Methods of Experimental Particle Physics Alexei Safonov Lecture
Methods of Experimental Particle Physics Alexei Safonov Lecture #5 1 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 2 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 3 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
238 U 234Th + 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 Thompsons 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 4 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 5 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 6 Fermi Contact Interaction Fermi proposed a 4 fermion contact interaction The Feynman rule is to put GF in the 4fermion 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 7 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 its 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 8 W Boson One obvious solution: Replace which is equivalent to introducing a propagator of a new particle W with mass m W 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: Ws change flavors of quarks They also convert leptons to neutrinos 9 . Parity Violation One can conclude from e.g. the muon decay properties that Ws 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 10 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 2dimensional complex space The corresponding symmetry is SU(2) 11 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 Its the Z boson 12 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
n n New contributions e.g. to the process of electron pair annihilation into muon pairs 13 W and Z Boson Discoveries at CERN First evidence for Z bosons from neutrino scattering using Gargamelle bubble chamber Sudden movement of electrons
e e 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 14
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