Study the MDT single-tube resolution in data and in MC and its impact on the muon momentum resolution.

Qualification Project summary

Introduction

This study investigates the impact of calibration uncertainties on the MDT performance. It focuses on high-pT muons as the impact on them is expected to be largest.

It employs tools specifically developed for this task, the T0ShiftSvc and the TMaxShiftSvc.

Background

Charge traveling through the gas volume of a MDT has a characteristic drift time spectrum. The drift time can be converted to a drift distance $r(t)$. The drift time measurement has an offset from the detector clock that is measured as $t_{0}$. The $r(t)$ relation is parametrised as a function of the maximum drift time $t_{\mathrm{max}}$. Both $t_{0}$ and $r(t)$ can be extracted from a parametric fit to the drift time spectrum. As fit parameters they carry uncertainties that to this day are not taken into account.

tspectrum.png

The impact of $t_{0}$ and $r(t)$ variations within their uncertainties is the main interest of this project. Simulated high pT muon samples are reconstructed using shifts of the $t_{0}$ and $r(t)$ values. The shifts are calculated for every tube, are normally distributed with central values of typical $t_{0}$ and $r(t)$ uncertainties, and are fixed values (i.e. they don't change from event to event, or run to run, or day to day, etc.).

$t_{0}$ transformation

Applying the $t_{0}$ uncertainty is straightforward and implemented as $t \to t + \delta t$. The $\delta t$ is a random number, drawn for every tube from a normal distribution with a central value of 0 and different $\sigma$ values. The values are summarised in Table 1 and shown on the right.

Central Value [ns] Sigma [ns] Comment
0.0 0.0 Used to perform null test
0.0 0.2 Bla 1
0.0 0.5 Bla 2
0.0 1.0 Bla 3

t0 shifts.png

Modifying $r(t)$

The $r(t)$ relation was modified in two ways. In a first study, the input value $t$ is shifted by a per-tube random but fixed integer which is drawn from a uniform distribution. In a second study the calculated $r$ value is shifted. Both approaches yield negligible specotrometer resolution deteriorations.

The $r(t)$ relation has a few solutions that are per definition correct. For example, the $t_{0}$ will always be mapped onto 0, $t_\mathrm{max}$ will always be mapped on the maximimal drift length of 14.6 mm. A track traversing the chambers with zero angle will also have zero error on the drifth length at $(t_{0} + t_\mathrm{max})/2$. This case is studied as a reference case to estimate the uncertainty introduced by modifying the $r(t)$ relation.

The uncertainties are point symmetric w.r.t. $(t_{0} + t_\mathrm{max})/2$ and modelled by a sinus with different amplitudes. The amplitudes are chosen such that the RMS values are 30, 50, and 80 $\mathrm{\mu m}$.

rt mod.png

-- AndreasHoenle1 - 2017-12-01

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Topic revision: r4 - 2017-12-20 - AndreasHoenle1
 
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