PhD Thesis -- Review of Previous Measurements -RPM CHAPTER COMMENTS: This sort of sets the stage for TWIST, and shows what we've already accomplished. Consider starting off with the Very First muon decay spectrum measurement (see my unused slide from my CAP 2007 talk), with the caption about errors being "unknown but large". :) (This might fit well in the Intro.) See if I can describe the other measurements without having to really expand the theory. But I may have to go back to the Theory chapter and talk about positron polarization and whatnot in order for some of these measurements to make sense... I should highlight the main limitations of each of the prior experiments. I don't think I need to directly address why TWIST is better, as that's what the rest of the thesis is for; rather the descriptions of limitations should give the reader something to watch for later on. One disadvantage of splitting theory and measurement apart like this is that I can't talk about what experimental limitations are on the SM extensions without having discussed the experiments. I guess it makes sense given that I'm going into some detail about the prior experiment, but it's annoying. It doesn't even make sense to relate these prior measurements back to the theories here, because I'd have to do that for pretty much every experiment. Ugly. - Maybe I can have a section on the Global Analysis after all, taking all the muon decay data listed here and relating it all back to the coupling constants (the physics), and from there to the SM extensions. Or maybe a section for a "Summary of Data and Implications", since some of the models (like LRS) are limited by MPs directly. Something to think about. - Might end up doing all of this in my Results chapter, though. - I need the eta result from the Global Analysis, at some point. I don't _really_ need it until I start analyzing results, so I guess I could start the Results chapter with the new Global Analysis, get eta out of that, and go from there. Actually, this works fairly well... Should I really ignore the PmuXi measurements? Or do I need the pre-TWIST PmuXi for something? (I think the PmuXiDelta/Rho result is all I need...) I think I'll leave it out for now, but I might come back to it when I write the Results... ===== CHAPTER OUTLINE: Introduction - Should be brief. Not sure what to say yet, but I should probably say something... Rho: Peoples 1966 (unpub) + Derenzo 1969 - Peoples did the rho measurement, but was limited in part by rho-eta correlations. - The experiment used a variable magnetic field (at several settings, to cover multiple overlapping momentum ranges). A series of spark chambers for helix reconstruction, and events which scattered too much were eliminated. (Although as near as I can tell the momentum is reconstructed just from the radius of curvature, i.e. only pt is measured! But I think they only used events within 12 deg of the measurement plane, which is a 2.2% error...) Energy loss in the detector materials was accounted for, and energy loss in the muon production target was actually measured. The muons were unpolarized (I don't know that the polarization was checked, but from the setup it was probably a good approximation), so the measurement was just the integrated momentum spectrum. - Main systematics were identified as: momentum scale (B field non-uniformities); track reconstruction biases; backgrounds and unidentified hard scatters; positron annihilation in flight; and chamber efficiencies. - Derenzo studied low-energy decay positrons (like <6 MeV) to measure eta, and used their very different rho-eta correllations to get a better measurement of both. The Derenzo number is what's used in the PDG pre-TWIST. - More precisely, Derenzo uses all rho data available at the time, but Peoples dominates; their error is about 3x smaller than anyone else's. - Will want to primarily discuss the Peoples measurement; the Derenzo update is something of an aside. I can mention this as a study of the momentum distribution below 6.8 MeV/c, a region sensitive to eta but not so much to the other parameters. Delta: Balke 1988 - Surface muon muSR measurement to get decay asymmetry vs momentum. - Multiple magnetic field settings were needed because the detector had a small momentum acceptance. Major source of error. - Assumes rho = 0.752 +- 0.003, the Derenzo result. Rho uncertainty was a semi-major systematic. - Major systematics were momentum calibration (including beamline calibration), radiative corrections, and uncertainty in the value of rho that they needed to use to get delta and xi out. PmuXiDelta/Rho: Jodidio 1986 - Endpoint rate measurement using TRIUMF surface muons. (Same apparatus used later to get the Delta measurement above; largely the same group, too.) Used "spin-held" and "spin-precessed" modes of running.*** - Major systematics include: momentum calibration and acceptance consistency between the two modes; Coulomb scattering corrections; chamber alignment; and reconstruction errors. Eta: Burkard 1985, Derenzo 1969, Danneberg 2005 - The Burkard value was a global fit to all available muon decay data (much like the current value). - Paper is a combination of the global analysis and a measurement of the transverse positron polarization. - Should I even include this? The Gagliardi et al global fit didn't, afaik, and I can't see it making sense to do so. I think I'll leave it out... - This number is what was typically cited for eta pre-TWIST, but I think it includes measurements with too many assumptions. - They _do_ have a direct measurement of their own, not used by the PDG (presumably because the PDG uses their global fit instead). Maybe I should include that one here instead of the fit...? OTOH, the global fit really was the best measurement available before Danneberg. But I want to discuss experiments and their limitations, to be able to say why TWIST is better (or not). - The Derenzo measurement mentioned above is the only other experiment (before Danneberg) included by the PDG. Leave Burkard's measurement out of my summary. - The Danneberg value is weird -- 10x larger than Burkard, with huge error bars. But it was apparently important in the 2005 global fit... (Double-check in the Gagliardi paper that this is the same value they used!) - I'll mention the Danneberg experiment mainly so that, when I talk about the 2005 global fit later, the eta value used there has some context. - Actually, it's really the best model-independent measurement so far. I'm not sure what assumptions went into the Burkard fit, but other than that the only experimental measurements of eta that were better than the Danneberg one had model assumptions (some parameter = 0, rho = 0.75, etc). - The Danneberg measurement determines limits on eta from limits on the transverse polarization of positrons in muon decay. The experiment involves stopping muons in a precessing magnetic field, and measuring the photons from the in-flight annihilation of the decay positrons; the orientation of the photon distribution depends on the transverse positron polarization. - Main systematic uncertainties include energy calibration, energy loss, and backgrounds.