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Methods of Experimental Particle Physics. Alexei Safonov Lecture #5. Today Lecture. So far we have learnt a lot about electromagnetic interactions and quantum field theory:

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today lecture
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
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
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
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
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 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
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
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
Parity Violation

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  • 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
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
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
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
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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