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*Elementary particles before the Standard model (Old discoveries 2016-09-13آ Proton Rutherford...*

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Elementary particles before the

Standard model

(Old discoveries and tricks)

Proton

Rutherford 1917

Electron

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

Neutron

1932 Chadwick alpha particle radiation from polonium fell on beryllium

Pion

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

m-3s-1

Cross section 𝜎

m-3s-1

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

positions

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

initial flux

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

quantum number.

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

of strangeness.

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.

Dynamics

Kinematics

3-particle final state in cms

Dalitz plot

scatter plot in the plain 𝒎𝒂𝒄 𝟐 ,𝒎𝒂𝒃

𝟐

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 nuclear theory.

• 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.

Resonances

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 ?

Optical theorem

web.science.uu.nl/itf/Teaching/2015/2015Rodenburg.pdf

web.science.uu.nl/itf/Teaching/2015/2015Rodenburg.pdf

http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf

http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf