arXiv subjects
Publications and source records attributed to Donald E. Groom.
The DREAM collaboration has introduced the "Q/S Method" for obtaining the energy estimator from simultaneous Cherenkov and scintillator readouts of individual hadronic events. We show that the algorithm is equivalent to an elementary method.
If the response to a hadronic shower in a semi-infinite uniform calorimeter structure is $S$ relative to the electronic response, then $S/E = [\fem + (1-\fem)(h/e)]$, where $E$ is the incident hadron energy, $\fem$ is the electronic shower fraction, and $h/e$ is the hadron/electron response ratio. In conventional calorimeters the energy resolution is dominated by the stochastic variable $\fem$, whose broad, skewed pdf has an energy-dependent mean. The slow increase of the mean with $E$ is responsible for response nonlinearity and the skewness results in a non-Gaussian response. If the cascade is observed in two channels with different values of $h/e$ (typically scintillator($S$) and Cherenkov ($C$)), $\fem$ can be eliminated. An energy estimator, linear in $C$ and $S$, is obtained which is proportional to the incident hadron's energy. The resolution depends upon the contrast in $h/e$ between the two channels. The Cherenkov $h/e$ will be 0.20--0.25. In sampling calorimeters, $h/e$ can be increased to about 0.7 by arranging for preferential absorption of the electromagnetic (EM) shower energy in the absorber (decreasing $e$) and using a hydrogenous detector (organic scintillator) to enhance $h$ through the contribution of recoil protons in $n$--$p$ scattering. Neither mechanism is available in a homogeneous crystal or glass scintillator,\rm where $h/e$is expected to be in the vicinity of 0.4 because of invisible hadronic energy loss and other effects. The $h/e$ contrast is very likely too small to provide the needed energy resolution. We support this conclusion with simple Monte Carlo simulations.
The hadronic cascade description developed in an earlier paper is extended to the response of an idealized fine-sampling hadron calorimeter. Calorimeter response is largely determined by the transfer of energy $E_e$ from the hadronic to the electromagnetic sector via $π^0$ production. Fluctuations in this quantity produce the "constant term" in hadron calorimeter resolution. The increase of its fractional mean, $f_{\rm em}^0 = \vev{E_e}/E$, with increasing incident energy $E$ causes the energy dependence of the $π/e$ ratio in a noncompensating calorimeter. The mean hadronic energy fraction, $f_h^0 = 1-f_{\rm em}^0$, was shown to scale very nearly as a power law in $E$: $f_h^0 = (E/E_0)^{m-1}$, where $E_0\approx1$ GeV for pions, and $m\approx0.83$. It follows that $π/e=1-(1-h/e)(E/E_0)^{m-1}$, where electromagnetic and hadronic energy deposits are detected with efficiencies $e$ and $h$, respectively. Fluctuations in these quantities, along with sampling fluctuations, are incorporated to give an overall understanding of resolution, which is different from the usual treatments in interesting ways. The conceptual framework is also extended to the response to jets and the difference between $π$ and $p$ response.