\addvspace {10\p@ }
\contentsline {figure}{\numberline {1.1}{\ignorespaces Theoretical momentum-angle spectrum}}{5}{figure.1.1}
\addvspace {10\p@ }
\contentsline {figure}{\numberline {2.1}{\ignorespaces Cut away view of the TWIST spectrometer}}{12}{figure.2.1}
\contentsline {figure}{\numberline {2.2}{\ignorespaces M13 beamline diagram}}{13}{figure.2.2}
\contentsline {figure}{\numberline {2.3}{\ignorespaces Pion decay kinematic}}{13}{figure.2.3}
\contentsline {figure}{\numberline {2.4}{\ignorespaces Pion decay kinematic edge}}{14}{figure.2.4}
\contentsline {figure}{\numberline {2.5}{\ignorespaces Side view of the spectrometer; DC geometry}}{16}{figure.2.5}
\contentsline {figure}{\numberline {2.6}{\ignorespaces DC position change for final analysis}}{18}{figure.2.6}
\contentsline {figure}{\numberline {2.7}{\ignorespaces Target module}}{20}{figure.2.7}
\contentsline {figure}{\numberline {2.8}{\ignorespaces Upstream beam package}}{22}{figure.2.8}
\contentsline {figure}{\numberline {2.9}{\ignorespaces Time Expansion Chamber (TEC)}}{24}{figure.2.9}
\contentsline {figure}{\numberline {2.10}{\ignorespaces TEC typical event}}{25}{figure.2.10}
\addvspace {10\p@ }
\contentsline {figure}{\numberline {3.1}{\ignorespaces Analysis flow diagram}}{29}{figure.3.1}
\contentsline {figure}{\numberline {3.2}{\ignorespaces Classification example}}{31}{figure.3.2}
\contentsline {figure}{\numberline {3.3}{\ignorespaces Hit clusters formation}}{33}{figure.3.3}
\contentsline {figure}{\numberline {3.4}{\ignorespaces ``First guess'' algorithm example}}{34}{figure.3.4}
\contentsline {figure}{\numberline {3.5}{\ignorespaces Hit association in $u$-$v$ by the ``first guess''}}{36}{figure.3.5}
\contentsline {figure}{\numberline {3.6}{\ignorespaces Helix winding number determination}}{36}{figure.3.6}
\contentsline {figure}{\numberline {3.7}{\ignorespaces Narrow windows algorithm}}{37}{figure.3.7}
\contentsline {figure}{\numberline {3.8}{\ignorespaces Drift distances calculation}}{38}{figure.3.8}
\contentsline {figure}{\numberline {3.9}{\ignorespaces Derivative spectra}}{41}{figure.3.9}
\contentsline {figure}{\numberline {3.10}{\ignorespaces Residuals from the muon decay parameter fit}}{42}{figure.3.10}
\contentsline {figure}{\numberline {3.11}{\ignorespaces Kinematic end-point edges}}{45}{figure.3.11}
\addvspace {10\p@ }
\contentsline {figure}{\numberline {4.1}{\ignorespaces Number of events before cuts}}{47}{figure.4.1}
\contentsline {figure}{\numberline {4.2}{\ignorespaces Beam time of flight structure}}{48}{figure.4.2}
\contentsline {figure}{\numberline {4.3}{\ignorespaces Typical histogram for each cut}}{50}{figure.4.3}
\contentsline {figure}{\numberline {4.4}{\ignorespaces PC 5 and PC 6 pulse width distributions}}{52}{figure.4.4}
\contentsline {figure}{\numberline {4.5}{\ignorespaces Cut on the pulse width distribution}}{53}{figure.4.5}
\contentsline {figure}{\numberline {4.6}{\ignorespaces Track matching cut}}{54}{figure.4.6}
\contentsline {figure}{\numberline {4.7}{\ignorespaces Closest distance of approach distribution}}{55}{figure.4.7}
\contentsline {figure}{\numberline {4.8}{\ignorespaces Tuning of the muon-positron vertex cut}}{56}{figure.4.8}
\contentsline {figure}{\numberline {4.9}{\ignorespaces Fiducial cuts}}{59}{figure.4.9}
\addvspace {10\p@ }
\contentsline {figure}{\numberline {5.1}{\ignorespaces PC time of flight measurement}}{63}{figure.5.1}
\contentsline {figure}{\numberline {5.2}{\ignorespaces Chamber response tuning}}{64}{figure.5.2}
\contentsline {figure}{\numberline {5.3}{\ignorespaces Muon stopping chamber distributions for data and MC}}{65}{figure.5.3}
\contentsline {figure}{\numberline {5.4}{\ignorespaces Event type distributions for data and MC}}{66}{figure.5.4}
\contentsline {figure}{\numberline {5.5}{\ignorespaces Scattering angle through the silver target module}}{68}{figure.5.5}
\contentsline {figure}{\numberline {5.6}{\ignorespaces Scattering angle through the aluminium target module}}{69}{figure.5.6}
\contentsline {figure}{\numberline {5.7}{\ignorespaces Energy loss through the silver target}}{70}{figure.5.7}
\contentsline {figure}{\numberline {5.8}{\ignorespaces Energy loss through the aluminium target}}{71}{figure.5.8}
\contentsline {figure}{\numberline {5.9}{\ignorespaces Reconstruction inefficiency from upstream stops}}{72}{figure.5.9}
\addvspace {10\p@ }
\contentsline {figure}{\numberline {6.1}{\ignorespaces Cathode foil bulge}}{74}{figure.6.1}
\contentsline {figure}{\numberline {6.2}{\ignorespaces Cathode foil bulge measurement}}{75}{figure.6.2}
\contentsline {figure}{\numberline {6.3}{\ignorespaces Hit time distribution for wire time offset measurement}}{77}{figure.6.3}
\contentsline {figure}{\numberline {6.4}{\ignorespaces Wire time offset match between data and MC}}{77}{figure.6.4}
\contentsline {figure}{\numberline {6.5}{\ignorespaces Wire time offset upstream-downstream asymmetry}}{78}{figure.6.5}
\contentsline {figure}{\numberline {6.6}{\ignorespaces STRs isochrons}}{80}{figure.6.6}
\contentsline {figure}{\numberline {6.7}{\ignorespaces Helix fit time residuals}}{81}{figure.6.7}
\contentsline {figure}{\numberline {6.8}{\ignorespaces Reconstruction resolution and momentum bias}}{81}{figure.6.8}
\addvspace {10\p@ }
\contentsline {figure}{\numberline {7.1}{\ignorespaces Number of broken tracks versus the bremsstrahlung momentum}}{87}{figure.7.1}
\contentsline {figure}{\numberline {7.2}{\ignorespaces Number of broken tracks versus the $\delta $-ray momentum}}{89}{figure.7.2}
\contentsline {figure}{\numberline {7.3}{\ignorespaces PC time of flight distributions}}{90}{figure.7.3}
\contentsline {figure}{\numberline {7.4}{\ignorespaces Comparison of the resolution in data and simulation}}{92}{figure.7.4}
\contentsline {figure}{\numberline {7.5}{\ignorespaces Helix fit time residuals in data and MC.}}{98}{figure.7.5}
\contentsline {figure}{\numberline {7.6}{\ignorespaces Contribution of the resolution to the STRs systematic uncertainty.}}{99}{figure.7.6}
\contentsline {figure}{\numberline {7.7}{\ignorespaces Track reconstruction efficiency difference between data and MC}}{101}{figure.7.7}
\contentsline {figure}{\numberline {7.8}{\ignorespaces Difference between input and output wire time offsets in MC}}{103}{figure.7.8}
\addvspace {10\p@ }
\contentsline {figure}{\numberline {8.1}{\ignorespaces Difference $\Delta \delta $ for each data set}}{111}{figure.8.1}
\contentsline {figure}{\numberline {8.2}{\ignorespaces Comparison of the measurements $\delta $}}{111}{figure.8.2}
\contentsline {figure}{\numberline {8.3}{\ignorespaces Difference $\Delta \eta $ for each data set}}{116}{figure.8.3}
\contentsline {figure}{\numberline {8.4}{\ignorespaces Comparison of the measurements $\eta $}}{117}{figure.8.4}
\addvspace {10\p@ }
\addvspace {10\p@ }
\addvspace {10\p@ }
\contentsline {figure}{\numberline {C.1}{\ignorespaces TEC calibration flow chart}}{129}{figure.C.1}
\contentsline {figure}{\numberline {C.2}{\ignorespaces TEC collimators}}{130}{figure.C.2}
\contentsline {figure}{\numberline {C.3}{\ignorespaces Hit time distribution for the collimator central hole}}{132}{figure.C.3}
\contentsline {figure}{\numberline {C.4}{\ignorespaces Time wire offsets versus wire number}}{133}{figure.C.4}
\contentsline {figure}{\numberline {C.5}{\ignorespaces Typical TDC signal shape}}{134}{figure.C.5}
\contentsline {figure}{\numberline {C.6}{\ignorespaces TEC drift times versus TDC widths}}{134}{figure.C.6}
\contentsline {figure}{\numberline {C.7}{\ignorespaces Discriminator amplitude walk versus wire number}}{135}{figure.C.7}
\contentsline {figure}{\numberline {C.8}{\ignorespaces TEC STRs measurement}}{137}{figure.C.8}
\contentsline {figure}{\numberline {C.9}{\ignorespaces TEC STRs temperature dependence}}{138}{figure.C.9}
\contentsline {figure}{\numberline {C.10}{\ignorespaces Differences between TEC calibrations}}{139}{figure.C.10}
\addvspace {10\p@ }
\contentsline {figure}{\numberline {D.1}{\ignorespaces Wire chamber alignment technique}}{144}{figure.D.1}
\contentsline {figure}{\numberline {D.2}{\ignorespaces Target kink effect on the alignment procedure}}{145}{figure.D.2}
\contentsline {figure}{\numberline {D.3}{\ignorespaces Wire chambers relative alignment precision}}{146}{figure.D.3}
\contentsline {figure}{\numberline {D.4}{\ignorespaces Yoke collimators}}{148}{figure.D.4}
\contentsline {figure}{\numberline {D.5}{\ignorespaces Fit of the beam spot positions}}{149}{figure.D.5}
\contentsline {figure}{\numberline {D.6}{\ignorespaces Measured misalignment versus the pion beam position}}{150}{figure.D.6}
\contentsline {figure}{\numberline {D.7}{\ignorespaces Effects of a magnetic field map misalignment}}{151}{figure.D.7}