Lecture 10 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 CP violation and the B-factories

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 Weak interactions & Parity violation

W and Z vertices

W couplings to quarks

The CKM matrix, values of elements & how we know

… transforms strong (flavour) eigenstates into weak eignestates

A handy parameterisation: Wolfensteien

gw Vud, Vcs, Vtb O(1)

gw Vcb, Vts O(λ2) gw Vcd, Vus O(λ)

… Parameterisation with 4 real parameters, λ, ρ, η, A

Phase contained in imaginary parts of Vub and Vtd à CP violation in at least some processes (but not all)

Unitarity Constraints on the CKM matrix

Unitarity V V† = 1 implies relationhips between the Matrix elements …

Normalisation / 1 quark in, 1 quark out

Orthogonality / No FCNC

Unitary triangle

Sum of 3 complex numbers = 0 … can be expressed as a triangle in the complex plane

“The” Unitary triangle

Im

Re

Traditionally divide through by VcdVcb* so baseline is unity by definition

-  There are other unitarity triangles based on other orthogonlity constraints in the CKM matrix - Area of triangle measures extent of CP violation -  By measuring 2 upper sides and 3 angles, over-constrain and determine whether triangle really is a triangle (`closes’) … clear & testable Standard Model prediction that’s sensitive to CP violation

à major theme of modern flavour physics

Snapshot of Recent Status

- Lengths of two upper sides obtained from ratios of rates of decay processes (see last lecture)

-  CP violation lives in the three angles …

-  Angle measurements require phase information … i.e. interference between diagrams

Reminder: Interfering Processes - Two processes can interfere if they have the same initial and final states - Then combining their sqaured matrix elements to a transition rate

No phase in Cabibbo à need process involving 2nd or 3rd gen’s

Usually consider ‘CP conjugate’ states in order to extract the phase dependent part from decay rate measurements:

Rate of processes Rate of CP process

=

b c

W-

gVcb b c

W+

gV*cb e.g…

Mixing and `Box’ diagrams Neutral mesons with different quark flavours can `mix’ with their antiparticles of opposite flavour and no other distinguishing quantum numbers (CP conjugates).

The mixing phenomenon is entirely due to weak interactions. We will study it first, which will lead us into CP violation

e.g. neutral kaon system: K0 and K0 can `evolve’ into one another via box diagrams … (18 in total, 2nd order in couplings) …

d

s d

s d

s d

s

- The relative fraction at any later point can be determined by measuring rates of semi-leptonic decays to (π- e+) versus (π+ e-)

- Charge of the observed pion (or lepton) tags the decay as from either a or because

NO but

… which provides a way of measuring oscillations experimentally

Observing and Measuring Mixing - Initially pure K0 beam will evolve with time into a mixture of K0 and K0-bar

… some slides from when Dave Charlton taught this course …

Summary

-  Unitary triangles and measuring sides and angles -  Neutral kaon system and mixing

d

s d

s

More on strangeness and beauty oscillations

CP violation …

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