Oedipus: Onium Evolution, Dipole Interaction and Perturbative Unitarisation Simulation * Program Summary

OEDIPUS is a Monte Carlo simulation program which can be used to determine the small-x evolution of a heavy onium using Mueller's colour dipole formulation, giving the full distribution of dipoles in rapidity and impact parameter. Routines are also provided which calculate onium-onium scattering amplitudes between individual pairs of onium configurations, making it possible to establish the contribution of multiple pomeron exchange terms to onium-onium scattering (the unitarisation corrections). Program language used: Fortran-90 Memory required to execute with typical data: 1–10 MB No. of bits in a word: 32/64 No. of lines in distributed program, including test data, etc.: 6186 Nature of the physical problem BFKL evolution [1] of a heavy (quark-)onium, to give full information on the rapidity and transverse positions of gluons carrying a small fraction x of the onium's longitudinal momentum. This information can be used to calculate a variety of onium-onium scattering cross sections, including multiple pomeron contributions, which restore unitarity. A Monte Carlo simulation of the evolution in rapidity of the gluon structure of the onium, using Mueller's colour dipole formulation of small-x physics [2]. Restrictions on the complexity of the problem The number of dipoles (gluons) in an onium grows as an exponential of the rapidity, and inversely with the value of a cutoff used to regulate an ultraviolet divergence. The time for evolution of an onium is proportional to the number of dipoles, while that for calculation of the onium-onium scattering amplitude goes as the square of the number of dipoles. Memory restrictions also arise from the need to store large configurations of dipoles (very large 1 fluctuations can occur in the number of dipoles present). Typical running time On a DEC Alpha 3000 processor, evolution generates about 10000 gluons per second. At a rapidity Y = 16 and an ultraviolet cutoff of 0.01 times the onium size, a day's running will generate about 10 5 onium-onium scatterings.