Transverse energy resolution

The transverse energy ($E_{t}$) resolution can be obtained by using single particles impinging the calorimeter, nearly parallel to the detector axis. Since in this case a $E_{t}$=0 is expected, the reconstructed one $E_{t}^{rec}$ depends only on the detector reconstruction capability. A good resolution in the $E_{t}$ reconstruction allows to increase the efficiency in the $\tau$ detection, where final states of the $\nu_\tau$ interaction are characterised by a transverse energy missing.

The used algorithm is:

$$E_t^{rec} = E \sin \bar{\Theta}$$

where

$$\bar{\Theta} = \frac{1.}{\Sigma _i Q_i} \cdot \Sigma _i Q_{i} \arcsin \frac{(x_i-x_v)}{\sqrt{(x_i-x_v)^2+(z_i-z_v)^2}}$$

where $E_{i}$ is energy deposited in the i-th bar, $x_i$, $z_i$ are the coordinates of the i-th bar in the XZ plane and $x_v$, $z_v$ are the impact coordinates on the calorimeter derived fitting the track in the TRD module.

Figure 17 shows the $E_{t}^{rec}$ distribution for a 2 GeV $\pi$; the relative resolution for 3 GeV pions is $\sigma_{E_{t}^{rec}}$=420 MeV, in excellent agreement with the Monte Carlo prediction.