Organisatorial Issues: Exam

Transcription

1 Organisatorial Issues: Exam Date: - current date: Tuesday :00 16:00h, gr. HS - alternative option to be discussed: - Tuesday :00 15:00h, gr. HS - Friday :00 16:00h, gr. HS Requirement: 60% of the points of the homeworks (12 exercise sheets) Exam: 90 min, 8-10 short exercises, covering the content of the lecture + homeworks Please bring your students card! Paper and Calculator will be provided own calculators are not allowed. You can bring one (double sided) sheet of paper with hand written notes If you are ill at the date of the exam, please bring a certificate from the doctor. If you can for a very good reason not participate in the exam, please contact me before hand. Depending on the number of students which need a second exam, it will be a written or an oral exam.

2 Organisatorial Issues: Homeworks - homework 11 will be put on the web Wed to be handed in Thu/Fr / homework 12 (last one) will be put on the web Fr to be handed in Thu/Fr 19.07/ Lecture on Friday will be given by Prof. U. Uwer

3 V-A Theory The requirement of Lorentz invariance of matrix elements severely restricts form of interaction vertex. There are in general only 5 possible combinations of two spinors and the gamma matrices that form Lorentz invariant currents, called bilinear covariants - pure vector and pure axial currents conserve parity - QED/QCD are described by pure vector currents, thus these IA per construction conserve parity - charge current (W± exchange) of weak IA violates parity (e.g. Wu experiment). The according vertex currents are a linear combination of vector and axial coupling. Nature has choose maximal parity violation V-A theory

4 Reminder: Chirality and Helicity Helicity is an conserved observable (measurement quantity), helicity is not lorentz invariant experimental values are between [-1,1] Dirac spinors for particle helicity eigenstates: h = +1 (right handed) momentum along z direction h = -1 (left handed)

5 Reminder: Chirality and Helicity Chirality is a quantum number; every particle is in chirality +1 or chirality -1 state. chirality operator: Projectors of chirality eigenstates: Chirality is not directly measurable.

6 Reminder: Chirality and Helicity momentum along z direction ~ 0 for E >> m ~ E for E >> m E >> m In the relativistic limit helicity eigenstates are also chirality eigenstates!

7 Definition: Polarization of particles with finite mass Assume a h=1 particle, what is the probability that it has RH chirality? Assume a h=+1 particle, what is the probability that it has LH chirality?

8 Connection to Fermi Theory

9 Strength of Weak Interaction

10 Structure of the CKM matrix Most preferred transition within the same quark family doublet In first order only Vtd and Vub are complex numbers, CKM matrix and their complex element important for meson mixing and CP violation

11 Experimental probes of V-A structure: Muon Decay L/R General form of matrix element: L/R L/R n,m = R/L given if coupling i and handiness of electron and muon are given ( L/R )

12 Measurement Idea: Consider muon rest system: maximum energy ( ; /2 ) of particle 1, if particle 2,3 fly in opposite direction expect energy distribution from kinematical point of view identical for gvll Fit to energy spectra + angular distribution of final state particles to determine current current couplings. gvrl

13 Energy spectrum of emitted electron: Michelparameters: V-A theory: Experiment:

14 Test of V-A structure: Decay of the pion Phase space argument: Phase phase for decay into electron significantly larger than for decay into muon Measurement: Qualitative explanation with V-A theory: Angular momentum conservation forces the lepton into the wrong helicity state, suppressed by S=0

15 Computation see homework 6.2 pion form factor Bounded quarks cannot be described by Dirac spinors of free particles excellent agreement with experiment

16 (Anti-)neutrino (anti-)quark scattering Differences in neutrino-quark and neutrino anti-quark scattering, direct consequence of V-A structure! Sideremark: is a hint that V-A theory cannot be complete

17 Weak neutral current

18 Gargamelle - first large bubble chamber: To detect neutrinos, needs large volume with high density gas due to small cross-section

19 Structure of Neutral Current Spin of Z0 : S =1 (similar to W exchange) general form of coupling is a linear combination of vector and axial coupling Neutral weak interaction couples to left- and right-handed fermion currents Contributions are however differently.

20 Vector and axial-vector coupling of Z0 Theory predictions for couplings to neutral current: Weinberg-angle: e.g. in case of neutrinos, pure V-A structure This structure is a very strong hint that weak and electromagnetic theory should be combined!

21 Coupling of Z0 boson One coupling for neutral and charged weak currents!

22 How to determine couplings: neutrino-electron scattering (NC) gr2 Integral over angel gl2

23 Theorie confirmed within uncertainties: