Discussion and detector response parameters

This variation in the ratio of observed to predicted photon yields throughout the runs considered, is consistent with the systematic uncertainties ascribed above. Significant disagreement between observed and predicted photon yields occurs only for the C₄F₁₀ data with the mylar-shielded HPDs. The other C₄F₁₀ datasets which cover that part of the spectrum relevant for LHCb show no discrepancy. The aerogel samples give reasonable agreement thoughout, with the aerogel sample 1 being systematically, slightly lower than expectations.

It is possible to convert the average photon yields of the two analyses from Tables 3 and 4 into values of the detector response parameter [4] assuming a perfect geometrical coverage and detection efficiency. This is referred to as N₀^perf and is defined here by :

$${\frac{N_{\mathrm pe} }{L \, sin^2 \theta_{\mathrm C} }}$$ (4)

where N_pe is the number of detected photoelectrons, corrected for backgrounds, and the effects of geometrical and threshold cut losses. A slightly modified quantity is that, taking into account the efficiency of the 3 sigma pedestal cut which is denoted by N₀^3$\sigma$. The values of these two estimates of the detector response parameter are given in Table 5 for each of the experimental layouts used.

Table: The observed mean $\theta_{\rm c}^{}$ and detector response parameters, with and without corrections applied for the efficiency of the 3 sigma cut on the HPD pedestal distribution.

Layout	$\theta_{\rm c}^{}$ (in mrad)	N0perf	N03$\sigma$
1	19.3	318.8	271.0
2	50.4	342.8	291.4
3	52.3	336.7	286.2
4	51.2	91.6	77.8
5	260.0	91.8	78.0
6	258.0	56.8	48.3
7	257.0	38.4	32.6
8	277.0	55.9	47.5