Lecture 11 0 Introduction to current particle physics

Lecture 11 0 Introduction to current particle physics 1 The Yukawa potential and transition amplitudes 2 Scattering processes and phase space 3 Feynman diagrams and QED 4 The weak interaction and the CKM matrix 5 Neutral Meson Mixing and CP violation 6 Neutrino masses and oscillations 7 Quantum chromodynamics (QCD) 8 Deep inelastic scattering, structure functions and scaling violations 9 Electroweak unification: the Standard Model and the W and Z boson 10 Electroweak symmetry breaking in the SM, Higgs boson 11 LHC experiments

Recap CKM matrix and Wolfenstein parameterisation Im Unitarity triangles Mixing of neutral mesons through `box’ diagrams Re d s s d Today: mixing of neutral mesons (neglecting CP violation)

Neutral Kaon system Pure K 0 beam can be produced eg by tuning pion energy in pp to be above threshold for pp LK 0 and below threshold for pp n. K 0 K 0 bar Remarkable early result: after a few metres, pure K 0 beam contains both K 0 and K 0 bar the two states convert into one another via box diagrams Kaons decay via the weak interaction mainly to pions Neutral kaon decays to two pions must occur in CP even (i. e. +1) eigenstates Neutral kaon decays to three pions must occur in CP odd (i. e. -1) eigenstates If weak interaction conserves CP (almost true …) See `additional material’ on web page CP EVEN CP ODD

Neutral Kaon system In fact: short-lived state “K-short” which decays to (mainly) to two pions long-lived state “K-long” which decays to (mainly) three pions In the absence of CP violation we can identify CP + with decays: CP - with decays: Given m(K) = 498 Me. V, 2 m( )=279 Me. V and 3 m( )=414 Me. V, very different Q values / much more phase space for 2 decay: Experimentally:

Time Evolution of an Initially K 0 Beam (assuming CP conservation) etc … where The intensity (i. e. fraction): (2) (3) Similarly Decays Oscillations between K 0 and K 0 -bar IF masses are different

Relation to Experimentally: i. e. the K-long mass is greater than the K-short by 1 part in 1016 Mass difference corresponds to oscillation period cf: Expect to see … … Tosc is relatively long compared to the KS lifetime After a few KS lifetimes, left with a pure KL beam which is half K 0 and half K 0 bar

The CPLEAR experiment CERN : 1990 -1996 An example of a CPLEAR event Production: Decay: Mixing • For each event know initial wave-function, e. g. here:

Tagged decay rates as a function of time for all combinations: e. g. [K 0] [K 0 -bar] [K 0] Express measurements as an “asymmetry” to remove dependence on

A. Angelopoulos et al. , Eur. Phys. J. C 22 (2001) Points show the data [ns] or CPLEAR results combined with experiments at Fermi. Lab:

Relation to CKM Matrix Consider the mixing term which arises from the sum over all possible intermediate states in the mixing box diagrams e. g. d s c t s d The differences in masses of the mass eigenstates can be shown to be: where and are the quarks in the loops and is a constant ~1. 2 mp describing probability for qqbar to annihilate inside kaon … was used to predict charm quark mass before its discovery.

B 0 mixing d b b d B much heavier than K : many more decay modes ! CP=-1 BL (“b light”) width L CP=+1 BH (“b heavy”) width H Very little difference between lifetimes or masses Small m, so higher frequency oscillations. Most decay modes are not CP eigenstates - “easy” to tag Discovery was by UA 1 (1987)

B 0 mixing d b b d … skipping straight to the dependence on VKM matrix elements: Top contribution dominates: Factors Bb and f. B describe annihilation probability Sensitive to Vtd (but difficult to pin down hadronic corrections)

BS mixing s b b s Top contribution dominates With (QCD) = 1. 21, so frequency for Bs oscillations is roughly Wolfenstein 1/l 2 ~ 25 times faster than Bd Observed experimentally in 2005 (D 0, CDF at Tevatron)

Comparison of systems / osc = x / 2 … x charaterises typical number of oscillations before decay … Define: x = m System Mass (Ge. V) (ps) m x K 0 0. 497 90 (Ks) 5. 3 ns-1 0. 477 (Ks) B 0 5. 28 1. 53 0. 5 ps-1 0. 77 Bs 5. 37 1. 47 17. 8 ps-1 26

Summary Neutral Kaon mixing and how to observe strangeness oscillations Quick overview of mixing of B mesons Next Some experimental results in (B 0, Bs) oscillations CP Violation