Energy weighting for the upgrade of the CMS HCAL

In these simulation studies an energy weighting method is applied to the signals of the CMS hadronic calorimeter readout with a longitudinal segmentation for a possible future upgrade. Tabulated weighting factors are used to compensate for the different response of hadronic and electromagnetic energy depositions of simulated pion showers in the hadronic calorimeter. The weighting improves the relative energy resolution: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ (\sigma _E /E)^2 = \left[ {((92.2 \pm 0.6)\% /\sqrt E )^2 + ((6.5 \pm 0.1)\% )^2 } \right] $$\end{document} (before weighting), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ (\sigma _{E,weight} /E)^2 = \left[ {((85.4 \pm 0.5)\% /\sqrt E )^2 + ((4.4 \pm 0.1)\% )^2 } \right] $$\end{document} (after weighting), where E in the square root has units of GeV.


INTRODUCTION
The hadronic calorimeter (HCAL) of CMS is a non-compensating sampling calorimeter with an e/π ratio of about 1.2 for 50-GeV pions [1]. Consequently, the response for electromagnetic energy depositions is larger than for hadronic ones which affects the energy measurement. An energy weighting method to compensate for the e/π ratio is possible if one can identify the electromagnetic-or hadroniclike origin of the energy deposition within a hadronic shower. For the CMS detector upgrade Phase I a longitudinal segmentation of the HCAL towers is under consideration, improving its longitudinal granularity by a factor of 4 (see Fig. 1). This offers the possibility to resolve parts of particle showers. A possible readout scheme ("1-4-4-8") is investigated here, where each digit represents the number of calorimeter cells which are read out in one channel. Other possible readout schemes has been investigated, too. However, it turned out that the readout scheme "1-4-4-8" yields the best result for the weighting.

THE METHOD AND REALIZATION
The method of the tabulated weighting factors [2,3] is a software-based method, aiming to compensate for the e/π ratio of a calorimeter. The basic idea is to distinguish between electromagnetic and hadronic * The text was submitted by the authors in English. 1) DESY, Hamburg, Germany.
2) University of Hamburg, Germany. ** E-mail: matthias.stein@desy.de energy depositions and to find appropriate weighting factors for the compensation. The discrimination criterion is the energy density where E i meas is the measured energy and V i a measure for the volume in arbitrary units, both for a readout channel i.
The weighting is based on the fact that the average energy density of electromagnetic depositions is larger than for hadronic ones. In a Monte-Carlo (MC) simulation it is possible to obtain weighting factors w i as a function of the energy density ρ i : where E shower is the total shower energy received from a 3 × 3 cluster and E i dep is the deposited energy given by where E i abs is the energy deposited in the absorber, E i sci the energy deposited in the scintillator, and E i inv the invisible energy (from neutrinos, nuclear excitation, etc.).
Once the weighting factors are obtained from a Monte-Carlo simulation, they can be applied to data (here: simulated data) to yield a weighted energy For the realization of the weighting method, a simulation of the CMS HCAL is necessary. In the presented studies, this is done via a Geant3 [4] standalone simulation, since the deposited energy E i dep left in a readout channel i of the HCAL, including the absorber energy, is presently not available in the CMS software. GCALOR is chosen as shower generator, in order to make the simulation as realistic as possible [5]. A simulated test beam of pions with an energy of 50 GeV is used to calibrate the HCAL. Since the weighting factors depend on the shower energy, it is necessary to create a set of them for multiple simulated test beam energies. This is done for the following energies: 10, 20, 30, 50, 100, 150, 225, 300 GeV. However, for any energy which does not correspond to one of these energies, an interpolation of the weighting factors is required. Here, a linear interpolation is used.

RESULTS
The relative energy resolution and linearity before and after weighting using the "1-4-4-8" design are shown in Figs. 2 and 3, respectively. Both results are obtained from a Gaussian fit. The 80 GeV sample is a statistically independent test sample for which no weighting factors exist. The final result is obtained by interpolation between weighting factors of different energies only.
The energy resolution is where E in the square root has units of GeV.

CONCLUSION/OUTLOOK
Applying the weighting method to the CMS HCAL with the readout design "1-4-4-8", the sampling term and constant term of the energy resolution improve. As the energy distributions contain non-Gaussian tails (especially for lower energies), the improvement of the linearity is more pronounced for the mean of the distributions than for the mean of a Gaussian fit.
The entry at 80 GeV of the energy resolution (for which no weighting factors exist) is in good agreement with the other energies. This is an important consistency check. However, for the linearity there is a kink at 80 GeV. This can be explained by the linear interpolation of the weighting factors. In further investigations different interpolation methods should be studied systematically in order to avoid this effect.
Test beam results of the CMS HCAL can be found in [6]. To test the weighting method with nonsimulated data, the weighting factors can be applied to test beam data of a CMS HCAL test setup. First investigations look very promising and showed an even larger improvement of the energy measurement using a two-dimensional fit of the weighting factors (in the ρ-E beam plane), instead of a one-dimensional linear interpolation.