Software corrections to charge measurements

Several methods have been developed in the last years to improve the hadronic energy resolution by means of software corrections. Following the CDHS collaboration prescription [8], the corrected total charge $Q_{\rm corr}$ can be defined as

$$Q_{\rm corr} = \sum{ADC_i \times ( 1 - K \times ADC_i)}$$

where $K$ has to be evaluated from data, by minimizing $\sigma ( Q_{\rm corr})/ Q_{\rm corr}$.

As far as CDHSis concerned $K$ is running with the energy of incident hadrons, $k= \eta / \sqrt{E}$ while in our case it turns out to be constant in the whole energy range explored, with $k=0.008$.

Figure 14 shows the distribution of the total charge reconstructed in the calorimeter before and after the described corrections, for 3 GeV pions.

As shown in Figure  the calorimeter linearity is fully preserved.

In the Figure 16 the hadronic energy resolution curve after ADC data corrections is shown. A hadronic energy resolution of $\sigma/E \simeq \sqrt{2}*37.4\% / \sqrt{E}+1.5\%$ is achieved, with an improvement in the stochastic term of about 15%.