide -- Version 4", CERN Program Library Y250, 1988.
[4] J. Harms et al., "DATIME: Job Time and Date", CERN Program Library Z007, 1991.
[5] G.A. Schuler, preprint CERN-TH/96-313 (1996).