P461 - particles VI 1

Particle-antiparticle mixing and CP violation

• There is another type of “mixing” which is related to quark mixing. This can lead to observation and studies of CP violation

• consider the mesons which are neutral and composed of different types of quarks

• Weak interactions can change particle into antiparticle as charge and other quantum numbers are the same. The “strangeness” etc are changing through CKM mixing

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P461 - particles VI 2

• Depends onVij at each W vertex • as V and V* are different due to phase,

gives particle-antiparticle difference and CP violation (any term with t-quark especially)

• the states which decay are admixtures of the “strong” state(a rotation). They can have different masses and different lifetimes

• #particle vs #antiparticle will have a time dependence. Eg. If all particle at t=0, will be a mixture at a later time

• the phenomenology of K’s is slightly different than B/D’s and we’ll just do K’s in detail. Kaons rotate and give long-lived and short-lived decays. B/D also rotate but lifetimes are ~same.

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P461 - particles VI 3

Neutral Kaon Semi-leptonicDecay

• Properties for “long” and “short” lived

• Semi-leptonic (Beta) decays. Positive or negative lepton tells if K or anti-K decayed

• partial width is exactly the same as charged K decay (though smaller BF for Short and larger for Long).

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P461 - particles VI 4

Neutral Kaon Hadronic Decays

• Also decay hadronically

• Both decay to same final states which means the mixed states K1 and K2 also decay to these 2pi and 3pi modes. Means initial states can mix and have interference

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P461 - particles VI 5

Sidenote C+P for Pions

• Parity operator Pf(x,y,z)=f(-x,-y,-z). Intrinsic parity for psuedoscaler mesons (like K,pi) is -1

• Charge conjugation operator C. Changes particle to antiparticle.

• Can work out eigenvalue. As C changes charge, C=-1 for photon

• given its decay, pion has C= +1

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P461 - particles VI 6

Neutral Kaon Hadronic Decays

• 2 pion and 3 pion are CP eigenstates with eigenvalue +1 for 2pi and -1 for 3pi

• K1 and K2 also CP eigenstates

• different values of matrix element if initial and final states are the same CP eigenstate or if they are not CP eigenstates (like K+ or beta decays)

• if CP is conserved, K1/Ks decays to 2 pions and K2/KL decays to 3 pions. More phase space for 2 pions and so faster decay, shorter lifetime.

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P461 - particles VI 7

Decay and Interference

• From Schrodinger eq. plane wave solutions

• the two amplitudes have to be added and then squared. Gives interference. Example: start with pure K0

• Intensity is this amplitude squared

• small mass difference between the two weak decay eigenstates

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P461 - particles VI 8

Decay and Interference

• Do the same for anti-K

• get mixing. Particle<->antiparticle varying with time.

• At large time get equal mixture = 100% KL

• the rate at which K->anti-K depends on 1/deltam. You need to mix K<->antiK before they decay to have KS and KL

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P461 - particles VI 9

KS Regeneration

• Assume pure KL beam• strikes a target made up of particles (p,n)• different strong interaction cross section for

K and anti-K

• mix of K-antiK no longer 1:1. Example, assume “lose” 0.5 antiK, 0.0 K. gives (ignoring phases and so not quite right)

• First observed by Lederman et al. measures particle/antiparticle differences. Useful experimental technique

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P461 - particles VI 10

CP Violation

• C changes particle to antiparticle• P operator flips space (mirror image)• T time reversal t --> -t• fundamental axiom (theory?) of quantum

mechanics CPT is conserved• Weak interaction violate all 3. CP violation

is the same as T violation. Three observations (so far) of this

1 Universe is mostly matter (Sakharov 1960s)

2 KL decay to 2 pions (Christianson, Cronin, Fitch and Turlay, 1964)

3 neutral B decays

P461 - particles VI 11

CP Violation in K decays

• Ks and KL (the particles which have different lifetimes) are NOT eigenstates of CP. Instead K1 and K2 are

• When KL decays, mostly it is decaying to a CP=-1 state(3 pions) but sometimes to a CP=+1 state (2 pions)

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P461 - particles VI 12

CP violation in K decays

• CP is then explained by having a phase in the mixing between K and anti-K

• other sources of CP violation (“fifth force”) are ruled out as inconsistent with the various ways of observing CP violation

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