PhD Thesis -- Muon Decay Theory -RPM CHAPTER COMMENTS: This is essentially the motivation for the whole project. The focus is the study of the Weak Interaction, specifically deviations from the V-A structure. Muon decay is a nice clean process for studying this. I might want to mention the normalization of the coupling constants, as I think that plays into the structure of some of the Michel parameter definitions. Include some extensions to the Standard Model that TWIST will test/limit; these can be referred back to in the Conclusion. Make sure I understand these! - Make particular note, of course, of the "Q_R" quantity, which represents a sum of all possible interactions of the right-handed muon. Make sure I understand why the sum is done the way it is! - There are a few variations on L-R Symmetric models that we can look at. (See e.g. Glen's recent talk.) - Describe the "kappa" parameter. Andrei's thesis doesn't seem to include it, but it has g_RR^T as a non-local (depends on "momentum transfer") coupling to which delta would be rather sensitive. See his ref [40]. It would be nice if I could include an actual derivation of the Michel distribution, at least under Standard Model conditions. CHAPTER OUTLINE: The Weak Interaction in the Standard Model - Very brief description of the Standard Model of Particle Physics. - Very successful description of particle physics. - It would be good to link to a good review article, but I don't know of any that would be useful; they seem either so brief as to add very little to what I'm saying, or are full text books. I think I'll just have to reference Griffiths. - Three generations of quarks, three generations of leptons. These are the particles which make up matter, and are called fermions. - Should probably reproduce the "box diagram", showing generations and particles. (Mention that masses increase from left to right.) - Each generation of quarks includes an up-type (charge +2/3e) and a down-type (charge -1/3e). - Each generation of leptons includes a charged lepton (charge -e) and its associated neutrino (charge 0). - Antiparticles have the same properties as particles, but with the signs flipped where applicable (i.e. there's no such thing as "negative mass", but charges and intrinsic chiralities are reversed). - Forces mediated by bosons. - Gluons for strong - Photons (gamma) for EM - W+, W-, Z for weak - The charged weak interaction is the only interaction able to change a particle from one type of fermion into another. Charged leptons are converted into neutral leptons of the same generation, and vice-versa. Up-type quarks are converted into down-type quarks and vice-versa, but for quarks this conversion does not need to be within the same generation. - The strengths of the charged weak interaction between different types of quarks are represented as elements of the Cabbibo-Kobayashi-Maskawa (CKM) matrix. (Show matrix.) The elements of the CKM matrix are often represented using sines and cosines of various angles, called "mixing angles." - Each particle has an intrinsic spin. For the particles described here, the fermions have spin 1/2, and the bosons have spin 1. - The spin of the boson corresponds to the "type" of interaction it mediates: spin 0 is a "scalar" interaction, spin 1 is "vector", spin 2 is "tensor". - For spin 1/2 fermions, their spin can essentially only point in one of two directions, often labeled "up" and "down", relative to any given axis. The relevant axis depends on the system in question. - Each particle has an intrinsic chirality -- left-handed or right-handed. - This property is related to the helicity (sigma*p/|p|, where sigma is the spin vector) in that as v/c->1 the helicity approached the chirality. - Chirality is essentially the particle's "weak charge", in that left-handed particles are affected by the weak interaction and right-handed particles are not; the opposite is true for anti-particles. - In the case that the weak interaction _does_ couple to right-handed particles at some undetected level, it is possible that the right-handed quarks have their own CKM matrix. Kinematics - Basic kinematics of the decay. - Pion decay - Useful to show the 2-body decay, with resulting muon momentum and polarization. Handy results for the rest of the thesis. - I don't think other decay modes of the pion are important here, except to point out that they don't produce muons. Mention them after discussing momentum and polarization from "standard decay". - Muon decay - Kinematic maximum energy - Costh dependence General Form of Muon Decay - Show the Big Sum of matrix elements. - Define the Gamma matrices. - Standard model values of the coupling constants. - Table of limits on the coupling constants. - Index this table! - Pre-TWIST limits. - Limits from previous TWIST measurements. (Taken from theses, presumably, unless they were included in our plublications.) The Michel Parameters - Show the Michel spectrum. - This would be a good place for the full derivation, under SM conditions, followed by the more general statement. - Write Michel parameters in terms of coupling constants. - Point out the pairing of Pmu and Xi. Remind the reader that Pmu is 100% in SM pion decay, but extensions might affect this as well, and TWIST cannot distinguish between that and Xi. - Limits (pre-TWIST, previous TWIST, final goals) on Michel parameters. - Index this table! - I'll probably reproduce this table later, replacing the previous TWIST measurements with my own and dropping the final goals list. - Include SM values here, too. Extensions to the Standard Model - State that this section is about SM extensions to which TWIST's MP measurements are sensitive. - "Q_R" - Various forms of L-R Symmetric models. - LRS just says that, in addition to "V-A", there's a "V+A" interaction, which is supressed but not zero. - Gauge group gets extended to include SU(2)R. - Mixing of charged bosons. - LRS models affect rho and xi, and Pmu. Show formulas relating these to LRS parameters. - Limits on LRS parameters from Michel parameters, including limits on mixing angle zeta independent of m2 mass and vice versa, plus correllated exclusion plot. - I think the only specific non-correllated limit of interest to this thesis is the mixing angle, which comes from rho, so that's all I'll draw attention to. The exclusion plot is interesting, but my own measurements won't do much to the curvy bit, I don't think; they'll just narrow the whole thing a little. - Minimal LRS simplifies parameter relations: gR=gL, the right-handed and left-handed CKM matrices are equal (implying alpha=0), and omega=0. - Andrei's ref.34 (also Blair's ref.27) looks important: P. Herczeg, "On muon decay in left-right symmetric electroweak models," Phys. Rev. D34, 3449 (1986) - ...? (See e.g. Glen's recent talk, Andrei's thesis, etc.)