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Manuscript Title: TOPAZ0 4.0 - A new version of a computer program for evaluation of de- convoluted and realistic observables at LEP 1 and LEP 2.
Authors: G. Montagna, O. Nicrosini, F. Piccinini, G. Passarino
Program title: TOPAZ0 4.0
Catalogue identifier: ACNT_v3_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 117(1999)278
Programming language: Fortran.
Computer: DEC-ALPHA 3000.
Operating system: VMS, UNIX.
RAM: 300K words
Word size: 32
Keywords: Elementary, Particle physics, E+e- annihilation, Bhabha scattering, Lep, Z resonance, Electroweak, Extrapolated and, Realistic experimental, Set-up, Qcd corrections, Corrections qed, Pure weak corrections, Radiative corrections, Minimal standard model, De-convoluted and, Realistic observables.
Classification: 11.5.

Nature of problem:
An accurate theoretical description of e+e- annihilation processes and of Bhabha scattering for centre of mass energies at the Z resonance (LEP 1) and above (LEP 2) is necessary in order to compare theoretical cross sections and asymmetries with the experimental ones as measured by the LEP collaborations (realistic observables). 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 the comparison of the Minimal Standard Model predictions with 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. The program offers also the possibility of computing the Z parameters (pseudo-observables) including the state-of-the-art of radiative corrections, which is important for the indirect determination of the fundamental Standard Model parameters.

Solution method:
Same as in the original program. A detailed description of the theoretical formulation and of a sample of physical results obtained can be found in ref. [2].

Summary of revisions:
The new version of the program TOPAZ0 4.0, includes several improvements:
  • recently computed two-loop electroweak next-to-leading O(alpha**2mt**2) corrections [3,4];
  • QCD radiative corrections tothe hadronic decay of the Z, providing complete corrections of O(alphaalphas) to Gamma(Z -> qqbar) with q = u, d, s, c and b [5];
  • purely weak boxes for s-channel processes [6];
  • next-to-leading O(alpha**2) and leading O(alpha**3) QED corrections to the cross section radiator [7,8];
  • improved treatment of the convolution integral for the forward-backward asymmetry [9].
All the new corrections are relevant for electroweak physics at LEP 1 and/or LEP 2.

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 to be larger than the one of the scattered fermion. The prediction for Bhabha scattering is understood to be for the large-angle regime. Initial-state next-to-leading O(alpha) QED corrections are treated exactly for a cut on the invariant mass of the event after initial-state radiation, in the soft photon approximation otherwise. This means that for centre of mass energies sensibly above the Z0 peak (typically in the LEP 1.5 - LEP 2 regime), the theoretical accuracy of the C branch is under control (theoretical error <= 0.3 per cent) when excluding the Z radiative return, whereas including it the theoretical error can grow up to some per cent depending on the final state selected [10]. In the same energy range, large angle Bhabha scattering becomes a t-channel dominated process: since all the QED corrections implemented are strictly valid for s-channel processes, this means that large angle Bhabha scattering off the Z resonance is treated at the leading logarithmic level.

Unusual features:
Subroutines from the library of mathematial subprograms NAGLIB [1] for the numerical integrations are used in the program.

Running time:
This depends strongly on the particular experimental set-up studied and on the energy range. As evaluator of realistic observables in seven energy points around the Z0 peak, between 10 (extrapolated set-up) and 270 (realistic set-up) CPU seconds for HP-UX 9000. Anyway, for the realistic observables the CPU time depends strongly on being at LEP 1 or LEP 2, and on the scaling factor SE controlling the accuracy of the numerical integrations. For the evaluation of pseudo-observables the program runs much faster.

[1] NAG Fortran Library Manual Mark 17 (Numerical Algorithms Group, Oxford, 1991).
[2] G. Montagna, O. Nicrosini, G. Passarino, F. Piccinini, R. Pittau, Nucl. Phys. B 401 (1993) 3.
[3] G. Degrassi, S. Fanchiotti, A. Sirlin, Nucl. Phys. B 351 (1991) 49; G. Degrassi, A. Sirlin, Nucl. Phys. B 352 (1991) 342; G. Degrassi, P. Gambino, A. Vicini, Phys. Lett. B 383 (1996) 219; G. Degrassi, P. Gambino, A. Sirlin, Phys. Lett. B 394 (1997) 188.
[4] G. Degrassi, P. Gambino, in preparation.
[5] A. Czarnecki, J.H. Kuhn, Phys. Rev. Lett. 77 (1996) 3955; hep-ph/ 9712228; R. Harlander, T. Seidensticker, M. Steinhauser, hep-ph/971228.
[6] F. Boudjema, B. Mele et al., Standard Model Processes, in: Physics at LEP2, Vol. 2, G. Alterelli, T. Sjostrand, F. Zwirner, eds., CERN Report 96-01 (Geneva, 1996) p. 229.
[7] F. Berends et al., Z Line shape, in: Z Physics at LEP 1, Vol. 1, G. Altarelli, R. Kleiss, C. Verzegnassi, eds., CERN Report 89-08 (Geneva, 1989) p. 89.
[8] G. Montagna, O. Nicrosini, F. Piccinini, Phys. Lett. B 406 (1997) 243.
[9] M. Bohm, W. Hollik et al., Forward-Backward Asymmetries, in: Z Physics at LEP 1, Vol. 1, G. Altarelli, R. Kleiss, C. Verzegnassi, eds., CERN Report 89-08 (Geneva, 1989) p. 203.
[10] G. Montagna, O. Nicrosini, F. Piccinini, Z. Phys. C 76 (1997) 45.