Systematic uncertainties

Results from the two analyses show general agreement. Larger systematic errors are expected for aerogel radiators due to the lower number of photons detected per event and the relatively large background. The differences in the ratio of observed to predicted photon yields which exist between the analyses, are used to assign a systematic uncertainty. The systematic errors are determined in terms of their effect on the mean ratio of observed to predicted photon yields and are ascribed as follows :

• Photon counting -  There are clearly substantial correlations between the two analyses, hence the full size of the differences is taken as the error on the mean ratio. These vary from run to run, but on average are 4% for the gas data and 10% for the aerogel data.
• Pedestal cut -  A contribution of 5% is added to cover the uncertainty in the effect of the pedestal cut. This error is conservatively assigned to all samples, although in principle it is less for the gas rings, where the fraction of hit pixels with two or more photoelectrons is significant.
• Refractive indices -  There is an uncertainty in the prediction due to imprecise knowledge of the refractive indices. It is important to note that variations in the number of produced photons with changes in refractive index, are anticorrelated with the change in geometric acceptance. Therefore the resulting error is relatively small. Changes of $\pm$10% in (n - 1) are considered for all samples, and the effect of alternative parameterisations of the chromatic dependence are studied. All variations are found to lie within 2.5% of the number of observed photons.
• Acceptance and optical properties -  Additional errors come from knowledge of the absolute geometric acceptance and from the modelling of the transmissions, reflectivity, aerogel clarity and photocathode quantum efficiency. These are estimated to result in a 7% uncertainty.

The total systematic error from the sum of all sources is 13% for the aerogel and 10% for the gas radiators.