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 itself (x-rays or something new?) 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 238U → 234Th + α • 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 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 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 8 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 9 . 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 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 • It’s 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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