% CORRETTO BABBO
A \textbf{hit} on a detector occurs when one of its readout channels collects enough charge to exceed the threshold set in the readout chip. This happens when an electron cloud crosses the last GEM foil. This occurs usually after a particle has started an avalanche in the multiplication volume, but noise and \textit{cross-talk} between adjacent readout channels can also produce a moderate number of hits.\\

We define \textbf{cluster} a set of adjacent hit channels along the $x$ or $y$ axis. A one-channel wide gap is allowed within the set.\\

During the test-beam, we needed to select a sbset of the data we collected, in order to speed up the analysis process. Therefore we reconstructed the tracks of the incident particles only if the following conditions were both satisfied:
\begin{itemize}
	\item all the chambers of the tracker presented exactly one hit cluster along the $x$ axis, and one along the $y$ axis;
	\item the hit number in each chamber of the tracker (that is the \textit{cluster size}, since we requested a single cluster) was $\leq 120$.
\end{itemize}

The track reconstructing algorithm exploits ROOT's class \texttt{TGraphErrors}. The algorithm structure is: 
\begin{enumerate}
	\item the previously measured distance along the $z$ axis between the tracker chambers is used as a constant;
	\item the $x$ position of clusters is plotted versus $z$ in a \texttt{TGraphErrors} object;
	\item the plot is fitted with a first order polynomial via the ROOT \texttt{Fit()} function.
\end{enumerate}
This way, the fit function itself and its parameters ($\chi^2$, residuals, $q$ and $m$) become available i the $x-$track object itself.
The same procedure is used to define $y-$track objects.\\

If we define n\subscript{act} as the actual number of hits collected by the LG, and n\subscript{exp} as the number of expected hits, then
$$\frac{n_{act}}{n_{exp}}$$
represents the Large GEM's \textbf{efficiency}. Every time the distance between the position $\mathbf{r}_{HIT}$ of the hit on the LG and the \textit{projection} $\mathbf{r}_{TRK}$ on the LG of the corresponding track is minor than a given efficiency radius $effrad$, we say that the chamber has been \textbf{efficient} (and thus we increment $n_{act}$ by 1):
$$
| \mathbf{r}_{HIT} - \mathbf{r}_{TRK} | \leq effrad \quad \Longrightarrow \quad n_{act} = n_{act} + 1
$$