Electromagnetic Radiative Corrections to Deep-inelastic Neutrino Interactions (1979)

III. Results

We present numerical values for the radiative-correction factor

in the process as a function of the kinematic variables , , and , defined by

where , , , and are the energies and four-momenta of the incoming neutrino and outgoing muon, respectively.

Figure 9 shows the correction to as a function of with and 500 GeV. Note that the model should not apply in regions where the out-going muon or parton has small momentum; for this case these regions are near 0 or 1. (A cut in to avoid the elastic region has no important effects.) The general shape of the curves in Fig. 9 may be understood intuitively; the muon loses energy through bremsstrahlung, shifting events to higher values. In Figs. 10, 11, and 12 we show corrections to various double-differential cross sections, as a function of (Fig. 10) and (Fig. 11) for various values of , and as a function of for various values of (Fig. 12). The model should not be valid for small .

The dependence of on at a given (Fig. 12) appears to be approximately linear. We have accordingly fitted straight lines to the results, of the form , and the values of and , for various and for neutrinos and antineutrinos, are tabulated in Table I. A simpler but adequate fit to all our results is given by the following: For neutrinos

and for antineutrinos

where and are in GeV. The rms difference between the value of according to the fit and the value as computed is around 0.01, i.e., 1% of the uncorrected cross section.

[ Table 1 ] Linear fits to the correction factor of the form

[ Table 1 ] Continued

Figure 13 shows the correction as a function of for the process . These radiative corrections are rather larger than those with final muons (see Fig. 9) and will therefore add further to the difficulties of high-energy experiments.