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## Methods of Experimental Particle Physics

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Today Lecture

- So far we have learnt a lot about electromagnetic interactions and quantum field theory:
- QED – is a relativistic quantum field theory describing interactions of charged fermions (electrons) with photons (electromagnetic field)
- We talked about calculations in QED, higher order corrections and renormalizability
- Today we will talk about weak interaction
- Another force, which was found to be responsible for radioactive decays

Discovery of Radioactivity

- Radioactivity was discovered by Becquerel in 1896 in uranium
- Later observed in thorium by Marie and Pierre Curie
- Crystalline crusts of potassium uranic sulfate together with photographic plates wrapped into thick black paper (to avoid exposure to the light from outside)
- After about a day of exposure the developed photographic plates have shown images of the crystals
- Metal pieces put in between would largely shield the images (see Maltese Cross on the bottom picture)
- He concluded that something must have been emitted from within the crystal itself (x-rays or something new?)

Further Developments

- In 1899 Rutherford found that there are two types of decay:
- In alpha decays emitted objects could penetrate several mm of aluminum
- Alpha particle is a helium atom
- In beta decays emitted objects could be stopped in a thin foil or even paper
- Becquerel has measured the charge-to-mass ratio of these particles using Thompson’s method measuring deflection of charged particles in crossed E and B fields
- He found that the new particles are electrons as they had the same e/m as an electron
- Neutron -> proton + electron

238U → 234Th + α

Beta Decay

- In 1911 Meitner and Hahn measured the energy spectrum of electrons in beta decay
- Two major findings:
- The energy spectrum was continuous and had an end-point
- Assumes energy is not conserved as one would expect in n->e+p
- Looked as if something light and invisible was emitted at the same time as the electron

Neutrino

- Following a lot of controversies, by 1927 continuous spectrum and energy non-conservation were confirmed
- In 1930 Pauli proposed a new “neutron”
- In 1933 Fermi proposed a theory of weak decays
- His manuscript was rejected by Nature for being “too speculative”
- He also renamed “neutron” into a “neutrino”

Fermi Contact Interaction

- Fermi proposed a 4 fermion contact interaction
- The “Feynman rule” is to put GF in the 4-fermion interaction vertex:
- Allowed a successful description of beta decay including the energy spectrum
- Also required some unusual features including not being symmetrical under parity
- Fermi theory was successfully applied to explain muon decay with high precision

Fermi Theory

- One problem with Fermi theory is that it is not well behaving
- Cross sections in Fermi theory behave as s~GFE2
- Ultraviolet divergences we talked about before
- And it’s also not renormalizable
- At energies above 100 GeV, unitarity gets violated
- “The probability of an interaction to happen becomes greater than 1”
- Fermi Theory is only an effective theory that works in the limit of small energies
- It must be somehow modified to be a more complete theory

W Boson

- One obvious solution:
- Replace which is equivalent to introducing a propagator of a new particle W with mass mW
- Then g is the weak coupling constant, several orders of magnitude smaller than that in QED
- Then neutron decay in the new terms looks like the following:
- W’s change flavors of quarks
- They also convert leptons to neutrinos

Parity Violation

.

- One can conclude from e.g. the muon decay properties that W’s couple only to the “left-handed” component of the electron wave-function
- Mathematically, that requires the lagrangian to use modified wave-functions
- The left-handness implies that electron spin projection on the momentum of the electron is negative 1/2

Constructing the Lagrangian - I

- Describing W coupling to both electrons and neutrinos requires something like this:
- so W is a matrix in a 2x2 space, and e and n stand for the wave functions of electrons and neutrinos
- E.g. W converting electron into a neutrino could correspond to something like this
- Given that wave functions are generally complex, we are dealing with rotations in 2-dimensional complex space
- The corresponding symmetry is SU(2)

Constructing the Lagrangian - II

- The SU(2) is the symmetry of rotations that preserve the length of the vectors you are rotating
- Applying W is like rotating the vector of (e,n)
- In group theory in the representation where you rotate 2-dim vectors these rotations are done by three generators which are Pauli matrices
- So W must be one of those generators
- Even two as you have W+ and W-
- But you must have all three!
- Need a new boson coupling electrons to electrons and neutrinos to neutrinos
- It’s the Z boson

Z Boson

- Assuming all leptons are treated the same, it should couple to electrons, neutrinos and quarks
- Z-exchange processes often called “neutral current” (Z is neutral), as opposed to “charged current” referring to W exchanges
- New contributions e.g. to the process of electron pair annihilation into muon pairs

W and Z Boson Discoveries at CERN

- First evidence for Z bosons from neutrino scattering using Gargamelle bubble chamber
- Sudden movement of electrons

- Discovery of W boson and a very convincing confirmation of Z by UA1/UA2 from SPS (Super Proton Synchrotron)
- 1981-1983
- UA=“Underground Area”
- 400 GeV proton-antiproton beams

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