Energy weighting for the upgrade of the CMS HCAL

AbstractIn 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: $$
(\sigma _E /E)^2 = \left[ {((92.2 \pm 0.6)\% /\sqrt E )^2 + ((6.5 \pm 0.1)\% )^2 } \right]
$$ (before weighting), $$
(\sigma _{E,weight} /E)^2 = \left[ {((85.4 \pm 0.5)\% /\sqrt E )^2 + ((4.4 \pm 0.1)\% )^2 } \right]
$$ (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 hadronic-like 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 four (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 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.