1. Alessandro Bettini Introduction to Elementary Particle Physics
SECOND EDITION
Cambridge University Press
2014
CHAPTER 1: Preliminaries

2. Today’s plan
Review calculations of s, the energy available in the CM frame to produce new particles.
Reminder about q2 (momentum transfer for a virtual photon)
Introduce hadrons, leptons, quarks and fundamental interactions.
Introduce cross-section, σ, used in particle and nuclear physics calculations of interaction probabilities (next time)

3. Diphoton mass ✔ Do you see why ?
Find the mass of this system when the two photon energies are equal
What is the first step ?
What relativistic invariant should we use ?
Do you see why ? ✔

4. CM and Fixed Target Frames
In the CM frame, the momenta sum to zero. What is s ?
In the special case, the beam energies are equal

5. CM and Fixed Target Frames
In the fixed target frame, the target particle is at rest. What is s ?
Do you see why ?

6. Fixed target vs CM conceptual question
For making new particles, which kind of experiment/accelerator is most effective ?
Is there any tradeoff ?
Ans: s (available energy for making new particles) is much larger with head-on collisions but luminosity/intensity can be orders of magnitude larger with fixed target geometry.

7. Fixed target vs CM example
Fermilab, located in Batavia, Il (suburbs of Chicago) used to collide 1 TeV protons on 1 TeV anti-protons. What is the available energy to produce new particles ?
What energy proton beam would be required to achieve the same available energy in fixed target ?

8. Fixed Target Example What is the invariant s for the final state ?
Question:
BTW why do we need 4 particles ?
What is the threshold (minimum) energy for making an anti-proton in this reaction ?
Let’s calculate s for the initial and final states.
Note that E=T+m_p, where T is the kinetic energy of the proton beam
What is the invariant s for the final state ?
N.B. The 4 nucleons are at rest in the CM frame not the lab frame

9. Discovery of the anti-proton
Berkeley, California 1955
Emilio Segre
A key ingredient was the construction of a new particle accelerator (“atom smasher”) called the Bevatron, which could operate just above the threshold for production of anti-protons. This was Billion Electron Volts (Bev) for the proton kinetic energy.
Owen Chamberlain

10. Problem 1.5: How to calculate q2
Figure from Bettini
Use this geometry and the fact that p’=p to obtain,
x vs t representation of particle interaction
We are probing the proton with a “virtual photon”. The wavelength of the photon (deBroglie wavelength associated with the momentum transfer) determines the length scale that is probed.

11. Problem 1.7: GZK energy cutoff
This reaction should limit the maximum energy of protons in cosmic rays
1966: Greisen, Katsepin and Kuzmin
Need to take into account interaction with the cosmic microwave background
Early claims of post GZK cosmic rays by AGASA in Japan not confirmed by Auger
N.B. these cosmic ray plots are on a log-log scale

12. Mandelstam Invariants
s: Available energy in CM for making new particles
t: 4-momentum transfer squared
Stanley Mandelstam, UC Berkeley ( )
Scattering processes in particle physics
Note s≥0, t≤0, u≤0
s channel
t-channel
u-channel

14. Classification of “Elementary” Particles
Section 1.8 of Bettini
In quantum mechanics, angular momentum is quantized. In particular, there is intrinsic spin associated with particles.

15. Question: Are leptons composite or point-like ?
Question: Are baryons bosons or fermions ?
Question: Are mesons bosons or fermions ?

17. Now pay close attention to the propagator particles