Elementary particles before the
(Old discoveries and tricks)
1896, the British physicist J. J. Thomson, with his colleagues John S. Townsend and H.
A. Wilson, performed experiments indicating that cathode rays really were unique
particles, rather than waves, atoms or molecules as was believed earlier
1932 Chadwick alpha particle radiation from polonium fell on beryllium
Theoretical work by Hideki Yukawa in
1935 had predicted the existence of
mesons as the carrier particles of the
strong nuclear force. From the range of
the strong nuclear force (inferred from the
radius of the atomic nucleus), Yukawa
predicted the existence of a particle
having a mass of about 100 MeV.
Nobel Prizes in Physics were awarded to
Yukawa in 1949 for his theoretical
prediction of the existence of mesons,
and to Cecil Powell in 1950 for developing
and applying the technique of particle
detection using photographic emulsions.
CDHS: Deep inelastic neutrino scattering
Cross section 𝜎
Cross section 𝜎
Problem: the bunch densities at LHC are not uniform and not exactly known.
How can I evaluate the integral to determine the cross section?
To get detector clicks one has to integrate over final states relevant to detector
This is not the cross section. It is number of detector clicks per second per unit
volume of space for incoming flux as corresponding to the initial wave functions used
to calculate the Feynman diagrams. To get cross section one has to divide by the
2-particle final state in cms
SLAC 1968: discovery of proton structure, partons
Feynman diagrams and spin
Unpolarized beam and detectors not sensitive to polarization of outgoing particles
Sum over final, average over initial polarizations
Parity of the orbital movement:
K mesons (strange particles discovery)
First hint in 1943 (cloud chamber in magnetic field in Alps: 500 MeV particle?)
Particles produced in strong interactions decaying into strongly interacting particles,
but long lifetime for the decay to be strong.
Produced in pairs.
New conservation law proposed for strong interaction: additive strangeness
Gell-Mann proposed that the strong interactions conserved isospin and
strangeness, and that electromagnetism conserved strangeness, but allowed a unit
change of isospin. The weak interactions violated isospin and allowed a unit change
If parity is conserved, then 𝜒 parity is easy: all spins are zero, orbital momentum
must be zero, positive parity.
tau parity is tricky: Dalitz.
3-particle final state in cms
scatter plot in the plain 𝒎𝒂𝒄
Theoretical physicists Tsung-Dao Lee and Chen-Ning Yang did a literature review
on the question of parity conservation in all fundamental interactions. They
concluded that in the case of the weak interaction, experimental data neither
confirmed nor refuted P-conservation. Shortly after, they approached Chien-
Shiung Wu, who was an expert on beta decay spectroscopy, with various ideas
for experiments. They settled on the idea of testing the directional properties of
beta decay in cobalt-60.
Nobel Prize for Lee and Yang in 1957.
Hunt for symmetry
Isospin was introduced by Werner Heisenberg in 1932 to explain symmetries of the then
newly discovered neutron:
• The mass of the neutron and the proton are almost identical: they are nearly
degenerate, and both are thus often called nucleons. Although the proton has a positive
electric charge, and the neutron is neutral, they are almost identical in all other aspects.
• The strength of the strong interaction between any pair of nucleons is the same,
independent of whether they are interacting as protons or as neutrons.
• Similar to a spin 1⁄2 particle, which has two states, protons and neutrons were said to be
of isospin 1⁄2. The proton and neutron were then associated with different isospin
projections I3 = +1⁄2 and −1⁄2 respectively.
• These considerations would also prove useful in the analysis of meson-nucleon
interactions after the discovery of the pions in 1947. The three pions (π+, π0, π−) could be
assigned to an isospin triplet with I = 1 and I3 = +1, 0 or −1. By assuming that isospin was
conserved by nuclear interactions, the new mesons were more easily accommodated by
• As further particles were discovered, they were assigned into isospin multiplets according
to the number of different charge states seen: 2 doublets I = 1⁄2 of K mesons (K−, K0),(K+,
K0), a triplet I = 1 of Sigma baryons (Σ+, Σ0, Σ−), a singlet I = 0 Lambda baryon (Λ0), a
quartet I = 3⁄2 Delta baryons (Δ++, Δ+, Δ0, Δ−), and so on.
Delta baryons (Δ++, Δ+, Δ0, Δ−)
Resonance: harmonic oscillator reminder
Do notice the pole in the propagator!
I = 3⁄2 Delta baryons (Δ++, Δ+, Δ0, Δ−),
Historical notation, 1238 resonances are called Δ(1232) today
Hunt for symmetry
Isospin (SU(2)) -> strangeness ->eightfold way (SU(3)) -> quarks
-> problem with Pauli in Δ++ (𝑢𝑢𝑢) → color -> QCD
What about the phase for resonances ?