\contentsline {chapter}{Supervisory Committee}{ii}{section*.1}
\contentsline {chapter}{Abstract}{iii}{section*.2}
\contentsline {chapter}{Table of Contents}{v}{section*.3}
\contentsline {chapter}{List of Tables}{ix}{section*.5}
\contentsline {chapter}{List of Figures}{x}{section*.7}
\contentsline {chapter}{Acknowledgements}{xiii}{section*.9}
\contentsline {chapter}{Epigraph}{xiv}{section*.10}
\contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.1}
\contentsline {section}{\numberline {1.1}Physics motivation}{1}{section.1.1}
\contentsline {section}{\numberline {1.2}Theoretical description of muon decay}{2}{section.1.2}
\contentsline {subsection}{\numberline {1.2.1}General 4-fermion interaction}{2}{subsection.1.2.1}
\contentsline {subsection}{\numberline {1.2.2}Momentum-angle spectrum parametrization}{3}{subsection.1.2.2}
\contentsline {section}{\numberline {1.3}Theoretical implications}{6}{section.1.3}
\contentsline {subsection}{\numberline {1.3.1}Global analysis}{6}{subsection.1.3.1}
\contentsline {subsection}{\numberline {1.3.2}Extended formalism for a non-local tensor interaction}{7}{subsection.1.3.2}
\contentsline {section}{\numberline {1.4}Experimental status of $\delta $ and $\eta $}{8}{section.1.4}
\contentsline {subsection}{\numberline {1.4.1}Previous measurements of $\delta $}{8}{subsection.1.4.1}
\contentsline {subsection}{\numberline {1.4.2}Previous measurements of $\eta $}{9}{subsection.1.4.2}
\contentsline {section}{\numberline {1.5}Overview of the TWIST experiment}{10}{section.1.5}
\contentsline {chapter}{\numberline {2}TWIST experimental setup and data}{11}{chapter.2}
\contentsline {section}{\numberline {2.1}Experimental setup}{11}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}Highly polarized muon beam}{11}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}Spectrometer}{15}{subsection.2.1.2}
\contentsline {subsubsection}{Drift chambers}{17}{section*.11}
\contentsline {subsubsection}{Proportional chambers}{19}{section*.12}
\contentsline {subsubsection}{PC target module}{19}{section*.13}
\contentsline {subsection}{\numberline {2.1.3}Superconducting solenoid and the yoke}{21}{subsection.2.1.3}
\contentsline {subsection}{\numberline {2.1.4}Beam package and scintillators}{21}{subsection.2.1.4}
\contentsline {subsection}{\numberline {2.1.5}Time expansion chamber (TEC)}{22}{subsection.2.1.5}
\contentsline {section}{\numberline {2.2}Experimental data}{25}{section.2.2}
\contentsline {chapter}{\numberline {3}Analysis}{28}{chapter.3}
\contentsline {section}{\numberline {3.1}Blind analysis}{30}{section.3.1}
\contentsline {section}{\numberline {3.2}Event reconstruction}{30}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}Data run unpacking}{30}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}Crosstalk signal removal}{30}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}Event identification}{31}{subsection.3.2.3}
\contentsline {subsection}{\numberline {3.2.4}First guess}{33}{subsection.3.2.4}
\contentsline {subsection}{\numberline {3.2.5}Helix fitter}{35}{subsection.3.2.5}
\contentsline {section}{\numberline {3.3}Extraction of the decay parameters}{39}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}Spectrum reconstruction}{39}{subsection.3.3.1}
\contentsline {subsection}{\numberline {3.3.2}Muon decay parameter fit}{39}{subsection.3.3.2}
\contentsline {subsection}{\numberline {3.3.3}Momentum calibration}{40}{subsection.3.3.3}
\contentsline {chapter}{\numberline {4}Event selection}{46}{chapter.4}
\contentsline {section}{\numberline {4.1}Beam and event type cuts}{46}{section.4.1}
\contentsline {subsubsection}{Time of flight cut}{46}{section*.14}
\contentsline {subsubsection}{Event type cut}{49}{section*.15}
\contentsline {section}{\numberline {4.2}Muon selection}{49}{section.4.2}
\contentsline {subsubsection}{Muon stopping plane cut}{49}{section*.16}
\contentsline {subsubsection}{Muon stopping radius cut}{49}{section*.17}
\contentsline {subsubsection}{PC 5 and 6 pulse width cut}{51}{section*.18}
\contentsline {section}{\numberline {4.3}Track selection}{51}{section.4.3}
\contentsline {subsubsection}{Number of reconstructed tracks cut}{51}{section*.19}
\contentsline {subsubsection}{Ierror code cut}{51}{section*.20}
\contentsline {subsubsection}{Start and stop plane cut}{51}{section*.21}
\contentsline {subsubsection}{Charge cut}{54}{section*.22}
\contentsline {subsubsection}{Pair matching cut}{54}{section*.23}
\contentsline {subsubsection}{Muon-positron vertex cut}{55}{section*.24}
\contentsline {subsubsection}{Distance to target selection}{56}{section*.25}
\contentsline {subsubsection}{Muon-positron vertex selection}{57}{section*.26}
\contentsline {subsubsection}{Decay fit time}{57}{section*.27}
\contentsline {section}{\numberline {4.4}Fiducial region selection}{57}{section.4.4}
\contentsline {chapter}{\numberline {5}Monte Carlo simulation}{60}{chapter.5}
\contentsline {section}{\numberline {5.1}Beam rate and profile}{60}{section.5.1}
\contentsline {section}{\numberline {5.2}Detector geometry}{61}{section.5.2}
\contentsline {subsection}{\numberline {5.2.1}Outside material}{61}{subsection.5.2.1}
\contentsline {section}{\numberline {5.3}Decay positron spectrum}{62}{section.5.3}
\contentsline {section}{\numberline {5.4}Chamber response}{62}{section.5.4}
\contentsline {section}{\numberline {5.5}Validation}{64}{section.5.5}
\contentsline {subsection}{\numberline {5.5.1}Target stops}{64}{subsection.5.5.1}
\contentsline {subsection}{\numberline {5.5.2}Far upstream stops}{65}{subsection.5.5.2}
\contentsline {subsubsection}{Positron interactions}{65}{section*.28}
\contentsline {subsubsection}{Track reconstruction efficiency}{67}{section*.29}
\contentsline {chapter}{\numberline {6}Detector calibration}{73}{chapter.6}
\contentsline {section}{\numberline {6.1}Cathode foil bulge}{73}{section.6.1}
\contentsline {section}{\numberline {6.2}Wire time offsets in the drift chambers}{74}{section.6.2}
\contentsline {section}{\numberline {6.3}Drift chamber space time relationships}{79}{section.6.3}
\contentsline {chapter}{\numberline {7}Systematic uncertainties and corrections}{83}{chapter.7}
\contentsline {section}{\numberline {7.1}$\delta $ systematic uncertainties}{84}{section.7.1}
\contentsline {subsection}{\numberline {7.1.1}Positron interaction}{84}{subsection.7.1.1}
\contentsline {subsubsection}{Bremsstrahlung rate}{84}{section*.30}
\contentsline {subsubsection}{$\delta $ ray rate}{87}{section*.31}
\contentsline {subsubsection}{Outside material}{88}{section*.32}
\contentsline {subsection}{\numberline {7.1.2}Reconstruction resolution}{89}{subsection.7.1.2}
\contentsline {subsection}{\numberline {7.1.3}Momentum calibration}{91}{subsection.7.1.3}
\contentsline {subsubsection}{Propagation model}{93}{section*.33}
\contentsline {subsubsection}{End points fits}{93}{section*.34}
\contentsline {subsection}{\numberline {7.1.4}Field map}{94}{subsection.7.1.4}
\contentsline {subsection}{\numberline {7.1.5}Pulse width cut}{95}{subsection.7.1.5}
\contentsline {subsection}{\numberline {7.1.6}Spectrometer alignment}{96}{subsection.7.1.6}
\contentsline {subsection}{\numberline {7.1.7}Chamber response}{97}{subsection.7.1.7}
\contentsline {subsubsection}{DC STRs}{97}{section*.35}
\contentsline {subsubsection}{Cathode foil position}{99}{section*.36}
\contentsline {subsubsection}{Upstream-downstream efficiency asymmetry}{100}{section*.37}
\contentsline {subsubsection}{Crosstalk}{101}{section*.38}
\contentsline {subsubsection}{Wire time offsets}{102}{section*.39}
\contentsline {subsection}{\numberline {7.1.8}Radiative corrections}{103}{subsection.7.1.8}
\contentsline {section}{\numberline {7.2}$\delta $ statistical uncertainties}{104}{section.7.2}
\contentsline {section}{\numberline {7.3}Corrections to the $\delta $ parameter}{105}{section.7.3}
\contentsline {section}{\numberline {7.4}$\eta $ uncertainties and corrections}{106}{section.7.4}
\contentsline {chapter}{\numberline {8}Results and conclusion}{109}{chapter.8}
\contentsline {section}{\numberline {8.1}Results of the measurement of $\delta $}{109}{section.8.1}
\contentsline {subsection}{\numberline {8.1.1}Blind analysis results}{109}{subsection.8.1.1}
\contentsline {subsection}{\numberline {8.1.2}Consistency test}{112}{subsection.8.1.2}
\contentsline {subsection}{\numberline {8.1.3}$P_\mu \xi \delta /\rho $ inconsistency}{112}{subsection.8.1.3}
\contentsline {subsection}{\numberline {8.1.4}New global analysis}{113}{subsection.8.1.4}
\contentsline {subsection}{\numberline {8.1.5}Limit on non-local tensor interactions}{114}{subsection.8.1.5}
\contentsline {section}{\numberline {8.2}$\eta $ measurement}{114}{section.8.2}
\contentsline {chapter}{Bibliography}{118}{section*.40}
\contentsline {chapter}{\numberline {A}Personal contributions}{122}{appendix.A}
\contentsline {chapter}{\numberline {B}Classification types}{124}{appendix.B}
\contentsline {section}{\numberline {B.1}Window types}{124}{section.B.1}
\contentsline {section}{\numberline {B.2}Event types}{125}{section.B.2}
\contentsline {chapter}{\numberline {C}Time Expansion Chamber (TEC) calibration}{128}{appendix.C}
\contentsline {section}{\numberline {C.1}Calibration data}{128}{section.C.1}
\contentsline {section}{\numberline {C.2}Characterization analysis}{131}{section.C.2}
\contentsline {section}{\numberline {C.3}Global time offset}{131}{section.C.3}
\contentsline {section}{\numberline {C.4}Wire time offsets}{132}{section.C.4}
\contentsline {section}{\numberline {C.5}Discriminator amplitude walk}{133}{section.C.5}
\contentsline {section}{\numberline {C.6}TEC Space Time Relationships (STRs)}{135}{section.C.6}
\contentsline {section}{\numberline {C.7}TEC calibration precision}{140}{section.C.7}
\contentsline {chapter}{\numberline {D}Relative alignments of the apparatus components}{142}{appendix.D}
\contentsline {section}{\numberline {D.1}Wire chambers relative alignment}{143}{section.D.1}
\contentsline {subsection}{\numberline {D.1.1}Drift chambers relative alignment}{143}{subsection.D.1.1}
\contentsline {subsection}{\numberline {D.1.2}Target kink corrections}{144}{subsection.D.1.2}
\contentsline {subsection}{\numberline {D.1.3}Precision of the DC alignment procedure}{145}{subsection.D.1.3}
\contentsline {subsection}{\numberline {D.1.4}Proportional chambers relative alignment}{147}{subsection.D.1.4}
\contentsline {section}{\numberline {D.2}Relative alignment of the spectrometer and the yoke}{147}{section.D.2}
\contentsline {section}{\numberline {D.3}Relative alignment of the spectrometer and the magnetic field map}{151}{section.D.3}