Lecture 11: Weak Interactions

Transcription

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

3 Beta Decay n p + e - + ν e (Pauli)

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5 ''Inverse" Beta Decay ν e + p n + e + (Pauli)

6 Inverse β-decay: (Pontecorvo) ''cross-sectional area" of ν wave packet ν e + p n + e + σ ~ λ 2 λ/c τ time spent by wave packet in presence of the proton typical timescale for weak interaction to occur From standard β-decay, the lifetime of the free neutron is τ ~ 1000 s and the energies of the e - and ν e are ~ 1 MeV λ = h/p 1200fm = 1.2x10-10 cm thus, σ ~ (1.2x10-10 cm) 3 /[(3x10 10 cm/s)(1000s)] ~ cm 2 Note σ E -3 t -1 and, from previous discussion, t -1 E 5 σ ~ (E MeV ) 2 cm 2 Almost exactly right! (and very, very small!!!)

7 Interaction Length for a 1 MeV Neutrino in Lead λ = 1/(σρ) σ ~ cm 2 (per proton) ρ = (11.4 g/cm 3 ) x [1/(207 g/mole)] x (6.02x10 23 atoms/mole) x (82 protons/atom) = 2.7x10 24 protons/cm 3 λ = 1/(2.7x10-19 ) cm = 3.7 x cm = 4 light-years!!

8 n p + e - + ν e ν e + p n + e + Reines and Cowan, 1956 (Nobel Prize 1995!!)

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

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11 Garwin, Lederman & Weinrich (1957) ν µ π+ e+ µ+ (polarised) ν µ ν e precess polarised muons

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

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

14 Assume some Yukawa-like exchange process is at work. β-decay (n p+e - +ν e ) tells us the exchange particle must be charged W ± It can change Weak interactions obey a simple symmetry : u d (like β-decay) s c t b and, for leptons, e ν e µ ν µ τ ν τ So, for example, for the process π - µ - + ν µ (pion decay): π - d u W - ν µ µ - but, unfortunately, it is found experimentally that the couplings are not the same! α W ud 0.95 α W

15 Another hitch: Κ - s u W - ν µ µ - 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: u dʹ c sʹ ( ) and ( ) where dʹ d cosθ C + s sinθ C sʹ -d sinθ C + s cosθ C θ C ''Cabibbo angle" or, alternatively d -sʹ sinθ C + dʹ cosθ C s sʹ cosθ C + dʹ sinθ C α W ud = α W cos 2 θ C α W us = α W sin 2 θ C

16 σ ( Κ - µ - ν µ ) σ ( π - µ - ν µ ) = α W us α W ud = tan 2 θ C ~ 1/20 ( θ C = degrees ) (The factor of 1/20 delineates ''Cabibbo-suppressed" and ''Cabibbo-allowed" processes) Generalizing to 3 generations and all possible mixings between quarks: ( ) [ ]( ) = dʹ sʹ bʹ V ud V us V V V V ub ud us ub V V V ud us ub dʹ sʹ bʹ CKM matrix (Cabibbo, Kobayashi and Maskawa)

17 Kaons: K o = ds K o = sd (S = +1) (S = -1) But S is not conserved in weak interactions so K o -K o mixing can occur: K o d s u W + W - u s d K o We can thus define two orthogonal mixtures: K 1o = 1/ 2 ( K o + K o ) K 2o = 1/ 2 ( K o - K o ) Note: C P K 1o = + K 1o and C P K 2o = - K 2o K 1 o π + π - ; π o π o K 2 o π + π - π o ; π o π o π o Allowed K 1 o π + π - π o ; π o π o π o K 2 o π + π - ; π o π o Forbidden

18 Experimentally, 2 kaon states are observed with different lifetimes: K S o π + π - ; π o π o τ 9x10-11 s K L o π + π - π ο ; π o π o π o ; π ± lepton ν (ν) τ 5x10-8 s ± So we associate K S o K 1 o and K L o K 2 o However, in 1964, Christenson, Cronin, Fitch & Turlay discovered K L o π + π - (branching ratio ~ 2x10-3 )

19 beam collimator lead-glass cuts out photons 30 GeV protons K S +K L K L 18 m steel target magnets sweeps out charged particles CM of π + π - pair )θ K L beam direction

20 K So = 1/ 1+ ε 2 ( K 1o - ε K 2o ) K Lo = 1/ 1+ ε 2 ( ε K 1o + K 2o ) where ε small complex number parameterizing the size of the CP violation (experimentally, ε 2.3x10-3 ) What does this mean?? Reason for antimatter assymmetry?? Perhaps we can learn more from studying CP violation in other particle systems...

21 Basically compare the rates for B 0 = Ψ + K S 0 versus (π + π - mode) B 0 = Ψ + K S 0 (π + π - mode)

22 CP violation could be parameterized as part of the mixing angles in the CKM matrix ( ) [ ] ( ) dʹ sʹ bʹ V ud V us V V V V ub ud us ub V ud V us V ub =?? dʹ sʹ bʹ Unitarity of the matrix is needed to allow for local gauge symmetry Which imposes constraints on the angles: η α ''Unitarity Triangle" γ ρ β

23 Matter-Antimatter Asymmetry Revisited: Sakarov Conditions (1967)!!! (GUTs) 1) Baryon Number Violation 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 Establishes Asymmetry Locks In Asymmetry