Radiative corrections to the Z0 resonance.

We review calculations of the radiative corrections to the Z” resonance, and we show that while the radiative corrections are quite large, they can be calculated and incorporated into the comparison with experiment so that there will be no significant theoretical uncertainties on the measurements of the 2’ mass and width at SLC and LEP. We compare calculations based on matrix elements and structure function methods, and discuss two Monte Carlo’s based on these calculations. We use the new calculations to refit the J/q resonance. Submitted to Physical Review D * Work supported by the Department of Energy, Contracts DE-AC03-76SF00515 (SLAC), DE-AC03-76SF00098 (LBL) and DE-AC02-84ER40125 (U. of Mich.). The experimental evidence supporting the standard model of electroweak interactions is impressive. Perhaps most spectacular of all has been the direct observation of the Z”, the heavy gauge boson predicted by the model, at the pp collider at CERN. Once one can directly produce Z’s, one is in an excellent position to do detailed studies of the electroweak interaction, both by studying in Z” decays how the 2’ couples to the matter fields of quarks and leptons, and by precision measurements of the resonance itself. The Z” resonance, in lowest order, has a Breit-Wigner line shape which is characterized by experimentally measurable quantities: the peak position or mass, the width, and the peak cross section. From an experimental point of view the three parameters, mass, width, and cross section, are independent quantities to be determined. Within the context of the standard model, however, they take on deeper significance that both motivates their measurement and sets the scale of precision at which the measurements may be considered interesting. The mass is, related to sin28w; the width depends on the number of particles of mass less than half the mass of the Z” which couple to the 2’; and the peak cross section is related to the vector and axial vector couplings, and hence sin28w. . Precision studies of the 2’ resonance have not been forthcoming from the Sp$3 where the 2’ was first discovered. The broad spectrum of parton energies in pp collisions means that only a small portion of the total luminosity manifests itself in production of the relatively narrow Z” peak, and the resonance is difficult to extract from the much larger nonresonant QCD background. In the exclusive leptonic decay modes of the Z”, which have clean signatures and can be easily extracted from the background events, the mass of the 2’ can only be determined from the invariant mass of the lepton pair, since the initial state energy is unknown. :. At the SLC and LEP, the situation is quite different. Because the electron and positron are pointlike, the center-of-mass energy of the interaction is defined by the beam energy. The beam energy spread is small compared to the resonance