Lecture 10: Weak Interaction http://faculty.physics.tamu.edu/kamon/teaching/phys627/ 1
Standard Model Lagrangian http://pdg.lbl.gov/2017/reviews/rpp2017-rev-standard-model.pdf
Standard Model Lagrangian
Standard Model Lagrangian
Weak Interaction Weak Isospin SU(2) Weak Isospin Doublets Massive Particle Exchange 5
Weak Interaction 6
Weak Interaction Processes Weak scattering : Neutron beta decay : Weak decay of top quark : Massive Objects 7
q g 2 W m Unified Picture g m 2 W 2 2 W q 2 m 2 2 W W G 8
Muon Decay 9
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Fermi Coupling Constant 12
Muon Decay - Summary Tree-level muon decay width: g g G F [Quick Quiz] why is Br ratio 0.973? 13
Neutral Current: Discovery of the Z 0 The Z 0 was indirectly observed in 1973 in the Gargamelle experiment at CERN via the processes The forward-backward asymmetry (AFB) in e+ e μ+ μ also indirectly showed the need for the Z 0 The Z 0 was directly observed in 1983 by the UA1 and UA2 detectors at CERN via protonantiproton collisions. The Z 0 is slightly heavier than the W ±, with M Z = 91.1876(21) GeV The Weak Mixing Angle Many of the parameters of the electroweak interaction are related to each other. The masses and couplings are related by weak mixing or Weinberg angle (θ w ) The vertex factor (g Z ) for the Z 0 is related to the W vertex factor (g w ) : g Z = g w cos θ w Both g w and g Z are related to the QED coupling constant g e 14
A Neutral Current (Z 0 Boson) q q Z 0 n m n m 15
A Neutral Current (Z 0 Boson) 16
A Neutral Current (Z 0 Boson) 17
1983 ~ 1984 CERN Courier (July/August 2009) 1983 Discovery of W s 1984 Nobel prize to Carlo Rubbia and Simon van der Meer 18
W/Z Production Cross Sections [Q] Why s(w+) > s(w-)? 19
Electroweak Unification Unification? 20
Electroweak Unification Unification at large Q^2 21
CKM http://pdg.lbl.gov/2015/reviews/rpp2015-rev-ckm-matrix.pdf 22
http://pdg.lbl.gov/2015/reviews/rpp2015-rev-ckm-matrix.pdf 1. N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963). 2. M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). 8. J.C. Hardy and I. S. Towner, Phys. Rev. C70, 055502 (2009) [arxiv:0812.1202 23
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Quark Mixing in 2 Generations 25
Testing Cabibbo Theory 26
Cabibbo Angle Determination When only d and s are considered, it is known as Cabibbo mixing. The π decay involves a ud coupling factor of cos θ C The K decay features a us coupling factor of sin θ C 27
Problem in Cabibbo Theory 28
Also, Problem with K 0 mm GIM Mechanism Glashow, Iliopoulos, and Maiani (GIM) proposed a solution in 1970 to explain this problem. This GIM required the postulation of the charm quark Instead of exchanging a u quark, a new quark (c-quark) is exchanged. In 1974 the c-quark was discovered. i.e., J/Psi particle. [Q] Discuss what properties (mass, chaege, spin etc.) are required for the c-quark? 29
BF(K 0 (dതs) μμ) = small 30
Charged current coupled with quarks For leptons, the W couples within a particular generation: For quarks it is a little complicated, known by quark mixing (between generations) The primed quarks (weak eigenstates) are related to the unprimed quarks (mass eigenstates) by the Cabibbo-Kobayashi- Maskawa (CKM) Matrix: i.e., (u,c,t) or (d,s,b) are mixed 31
Cabbibo-Kobayashi-Maskawa Matrix Kobayashi-Maskawa (KM) is a generalization of Cabibbo- GIM for three generations of quarks. The weak interaction quark generations: The CKM matrix can be parametrized in terms of 3 rotation angles and 1 CP-violating complex phase. 32
Cabbibo-Kobayashi-Maskawa Matrix Kobayashi-Maskawa (KM) is a generalization of Cabibbo- GIM for three generations of quarks. The weak interaction quark generations: The CKM matrix can be parametrized in terms of 3 rotation angles and 1 CP-violating complex phase. 33
Cabbibo-Kobayashi-Maskawa Matrix Kobayashi-Maskawa (KM) is a generalization of Cabibbo- GIM for three generations of quarks. The weak interaction quark generations: The CKM matrix can be parametrized in terms of 3 rotation angles and 1 CP-violating complex phase. 34
CKM Matrix 35
Quark Mixing & CKM Matrix 36
Determination of CKM Matrix 37
Recap: Weak interaction is [Electromagnetic Interaction] Dirac equations are build up with point-like spin-1/2 particles. The current-current structure of g m worked well initially for e-m collision. When we apply for e-p collision, we modify the current with two form factors, reflecting neutron and proton have substructure. [Weak Interaction] Electric charge -> Weak isospin charges Observation of parity violation with neutrinos (W eν). This forces us to modify the structure of current: g m -> g m (1 g 5 ) This works very well for μ ν μ e ν e ҧ. Then looked for n pe ν e ҧ. We found : g m (1 g 5 ) -> g m (1 C g 5 ), where C ~ 1.25 (neutron and proton have substructure) The history is a series of modification reflecting the nature of (sub)structure. 38
Feynman Diagram in Week Interaction g w V ud g w Propagator for W boson: Dimensionless coupling constant g w for leptons modified by CKM factors for quarks (V ud ) Charged Current: V - A 39
arxiv:1509.06521 replaced with revised version Fri, 12 Feb 2016 15:46:21 GMT 40
Physics 41
Feynman Diagram? 42
Charged Current 43
Experimental Method 44
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