Mike, Before corrections: With corrections: Tex to allow you to carry out a diff Mike, there are a few with *'s that I want you to check carefully. ___ Corrections implemented ___ AM = Andrew MacFarlane JM = Janis McKenna DM = David Measday (Me) Front cover date changed (JM) Abstract p.ii "the weak interaction maximally violates parity" -> "the weak interaction maximally violates parity conservation" (JM,DM) Abstract Grudgingly inserted result *** Check (LR) p.1 Added paragraph giving overview of experiment. (LR) p.1 Added note that results chapter also describes how to measure at 1e-4. (DM) p.2 example of antiparticle changed from muon neutrino to proton (AM) p.4 "For an ensemble of particles with spin, the ``spin polarisation'' can be introduced, which describes the degree to which the spins are aligned in a particular direction." Added "; this is a scalar quantity." Removed "This gives a space direction about which to define a probability distribution". (Aim is to remove confusion about scalar vs. vector in text) (AM) p.5 "The muons in the experiment were produced from pions that decayed while at rest." -> "The muons in the experiment were produced from pions that decayed while at rest, in the lab frame." (AM) p.5 "which then decayed" -> "which then slowed down and decayed" ** Check (AM) p.5 "Finite neutrino mass reduces the neutrino's helicity by a factor $(1-p/E)$." -> "... by a factor of $(1-p_{\nu}/E_{\nu})$." (AM) p.6 "so that the loss of polarisation due to the radiative decay mode is negligible" -> "so that the loss of polarisation due to _this_ radiative decay mode is negligible." (Me) p.7 Bad notation in Eq. (1.7) fixed, and text immediately below. ** Mike, you should check the change I have made here. (AM) p.10 "The current analysis includes the following levels of correction: full first order ..." Added: "where $\alpha$ is the fine structure constant." (AM) p. 10 / p. 12 Error: I use "upstream" and "downstream" without definition, and it's confusing since I used "forward" and "backward" in Eq. 1.20. I've cleaned it up now. Text in Sec 1.4.5 before Eq. (1.20) is generally cleaned up ** Mike, you should check the changes here. (JM) p.10 "Radiative decays with internal and external lines are treated as spectrum corrections." -> "Radiative decays with internal and external particles are treated as spectrum corrections." (AM) p.11 "The asymmetry of the spectrum can be constructed from" -> "The experimental asymmetry of the spectrum is defined as" (AM) p.11 "hard scattering interactions ($>1\MeV$)" -> "hard scattering interactions ($>1\MeV$ energy loss)" (AM) p.11 Caption for Fig. 1.3 is re-written. ** Mike, you should check this. (LR) p.11 Added whole page of Feynman diagrams. And another figure showing relative contribution of each order. It would be a mess to break down the contributions further. ** Needs careufl checking (AM) p.12 Caption for Fig. 1.4 is re-written. ** Mike, you should check this. (JM) p.15 Removed quotation marks around manifest, confirmed no use of quotation marks in rest of thesis. (DM) p.15 "The TWIST experiment's most precise lower mass limits are" -> "The published lower mass limits from TWIST are" (AM) p.16 Made sure ALL symbols are defined, including beta, gamma, spin, B-field etc. etc. (JM) p.17 "and for muons with momentum $29.6\MeVc$ that entirely slow down in aluminium, the resulting depolarisation is $\approx 4 \times 10^{-5}$\cite{tn100}" -> "... that entirely slow down and stop in aluminium ..." (JM) p.17 "pionium" -> "pionium (or pion-onium)" (google shows that some people do indeed use pion-onium) (AM) p.17 "there is an electric field between the nucleus and the atomic electrons" -> "an electric field within the material's atoms" (AM) p.18 "but instead it diffuses (``hops'') between energetically" -> "but instead it usually diffuses..." Added "(there is also a zero-point motion that causes the muon to undergo spin exchange with its nearest neighbours)" (AM) p.19 Immediately after Eq. (1.41), insert space before $\Delta$. (AM) p.19 "the envelope limits to a Gaussian time dependence" -> "the envelope limits __instead__ to a ..." (AM) p.19 Footnote: "Each field component is modelled" -> "Each field component is independently modelled" (LR) p.19 BMT -> "Thomas-BMT" (and added ref) (AM) p.20 "The impurities take the place of an aluminium or silver nucleus." -> "The impurities take the place of an aluminium or silver __atom__." (AM) p.20 "the signature of Korringa relaxation is an increase in rate with temperature" -> ".... linear increase in rate with ...." (AM) p.21 "the muons are expected to be in rapid motion" Added "(the experiment is performed at room temperature)" (JM) p.22/23 Added "Garwin" to make it clearer. Moved up ref for Bardon, Berley. (JM,DM) p.23 "Beryllium" -> "beryllium" (JM) p.24 Added Rob's measurements of rho and delta, since I quote Jodidio indirect limit. (AM) p.26 "that decayed from stationary pions at the surface of the production target." -> "that decayed from stationary pions within microns of the production target surface." (AM) p.28 "Gaussian acceptance of the channel." -> "Gaussian momentum acceptance of the channel." (Me) p.29 Added average depth for selected muons (about 16 mum). (Me) p.29 Added note that we make a systematic correction for depol in production target. (Me) p.29 Removed text comparing momentum resolution to previous pmuxi measurement. (LR) p.34 "In the previous \pmuxi\ analysis the muon beam was found" -> "The muon beam from M13 used to be" "For the current pmuxi measurement" -> "For this measurement" (LR) p.36 "The spacing of the chambers has been changed since the previous analysis; this has helped to resolve wavelength degeneracies." -> "... has been changed for this measurement, which has helped ..." (AM) p.42 "removable upstream beam package" -> "upstream beam package" (invites too many questions otherwise) (LR,me) p.42 Removed sentence "In the previous \pmuxi\ analysis the feedback loop was only in operation towards the end of data acquisition. I give up arguing on this one. (LR,me) p.42 Removed sentence "For the previous \pmuxi\ analysis the fraction was $\approx 37\%$." (LR) p.43 "for the previous \pmuxi\ measurement" -> "for the previous TWIST \pmuxi\ measurement\cite{Blairpaper}" (LR) p.45 "The previous \pmuxi\ measurement found that" -> "A previous TWIST analysis found that" (AM) p.53 "if a narrow pulse ... occurred within $50\ns$ of a good pulse, then it was removed." -> "if a narrow pulse ... occurred within $50\ns$ of a good pulse, then the narrow pulse was removed." (AM) p.53 "Crosstalk removal was disabled when analysing the simulation." -> "The simulation did not reproduce the crosstalk mechanisms. Therefore the crosstalk removal code was disabled when analysing the simulation." (AM) p.53 "The 1.05 mus window was necessary to allow the ionisation in the drift chamber's slow gas to register at the wires." -> "All subsequent hits within $1.05\mus$ were put into this time window. Historically the window was chosen to be $1\mus$, which is sufficiently long for the ionisation in the drift chamber's slow gas to register at the wires; an extra $50\ns$ was later added to account for the PC rise time." (AM) p.54 "The wavelength degeneracy was resolved using two additional pieces of information: higher angle tracks registered in more than one drift cell\footnote{Further detail can be found in Section 4.2.1 of Ref. \cite{James:1982}.}, and tracks could not be reconstructed if they changed by more than $2\pi$ between pairs of drift chambers\cite{Blair:2006}." -> "The wavelength degeneracy was resolved since higher angle tracks registered in more than one drift cell\footnote{Further detail can be found in Section 4.2.1 of Ref. \cite{James:1982}.}." (AM) p.57 "\subsection{Fitting the helical trajectory}" -> "\subsection{Fitting the helical trajectory of the decay positron}" (LR) p.59 "The previous \pmuxi\ analysis" Added "\cite{Blairpaper}" (AM) p.59 Added " (see Section \ref{s:wire_chambers})" (ref to description of chambers) (AM) p.60 Added to figure caption: "The elliptical contours arise due to the geometry of the drift planes (see Section \ref{s:wire_chambers})" (AM) p.62 Updated caption for Fig. 3.8: "The resolution is worse at longer distances from the wire due to diffusion. The new resolution function is ad hoc." (AM) p.63 Added to caption of figure: "The figure shows that after applying the fiducial cut, less than $15\%$ of the original surface muons remain." (AM) p.64 Fig. 3.10 (CPTOF) improved -- backgrounds identified, caption expanded. ** Mike, please check. (AM) p.66 and p.67 I didn't say anywhere why muons stopping US will have different pulse widths. Explanations added in text, and in Fig. 3.11 caption. "The pulse widths were used to reject muons stopping in the PC gas rather than in the metal target" Added: "since these muons will deposit more energy in both PC5 and PC6." (AM) p.69 p.70 Updated caption: "The lower plot shows the fiducial region" -> The lower plot shows the fiducial region, which is \emph{within} the dashed white lines. (similar change made to text) (AM) p.72 "Recall the expression for the differential decay rate," -> "Recall the expression from Section \ref{s:diff_dec_rat} for the differential decay rate," Also added definiton of $x$ as reduced energy. (me,JM) p.75 Changed Fig. 3.14 to a cleaner version -- one that includes normalisation (AM) p.75 Updated caption in Fig. 3.14 to include forward ref. Added: "The endpoint positions for all angles are shown in Fig. \ref{f:endpoint_data_sim_cos}." (me) p.75 Removed sentence "The previous \pmuxi\ analysis had endpoints that were further away from the kinematic prediction since energy loss was not taken into account when fitting the positron helices." (brings nothing to this thesis) (me) p.76 "The previous \pmuxi\ analysis" Added \cite{Blairpaper} (LR) p.76 Added another sentence on origin of mismatch in data-sim at endpoint. "Specifically, an energy loss error in the simulation should result in a data-simulation difference that is strongly angle-dependent. However, we apply an STR calibration procedure, and this appears to convert the data-simulation difference into an angle-independent offset of about $10\keVc$ at the spectrum endpoint. (me) p.79 Removed grey background in Fig. 3.17. (DM) p.79 Added caveat: "Note that the weighting technique is only applied to the asymmetry analysis that determines the time dependence of $P_\mu$. It is \emph{not} applied to the normal spectrum analysis." (me) p.81 Removed grey background in Fig. 3.18. (AM) p.83 "position annihilation" -> "positron annihilation" (AM) p.86 Defined all terms in Thomas equation, again. (AM) p.86 "effectively cancelling the change in spin from this term." -> "which effectively cancels the change in spin from this term." (LR) p.87 "and for the previous analysis this solution was used to validate the numerical method\cite{Blair:2006}" -> "and this solution has been used to validate the numerical method\cite{Blair:2006}." (LR,me) p.90 "which is a factor of three larger than the sets used for the previous \pmuxi\ measurement. There were also twice as many sets as the previous \pmuxi\ measurement." -> "which is a factor of three larger than the previous TWIST \pmuxi\ measurement\cite{Blairpaper}". (LR) p.93 "The previous \pmuxi\ measurement" -> "The previous \pmuxi\ measurement\cite{Blairpaper}" (AM) p.95 "The set with the nominal beam tune and the TECs in place allowed a high precision measurement of the muon beam stability" Added "(position, angle, size, correlation between angle and position {\it etc.})" (AM) p.95 and Section 5.4.7 in general Sections of this were just wrong. Also I hadn't defined wavelength, phi etc., so I have now simplified p.97 figure. ** Mike, this needs a careful check (AM) p.100 "In the most recent TWIST analysis (MacDonald '08), the polarisation uncertainties were not re-evaluated since it was a measurement of only $\rho$ and $\delta$." -> "MacDonald '08 measured $\rho$ and $\delta$, but not \pmuxi." (i.e. removed confusing mention of recent/previous analyses) (LR) p.102 "TWIST \pmuxi\ analysis" Added \cite{Blairpaper} (LR) p.103 *** Read this Added a few sentences on correlation, asymmetry uncertainties, obtaining correct totals. I have seen external examiner's spreadsheet, and the problem is due to lambda (stat). (LR) p.112 "previous TWIST \pmuxi\ analysis" Added \cite{Blairpaper} (AM) p.115 "Three on-axis coils were added to the original \texttt{Opera} map..." -> "The fields from three on-axis coils were added to the original \texttt{Opera} map..." (AM) p.121 "This selected a sample of muons that mostly stopped in the metal foil." Removed 'mostly' (AM) p.126 "set74" -> "set 74" (LR) p.129 "In the previous \pmuxi\ analysis" -> "In the previous TWIST \pmuxi\ analysis\cite{Blair:2006}" (LR) p.137 "In the previous \pmuxi\ analysis" -> "In the previous TWIST \pmuxi\ analysis\cite{Blairpaper}" (AM) p.138 "An additional three chamber response systematic uncertainties were considered, but were not..." -> "Three additional chamber response systematic uncertainties were considered, but they were not ..." (LR) p.138 "although they were included in the previous \pmuxi\ analysis." -> "... previous TWIST \pmuxi\ analysis\cite{Blairpaper}" (LR) p.138 "For the previous \pmuxi\ analysis" -> "For the previous TWIST \pmuxi\ analysis\cite{Blairpaper}" (LR) p.146 "A previous analysis found this difference in width had a non-trivial dependence on $p$ and \ct;" -> "A previous analysis\cite{MacDonald:2008}" (AM) p.148 "the width of the energy loss and angle change distributions is sensitive to the resolution." -> " ... are sensitive to the resolution." (me) p.158 Updated caption: Added: "(the region inside the lines is accepted)" (DM) p.167 "see Ref. \cite{alex_muminus} for such a measurement (the first of its kind) that used the TWIST apparatus." --> Removed claim its first of its kind (although I maintain it's the first full spectrum measure [i.e. not just a lifetime measure], including residual polarisation) (AM) References: Added title for Ref 66 (Akhmanov) and Ali-Zade (JM) Added years to all private communications. Added (TWIST) to title of all TWIST theses. (LR) p.181 Added Kunze reference for first observation of muon. (DM) p.185 Fixed Lee ref (should have been a 1994 article, not the original Lee/Yang) (AM) Appendix D, p.186 "NMR" -> "NMR probe" (AM) Appendix D, p.186 Added: "The magnetic field from the TRIUMF cyclotron was not included since it is only $\approx 4\,\mu\textrm{T}$ at the TWIST detector." (LR) p.195 "In the previous \pmuxi\ analysis, the" -> "In the previous \pmuxi\ analysis\cite{Blair:2006}, the" (LR) p.200 "The previous analysis found similar features that" -> "The previous analysis\cite{Blair:2006} ..." (AM) Appendix H (muSR) p.205 "the author is unaware of any credible models for muon depolarisation within the first $5 \ns$ in metals." -> "... in __nonmagnetic__ metals." p.207 Added footnote: "where muons entered from the left and could stop in the $99.99\%$ purity silver mask\footnote{This is less pure than the TWIST stopping target, which is $>99.999\%$ pure.}"