Particle Physics WS 2012/13 (14.12.2012) Stephanie Hansmann-Menzemer Physikalisches Institut, INF 226, 3.101 Content of the Lecture 1. Introduction 8. Elastic and inelastic electron 1.1 Natural units Proton scattering and the quark model 1.2 Standard model basics 1.3 Relativistic kinematics 9. Strong Interaction (QCD) 9.1. Symmetries and conservation laws 2. Interaction of Particles with Matter 9.2. Local gauge invariance 9.3. Bound states 3. Detectors for Particle Physics 9.4. Quark Gluon Plasma 3.1 General Detector Concepts 3.2 PID Detectors 10. Weak Interaction w 3.3 Tracking Detectors 10.1. Parity, Wu Experiment, Goldhaber eak Experiment 4. Scattering process and transition amplitudes 10.2. Left right handed couplings 4.1. Fermi’s golden rule 10.3. CKM Matrix interaction 4.2. Lorentz invariant phase space and matrix element 4.3 Decay Width and Lifetime 11. The Standard Model 4.4 Two and Three Bod decay rate, Dalitz plot 11.1 Electroweak unification 4.5 Cross section 11.2 Precision tests 11.3 Higgs mechanism 5. Description of free particles 5.1. Klein-Gordan equation 12. Neutral Meson Mixing 5.2. Dirac equation 5.3. Plane Wave solutions 13. CP Violation 6. QED 14. Neutrinos 6.1 Interaction by particle exchange 6.2 Feynman rules 6.3. Electron-Positron annihilation 6.4. Electron Scattering 7. Radiativ correction and renormalization 2 Content of Today Hadronic decays of weak interaction Reminder of Parity Partiy conservation in QED/QCD The ϴ/τ puzzle Discovery of Partiy Violation: Wu-Experiment Goldhaber-Experiment: Helicity of the Neutrino Structure of vertex current weak IA 3 colour hypercharge Y = λ8/3 Phenemenology of weak IA (charged current) All particles (except photons and gluons) take part in weak IA. Massive exchange bosons: W± (m=80 GeV), Z0 (m=91 GeV) polarization 2 [푔μν −푞μ푞ν /푚푊 ] Propagator term for massive spin=1 particle: -i 2 2 푞 −푚푊 For q < mW/mZ weak IA is negligible small compared to QED/QCD (for large q, weak IA comparable to electromagnetic IA) Observation of weak IA mainly in decays which are forbidden in strong/elm IA Due to conservation and/or which involve neutrinos 푢 푢 τ(φ) ~ 1.6 10-22s - π0 - -6 K s u τ(μ ) ~ 2.6 10 s s - s W e- φ K- 푠 푢 change of ν 푒 νμ quark flavour u - + μ - -6 푠 K W- e τ(K) ~ 3.1 10 s ν 푒 4 colour hypercharge Y = λ8/3 Weak Hadronic Decays dominant decay mode at quark level e.g. β decay u d n → p e- ν 푒 u d - ν W- e W+ e u u p + ν 푒 e d d n u M2 ~ cos2ϴ ~ 0.95 d c - 푢 푐 W- e ϴc : Cabbibo angle ν 푑 푠 푒 ΔI = 1 subpressed decay modes 3 푢 푢 Weak IA does not conserve isospin, - π0 K s u strangeness or any other quark flavour number. W- e- ν Lepton numbers is however conserved ΔS = 1 푒 푢 푐 2 2 M ~ sin ϴc ~ 0.05 푑 푠 5 colour hypercharge Y = λ8/3 Reminder of Parity 푖(푝 푥 −퐸푡) particle solution Ψi = ui(E,푝 ) 푒 1 0 0 1 푝 푧 푝푥 −푖푝푦 u1 = 퐸 + 푚 u2 = 퐸 + 푚 퐸+푚 퐸+푚 푝 +푖푝 −푝 푥 푦 푧 퐸+푚 퐸+푚 −푖(푝 푥 −퐸푡) antiparticle solution Ψi = vi(E,푝 ) 푒 푝 −푖푝 푥 푦 푝푧 퐸+푚 퐸+푚 Partity operator P: −푝 푧 푝푥+푖푝푦 v = 퐸 + 푚 v = 퐸 + 푚 1 퐸+푚 2 퐸+푚 1 0 1 0 0 0 1 γ0 = 0 1 0 0 0 0 0 −1 0 These solutions have positive energies. 0 0 0 −1 Spin ½ particles AT REST have intrinsic partiy P = +1 Spin ½ particles AT REST have intrinsic parity P=-1 6 Reminder of Parity P Ψ(푥 , 푡)= Ψ(−푥, 푡) P2 Ψ(푥 , 푡)= Ψ(푥 , 푡) Parity is conserved in strong and electromagnetic IA (to be shown next slide) Parity and momentum operator do not commute! 푃 푝 = −푝푃 ∶ „Operator“ Therefor intrinsic partity is (strictly speaken) defined only for particles AT REST. If a system of two particles has a relative antular momentum L, total parity is given by: L P(x1 x2) = P(x1) P(x2) (-1) (*) Parity of W, Z, photon, gluons: P=-1 (result of gauge theory) [parity of photon and gluons are not well defined, use definition of fields ] For all other composed and excitd particles (e.g. kaon, proton, ion) use rule (*) and parity conserving IA to determine intrinsic parity. 7 Parity Conservation in QED/QCD − − 푔 푒 푒 M = -q q 푢 (푝 )γμ u (p ) μν 푢 (푝 )γνu (p ) e τ 푒 2 e 1 푞2 τ 4 τ 3 푞 푞 p1 p2 = - 푒 τ j μ gμν j v 푞2 e τ p4 푞 푞 M = - 푒 τ j j p 푞2 e τ 3 − − P τ τ u γ0 u † 푢 = 푢 γ0 (Pu)†γ0 = (γ0u)†γ0= u†γ0†γ0 = u†γ0γ0 = 푢 γ0 j = 푢 γμ 푢 푢 γ0γμγ0 푢 j0 = 푢 γ0 푢 푢 γ0γ0γ0 푢 = 푢 γ0 푢 = j0 k 푘 k 0 푘 0 푘 0 0 k j = 푢 γ 푢 j = 푢 γ γ γ 푢 = − 푢 γ γ γ 푢 = -j k = 1,2,3 푞 푞 푞푒푞τ 푞푒푞τ 푒 τ 0 0 k k M = - j j - 2 (je jτ - (-je )(- jτ )) = - 2 je jτ 푞2 e τ 푞 푞 parity conservation! 8 Historical ϴ/τ 9 colour hypercharge Y = λ8/3 Wu-Experiment 1956: Lee and Yang: No evidence for parity conservation in weak IA, thus proposed set of measurements on of them was the Wu-Experiment Wu-Experiment: (performed by Mme Wu and collaborators) 10 Wu-Experiment Partiy conservation: physics stays invariant under parity conservation Idea: Check that number of electrons emitted in direction of spin (퐽 ) of 60Co and in opposite direction (-퐽 ) are the same. P퐽 = P(푟 푥 푝 ) = (-푟 ) 푥 푝 = −퐽 P J=5 J=4 Experiment: Invert polarization of 60Co and compare electron rate in same angle ϴ photons are preferentially emitted in direction of spin. Use photon distribution to test polarization of 60Co. (elm IA conserves parity) 11 60 MAIN CHALLENGE: Polarization of C0 M=5 Spin of 60Co: J=5 → M = -5,-4, …., 4, 5 ΔE = g μK B -27 . μK ~ 5.05 x 10 J/T Population of energy levels follows . Boltzmann distribution: . 퐸 − 푘 푇 푒 퐵 M=-5 for ΔE >> kBT only lowest energy level is populated, however for given B field in experiment (2.3 T) very low temperatures needed g factor depends on gitter structure Example: g= 7.5 (60Co), B = 2.3 T, T = 0.003 K Δ퐸 푃(푚=−4) − = 푒 푘퐵푇 = 0.074 → 92% polarized 60Co 푃(푚=−5) 60 Solution Part-I: embedding C0 in a paramagnetic material (B ~ μr ; μr ~ 3-4) still temepratures of T=0.01K needed 12 Adiabatic Colling 1926 von Debye proposed method to create low temperature Fundamental relation of thermodynamics: dU = T dS – p dV 1. Step: isotherm magnetisation - paramagnetic material in helium gas is put into magnetic field - energy levels are split up, only lower once are populated - entropy gets smaller: dS <0 → dU <0, helium gas absorbes heat 2. Step: helium gas removed → thermal isolation of nitrit 3. Step: adiabatic cooling - magnetic field is slowly switched off - split off of energy levels get smaller Caveat: need magnetic field to - system likes to polpulate higher states, 60 get polarized Co however dU = const due to isolation - dS gets larger thus T gets smaller 13 How to combine Cooling and Polarization? Two competing effects needed in the nitrit-crystal to get high degree of ploarization 1) Need high B field and low temperature to get polarization 2) Switch off B field to lower temperature via adiabatical cooling B field on → warm up, B field off → cool down How does this work? Solution: Some paramagnetic material have large anisotropic distribution of g-factors (artefact of crystal structure, different binding mechanisms) B field for adiabatic cooling in direction with high g-factor Thus large split up of energy levels, thus large cooling effect B field for polarization in direction of low g-factor, thus only little warm up 14 Wu-Experiment Requirements: - 2 B fields in orthogonal directions - detection of emitted electron (cover a small opening angle ϴ) - detection of emitted gamma (to test polarization of 60Co) - crystal needs to be located in helium bath first than in vacuum 60Co 15 Wu-Experiment: Results ) ) rate measure photon anisotropy, to determine unpolarized degree of polarization warm ( warm w to rate relative relative rate electron rates are different ounting c depending on the polarization! parity violation warm up with time 1616 Qualitative Explanation Wu experiment established CP violation! It was however not precise enough to measure helicity of neutrino H ~ 0.7 ± large uncertainties Goldhaber experiment 17 Goldhaber Experiment 152 152 Eu + e- → Sm* + νe 152 Sm + γ Light blue and green arrows indicate possible spin configurations 152 152Eu, J = 0; + e- Sm*, J = 1 + νe center of mass system spin of neutrino is in opposite direction than the one of 152Sm*, momentum of is in opposite direction than the one of 152Sm* 18 Goldhaber Experiment 152Sm*, J = 1 152 152 Eu + e- → Sm* + νe 152 Sm + γ 152Sm get's small recoil from photon! 152Sm, J = 0 or direction of spin of photon is opposite of neutrino emitted in direction of Sm* emitted in opposite direction of Sm* Two open question: 1) What is the direction of emission of the photon? 2) What is the polarization of the photon? 19 Resonant Scattering foto of exeperiment 20 Measurement of Polarization of Photon iron in B field 21 Goldhaber Experiment: Result Due to geometry of experiment, only resonant scattered photons are detected different rescatter object Helicity of detected photons identical to helicity of neutrino.