09part2 - P461 particles III 1 Mixing in Weak Decays •...

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Unformatted text preview: P461 - particles III 1 Mixing in Weak Decays • Charged Weak Current (exchange of Ws) causes one member of a weak doublet to change into the other • Taus and muons therefore decay into the lightest member of the doublet (their neutrinos) • electrons are stable as the (e,nu) doublet is the lightest doublet. The virtual W can’t convert to anything W e μ μ ν e ν μ ν ν μ + + → − − e e e ν W e “e decay” P461 - particles III 2 Mixing in Weak Decays • In the same context, the heavier quark doublets decay via as c,t are heavier • s and b quarks should then be stable (their lightest baryons) as the lightest member of their doublets • But they aren’t……due to mixing between the 3 generations • for quarks the mass eigenstates are not the same as the decay eigenstates • b mass eigenstate: what has m b • b decay eigenstate: what interacts with W-t " " ; " " W b t W s c b t s c + → + → P461 - particles III 3 Quark Mixing: 2 Generations • If assume only 2 generations. Mixing matrix • where θ C is the Cabibbo angle • M then rotates from the mass eigenstates (d,s) to the decay eigenstates (d’,s’) (usually deal with mixing of charge 1/3 quarks but both mix) • look at weak vertices (2 identical ways) = − = cs cd us ud C C C C V V V V M θ θ θ θ cos sin sin cos = ′ ′ = ′ ′ c u M c u s d M s d W c s’ u d’ c s d c V cs V cd P461 - particles III 4 Charm Decay • Charmed meson can Beta decay to lighter mesons which have either s or d quarks • • Modulo slightly different phase space, the ratio of these decays depends only on the different mixing. Direct measurement of the mixing angle. 95 . 05 . cos sin 043 . 07 . 003 . 003 . ) ( 07 . ) ( ) ( 2 2 2 2 = = ≈ = = + + → = + + → + + + + C C cs cd V V BF d d or D BF d s K d c D θ θ ν μ ρ π ν μ μ μ ν μ W s d ′ c d P461 - particles III 5 Kaon Decays • Historically first place mixing observed • decay rates depend on same phase space and spin factors as charged pion decay • Observed rates only 5% of what they “should” be and Cabibbo proposed a mixing angle whose source was unknown at the time • This (partially) lead to a prediction that the c quark must exist % 8 % 7 % 21 % 64 ) ( sec 10 2 . 1 494 8 = → = → = → = → × = = + + + + − + + + + + + + − BF e or K BF or K BF K BF s u K MeV m K ν π ν μ π π π π π π π π π ν μ τ P461 - particles III 6 3 Quark Generations • For 3 generations need 3X3 matrix. It is unitary and has some phases which don’t matter and can be defined by 3 angles and 1 phase (phase gives particle antiparticle differences….antiparticles use M* Hermitian adjoint) • called Cabibbo-Kobyashi-Maskawa (CKM) matrix and was predicted by K-M before the third...
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This note was uploaded on 10/02/2009 for the course PHYS 460 taught by Professor Johnson,c during the Spring '08 term at Northern Illinois University.

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09part2 - P461 particles III 1 Mixing in Weak Decays •...

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