Energy flow in a hadronic cascade: Application to hadron calorimetry

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 $\pi^0$ 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 $\pi/e$ 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 $\pi/e=1-(1-h/e)(E/E_0)^{m-1}$, 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 $\pi$ and $p$ response.