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
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
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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 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
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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
𝑮𝟐𝑭
→
𝒈𝟐
𝒒𝟐 −𝒎𝟐𝑾
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:
• 𝒆𝝂 𝑾 𝝂𝒆 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
𝟎 𝟏 𝟏
𝟎
correspond to something like this
=
𝟏
𝟏 𝟎 𝟎
• Given that wave functions are generally
complex, we are dealing with rotations in 2dimensional 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
n
n
• New contributions e.g. to the
process of electron pair
annihilation into muon pairs
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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
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
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