Further observations on midrapidity et distributions with aperture corrected scale

In a previous publication [T. Abbott et al., E802 Collaboration, Phys. Rev. C 63, 064602 (2001); 64, 029901(E) (2001)], measurements of the A dependence and pseudorapidity interval $(\ensuremath{\delta}\ensuremath{\eta})$ dependence of midrapidity ${E}_{T}$ distributions in a half-azimuth $(\ensuremath{\Delta}\ensuremath{\varphi}=\ensuremath{\pi})$ electromagnetic calorimeter were presented for $p+\mathrm{Be},$ $p+\mathrm{Au},$ O+Cu, Si+Au, and Au+Au collisions at the BNL-AGS. The validity of the ``nuclear geometry'' characterization versus $\ensuremath{\delta}\ensuremath{\eta}$ was illustrated by plots of the ${E}_{T}(\ensuremath{\delta}\ensuremath{\eta})$ distribution in each $\ensuremath{\delta}\ensuremath{\eta}$ interval in units of the measured $〈{E}_{T}(\ensuremath{\delta}\ensuremath{\eta}){〉}_{p+\mathrm{A}\mathrm{u}}$ in the same $\ensuremath{\delta}\ensuremath{\eta}$ interval for $p+\mathrm{Au}$ collisions. These plots, with aperture corrected scale in the physically meaningful units of number of average observed $p+\mathrm{Au}$ collisions, were nearly universal as a function of $\ensuremath{\delta}\ensuremath{\eta},$ confirming that the reaction dynamics for ${E}_{T}$ production at midrapidity at AGS energies is governed by the number of projectile participants and can be well characterized by measurements in apertures as small as $\ensuremath{\Delta}\ensuremath{\varphi}=\ensuremath{\pi},\ensuremath{\delta}\ensuremath{\eta}=0.3.$ A key ingredient in these analyses is the probability ${p}_{0}$ for no signal to be detected in a given aperture $\ensuremath{\delta}\ensuremath{\eta}$ for the fundamental $p+\mathrm{Au}$ collision. In fact the measured $〈{E}_{T}(\ensuremath{\delta}\ensuremath{\eta}){〉}_{p+\mathrm{A}\mathrm{u}}$ is biased and the true $〈{E}_{T}(\ensuremath{\delta}\ensuremath{\eta}){〉}_{p+\mathrm{A}\mathrm{u}}^{\mathrm{true}}$ for the detector aperture is the measured value times $1\ensuremath{-}{p}_{0}.$ The issues and merits of measuring the ${E}_{T}(\ensuremath{\delta}\ensuremath{\eta})$ distribution in units of $〈{E}_{T}(\ensuremath{\delta}\ensuremath{\eta}){〉}_{p+\mathrm{A}\mathrm{u}}$ or $〈{E}_{T}(\ensuremath{\delta}\ensuremath{\eta}){〉}_{p+\mathrm{A}\mathrm{u}}^{\mathrm{true}}$ in the same $\ensuremath{\delta}\ensuremath{\eta}$ interval are presented and discussed. This method has application at RHIC, where p-$p$ data could be used as the reference distribution for two participants. The ${E}_{T}$ distributions for $B+A$ collisions, with ${E}_{T}(\ensuremath{\delta}\ensuremath{\eta})$ scale normalized by $〈{E}_{T}(\ensuremath{\delta}\ensuremath{\eta}){〉}_{p\ensuremath{-}p}^{\mathrm{true}}$ in the same aperture for $p\ensuremath{-}p$ collisions, would then be given directly in the popular unit ``per participant-pair'' [K. Adcox et al., PHENIX Collaboration, Phys. Rev. Lett. 86, 3500 (2001); I. G. Bearden et al., BRAHMS Collaboration, Phys. Lett. B523, 227 (2001); B. B. Back et al., PHOBOS Collaboration, Phys. Rev. C 65, 031901(R) (2002); C. Adler et al., STAR Collaboration, Phys. Rev. Lett. 89, 202301 (2002)].