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Methods of Experimental Particle Physics

Alexei Safonov

Lecture #5

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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

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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?)

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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

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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

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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”

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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

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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

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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

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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

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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)

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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

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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

n

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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

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