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Manuscript Title: TOPAZ0: a program for computing observables and for fitting cross sections and forward-backward asymmetries around the Z0 peak.
Authors: G. Montagna, F. Piccinini, O. Nicrosini, G. Passarino, R. Pittau
Program title: TOPAZ0
Catalogue identifier: ACNT_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 76(1993)328
Programming language: Fortran.
Computer: VAX.
Operating system: VMS, UNIX.
RAM: 600K words
Word size: 32
Keywords: Particle physics, Elementary, E+e- annihilation, Bhabha scattering, Lep, Z0 resonance, Electroweak, Extrapolated and Realistic experimental Set-up, Qcd corrections, Corrections qed, Pure weak corrections, Radiative corrections, Minimal standard model, Fit to cross sections And forward-backward Asymmetries.
Classification: 11.5.

Nature of problem:
An accurate theoretical description of e+e- annihilation processes and of Bhabha scattering at the Z0 resonance is necessary in order to compare theoretical cross sections and asymmetries with the experimental ones as measured by the LEP collaborations. In particular a realistic theoretical description, i.e. a description in which the effects of experimental cuts, such as maximum acollinearity, energy or invariant mass and angular acceptance of the outgoing fermions, are taken into account, allows to fit the unknown parameters of the Minimal Standard Model, Mz, mt, mH and alphas, over experimental raw data, i.e. data corrected for detector efficiency but not for acceptance. The program takes into account all the corrections, pure weak, QED and QCD, which allow for such a realistic theoretical description.

Solution method:
Pure weak corrections are taken into account at the one loop level [2] within the MS bar scheme and higher order corrections are implemented whenever possible, according to [3]. QCD corrections are implemented by following the most recent calculations [4]. Initial state QED corrections are computed within the framework of the electron structure functions, both for completely inclusive and realistic experimental set- up [5]. Final state QED corrections are included exactly at 0(alpha) even in presence of experimental cuts [6] and higher order effects are also taken in account. The calculation of the observables has been worked out analytically as much as possible, in order to obtain accurate and fast numerical predictions. In order to fit the unknown parameters of the Minimal Standard Model, a least square procedure has been adopted, allowing for several choices on the parameters to be fitted and contemplating the possibility of taking into account proper penalty functions [7]. A detailed description of the theoretical formulation and of the physical results obtained up to now can be found in [8].

Restrictions:
The theoretical formulation is specifically worked out for energies around the Z0 peak. Analytic formulas have been developed for an experimental set-up with symmetrical angular acceptance. Moreover the angular acceptance of the scattered antifermion has been assumed larger than the one of the scattered fermion. The prediction for Bhabha scattering is understood to be for the large angle regime.

Unusual features:
Subroutines from the library of mathematical subprograms NAGLIB both for the numerical itegrations and the minimization procedure are used in the program.

Running time:
Dependent on the required experimental set-up. As evaluator of observables in seven energy points, between 10 (extrapolated set-up) and 270 (realistic set-up) CPU seconds for HP-APOLLO 7000, corresponding to 100 - 2500 CPU seconds for VAX 6410. As fitter, the running time is roughly given by the time needed as evaluator times the number of iterations requested to obtain convergence: dependent on the data sample.

References:
[1] NAG Fortran Library Manual Mark 15 (Numerical Algorithms Group, Oxford, 1991).
[2] G. Passarino and M. Veltman, Nucl. Phys. B160(1979)151; G. Passarino, in Radiative Corrections for e+e- Collisions, J.H. Kuhn ed. (Springer, Berlin, 1989) 179.
[3] D. Bardin et al., CERN-TH.6433/92 and references therein; R. Barbieri, M. Beccaria, P. Ciafaloni, G. Curci and A. Vicere, CERN-TH.6713/92; Phys. Lett. B288(1992)95.
[4] A.L. Kataev, Cern preprint, CERN-TH.6465/92 (1992); K.G. Chetyrkin, J.H. Kuhn and A. Kwiatkowski, Phys. Lett. B282(1992) 221; K.G. Chetyrkin and J.H. Kuhn, Phys. Lett B248(1990)359.
[5] O. Nicrosini and L. Trentadue, Phys. Lett. B196(1987)551; in Radiative Corrections for e+e- Collisions, J.H. Kuhn ed. (Springer, Berlin, 1989)25; in QED Structure Functions, G. Bonvicini ed., AIP Conf. Proc. No. 201(AIP, New York,1990)12; G. Montagna, O. Nicrosini and F. Piccinini, Structure Function Formulation of e+e- -> ffbar Around the Z0 Resonance in Realistic Set-up, University of Pavia preprint FNT/T - 93/06.
[6] G. Montagna, O. Nicrosini and G. Passarino, Analytic Final State Corrections to e+e- -> ffbar with Realistic Cuts, Submitted to Phys. Lett. B.
[7] G. Montagna, O. Nicrosini and G. Passarino, Standard Model Paramet- ers From a Global Fit to LEP Data, to appear in Phys. Lett. B.
[8] G. Montagna, O. Nicrosini, G. Passarino, F. Piccinini and R. Pittau, On a Semi-analytical and Realistic Approach to e+e- Annihilation into Fermion Pairs and to Bhabha Scattering within the Minimal Standard Model at LEP energies, to appear in Nucl. Phys. B.