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Lecture 11: Weak Interactions

Lecture 11: Weak Interactions. Cross-Section and the W Coupling The Cabibbo Angle and the CKM Matrix Parity Violation Kaons and Mixing CP Violation. Useful Sections in Martin & Shaw:. Sections 4.51, 8.1, Chapter 10. Cosmic Gall. Cosmic Gall. in fact, point-like in the Standard Model.

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Lecture 11: Weak Interactions

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  1. Lecture 11:Weak Interactions • Cross-Section and the W Coupling • The Cabibbo Angle and the CKM Matrix • Parity Violation • Kaons and Mixing • CP Violation Useful Sections in Martin & Shaw: Sections 4.51, 8.1, Chapter 10

  2. Cosmic Gall Cosmic Gall in fact, point-like in the Standard Model and little hardly true interaction cross-section much higher than for typical neutrino energies obvious foreshadowing of electroweak theory Neutrinos, they are very small. They have no charge, they have no mass And do not interact at all. The earth is just a silly ball To them, through which they simply pass, Like dustmaids down a drafty hall Or photons through a sheet of glass... John Updyke (< 2eV) should not be taken to indicate a sensitive detection technique (from ''Telephone Poles and Other Poems," 1963)

  3. Beta Decay e Beta Decay n p + e- + (Pauli)

  4. Reversed Beta-Decay

  5. Inverse Beta-Decay ''Inverse" Beta Decaye + p n + e+ (Pauli)

  6. Pontecorvo Estimate e + p  n + e+ time spent by wave packet in presence of the proton /c  ~2 typical timescale for weak interaction to occur ''cross-sectional area" of  wave packet ~ 10-43 (EMeV)2 cm2 Inverse -decay: (Pontecorvo) From standard -decay, the lifetime of the free neutron is ~ 1000 s and the energies of the e and e are ~ 1 MeV  = h/p ≃ 1200fm = 1.2x10-10cm thus, ~ (1.2x10-10cm)3/[(3x1010 cm/s)(1000s)] ~ 10-43cm2 Note  E-3t-1 and, from previous discussion, t-1 E5 Almost exactly right! (and very, very small!!!)

  7. Interaction Length in Lead = 4 light-years !! Interaction Length for a 1 MeV Neutrino in Lead  ~ 10-43 cm2(per proton) x [1/(207 g/mole)]  = (11.4 g/cm3) x (6.02x1023 atoms/mole) x (82 protons/atom) = 2.7x1024 protons/cm3  = 1/(2.7x10-19) cm = 3.7 x 1018 cm

  8. First Neutrino Detection n p + e- + e epn + e+ Reines and Cowan, 1956 (Nobel Prize – 1995 !!)

  9. Parity Violation Directly observed by Wu et al. in 1957 from the decay 60Co 60 Ni* + e + e g(1.173 MeV) + g(1.332 MeV) e P 60Co 60Co e Parity Violation in Weak Interactions First suggested in 1956 by Lee & Yang based on review of kaon decay modes nuclear spins aligned by cooling to 0.01 oK in a magnetic field (degree of polarisation determined from the anisotropy of g-rays) Should be the same under parity transformation, but fewer electrons are actually seen going forward !

  10. ne nm m+ p+ precess polarised muons e+ nm Garwin, Lederman & Weinrich (1957) (polarised)

  11. Neutrino Helicity e + 152Eu(J=0) 152Sm*(J=1)+ e all neutrinos are left-handed ! Also, in 1958, Goldhaber et al. measured the helicity of the neutrino: 152Sm(J=0)+  events were chosen with the final states collinear  and e travel in opposite directions, so helicity of the neutrino is found from that of the gamma

  12. Neutrinos of the 2nd Kind Neutrinos of the ''Second Kind" (not as popular as the Spielberg sequel) Leon Lederman, Melvin Schwartz and Jack Steinberger, 1962

  13. ''Near Symmetry" and the W -decay (np+e+e) tells us the exchange particle must be charged So, for example, for the process  +  (pion decay): d u   W  Assume some Yukawa-like exchange process is at work. W Weak interactions obey a simple symmetry : It can change ud(like -decay) sc tb and, for leptons, ee   but, unfortunately, it is found experimentally that the couplings are not the same! Wud≃ 0.95 W

  14. The Cabibbo Angle s u   W  c s u d ( )and ( ) C''Cabibbo angle" Wud = W cos2C Wus = W sin2C Another hitch: shouldn’t occur, but does !(albeit infrequently) We can explain all this (or, at least, parameterize our ignorance) by adopting the somewhat bizarre notion that the weak interaction actually couples to mixtures of quarks. So, initially just considering the first two generations, the relevant quark doublets are: where d d cosC + s sinC sd sinC + s cosC or, alternatively d s sinC + d cosC s s cosC + d sinC

  15. The CKM Matrix Wus Wud = ( ) [ ] ( ) Vud Vus Vub Vud Vus Vub Vud Vus Vub d s b d s b = CKM matrix   = tan2C ~ 1/20 C = 12.7 + 0.1 degrees ) (The factor of 1/20 delineates ''Cabibbo-suppressed" and ''Cabibbo-allowed" processes) Generalizing to 3 generations and all possible mixings between quarks: (Cabibbo, Kobayashi and Maskawa)

  16. Neutral Kaons Ko = ds Ko = sd (S = +1) (S = 1) u d s s d But S is not conserved in weak interactions so Ko-Ko mixing can occur: Ko Ko W+W u K1o = 1/2 ( Ko + Ko ) K2o = 1/2 ( KoKo ) K1o + ; oo K1o +o ; oo o K2o +o ; oo o K2o + ; o o Allowed Forbidden Kaons: We can thus define two orthogonal mixtures: Note: CPK1oK1oand CPK2oK2o

  17. CP Violation  KLo  ; ooo ; lepton() ≃ 5x10s KLo+ (branching ratio ~ 2x103) Experimentally, 2 kaon states are observed with different lifetimes: KSo  ; oo ≃ 9x1011s So we associate KSo K1o and KLo K2o However,in 1964, Christenson, Cronin, Fitch & Turlay discovered

  18. CP Experiment lead-glass cuts out photons beam collimator KS+KL KL 18 m steel target magnets sweeps out charged particles CM of + pair  KL beam direction 30 GeV protons

  19. CP Violating Term KSo = 1/  ( K1o K2o ) KLo = 1/  (  K1o + K2o ) (experimentally, ≃ 2.3x103 ) where  small complex number parameterizing the size of the CP violation What does this mean?? Reason for antimatter assymmetry ?? Perhaps we can learn more from studying CP violation in other particle systems...

  20. BaBaR Basically compare the rates for B0 =  + KS0 (+ mode) versus B0 =  + KS0 (+ mode)

  21. Unitarity Triangle ( ) ( ) [ ] d s b d s b Vud Vus Vub Vud Vus Vub Vud Vus Vub =  ''Unitarity Triangle"     CP violation could be parameterized as part of the mixing angles in the CKM matrix ?? Unitarity of the matrix is needed to allow for local gauge symmetry Which imposes constraints on the angles:

  22. Sakarov Conditions Establishes Asymmetry Locks In Asymmetry Matter-Antimatter Asymmetry Revisited: Sakarov Conditions (1967) !!! 1)Baryon Number Violation (GUTs) allows baryons and anti-baryons to appear and disappear independently of each other 2)CP Violation so the rate of appearance/disappearance of baryons is different from anti-baryons 3)Non-Equilibrium Conditions since equilibrium would then tend to ''average-out" any asymmetry

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