Alignment of the silicon telescope

The beam telescope is used to provide an event-by-event track direction for the Cherenkov angle reconstruction. To achieve this, the alignment uncertainty of the telescope must be significantly less than 0.4 mrad with respect to the RICH vessel.

Internal alignment of the telescope is achieved by selecting events with precisely one hit in each plane and studying fit residuals with respect to a straight line. External alignment is performed using events with $\ge$2 detected photons in the RICH. For measured track slopes (m_x, m_y) different from their true values :

$$\delta_{m_x}^{} \delta_{m_y}^{}$$

then a shift of the measured Cherenkov angles is induced. By minimising the spread in the measured Cherenkov angles, as a function of ($\delta_{m_x}^{}$,$\delta_{m_y}^{}$), their optimum values are determined as shown in Figure 7.

Figure 7: Variance of the measured Cherenkov angles as a function of the constant offsets, $\delta$m_x and $\delta$m_y, applied to the gradient of the silicon telescope beam vector.

The values of $\delta_{m_x}^{}$ and $\delta_{m_y}^{}$ which minimize the average variance < $\sigma^{2}_{}$($\theta_{1}^{}$,$\theta_{2}^{}$,...,$\theta_{\mathrm{n_{\gamma}}}^{}$) > are of the order of $\pm$1 mrad, and are used to correct the event-by-event beam direction determined from telescope data.