1. Wolfgang Panofsky, SLAC director
American History: John F. Kennedy signing the first test-ban treaty in August 1963.
On August 5, 1963, representatives of the United States, Soviet Union and Great Britain signed the Limited Nuclear Test Ban Treaty, which prohibited the testing of nuclear weapons in outer space, underwater or in the atmosphere.
The Comprehensive Nuclear-Test-Ban Treaty (CTBT) is a multilateral treaty that bans all nuclear explosions, for both civilian and military purposes, in all environments. It was adopted by the United Nations General Assembly on 10 September 1996 but has not entered into force as eight specific states (including the US) have not ratified the treaty.
Wolfgang Panofsky, SLAC director
China, Egypt, Iran, Israel and the United States signed but not ratified

2. Nuclear Physics back to Particle Physics
“If I could remember the names of all these particles, I’d be a botanist” – Enrico Fermi

3. Today’s plan Collect homework Overview of fundamental Interactions
Introduce decay width, branching fraction
Introduce cross-section, σ, used in particle and nuclear physics calculations of interaction probabilities.
Discuss detectors and accelerators (sources of particles) (may start next time).

4. Electromagnetic interaction
Why the factor of (2/3)2 ?

5. Strong Interaction

6. Weak Interaction (“neutral currents”)

7. Weak interaction (“charged current”)

8. Conceptual Questions about Fundamental Interactions
Is the EM interaction long-range or short range ?
Is the strong interaction long-range or short range ?
Is the weak interaction long-range or short range ?
Bettini 1.9
Question: What is the typical range/length scale of the strong interaction ?
Ans: around 1 fm =10-15m, the nuclear scale.
Since the masses of the propagators of the weak interaction, W+-, Z are ~80, 90 GeV, can you estimate the range of the weak interaction ?
How did Hideki Yukawa (1935) predict the existence of the pion, which was subsequently found in cosmic rays ?

9. Lifetime and width The π0 lifetime 8.4 x 10-17 s, what is its width ?
Short-lived particles are “resonances”. Their width and lifetimes are inversely proportional.
Like the response curve of a radio tuner or RLC circuit.
Heisenberg’s uncertainty principle implies
The π0 lifetime 8.4 x s, what is its width ?
The width of the Z resonance is determined by the number of open decay channels. (more in Chap 9.)
Width of the pi^0 is impossible to measure directly while the lifetime of the eta is too short to be measured directly.
The width of the η is 1.3 keV, what is its lifetime ?

10. Branching fraction, branching ratio
Short-lived particles may have multiple decay channels.
Example (B is used for branching fraction following the PDG)
If ab + c + d, then we can define the branching fraction or branching ratio.
For example, the D+ meson decays about 17% of the time to a final state with an electron.
The D0 meson decays to an electron about 7.5% of the time to a final state with an electron.

11. Bettini, p.14
Cross-section is a measure of the strength of interaction between two-particles. It has dimensions of area (m2) or barns (10-28 m2)
Let’s try to work out the cross-section for a fixed target reaction with a collimated incident beam.
Here nt=number of scattering centers per unit volume; Nt is the total number of scattering centers.
Question:
What is the intensity of the beam ?
What is the flux of the incident beam ?
(or what are the dimensions of these quantities ? And how do they differ ?)
Intensity is number of incident particles per sec

12. 1 barn = 10-28m2 and is about the size of an A=100 nucleus (huge !!).
Recall one gram of matter contains Avogadro’s number of nucleons. (6 x 1023)
BTW: what happened to the electrons in the target ??
The second expression is if the target is not hydrogen.
1 barn = 10-28m2 and is about the size of an A=100 nucleus (huge !!).
Unit invented by Midwestern “farm boy” nuclear physicists at Purdue University. Also trying to confuse the enemy during WWII. (source FNAL symmetry magazine)

13. Most cross-sections in particle physics as opposed to nuclear physics are somewhat smaller than in a barn and are measured in mb (“millibarns”), μb (“microbarns”), nb (“nanobarns”), pb (“picobarns”).
Examples:
Let’s move on to total absorption cross-sections in a long target
Units:
(#/m3 )x m2
Question: What would be a characteristic absorption length by dimensional analysis ?

14. “It’s the luminosity, stupid”-remark often heard at accelerator experiments
Luminosity has units of #/m2/sec
Fixed target again
Question: Can we check the units on the right-hand side ?
Ans: Intensity is #/sec;
Σ is m2; so it works.

15. Question: how do we calculate the number of protons in the target ?
Example: A liquid hydrogen target of volume m3 and density 71 kg/m3 is exposed to a wide uniform monoenergetic beam of negative pions with a flux of 107 particles/m2/s and the reaction π- p  K0 Λ is observed.
If the cross-section, σ, for this reaction is 0.4 mb, what is the rate of production of Λ particles ?
Solution has two steps: (1) calculate the reaction rate per target particle and (2) the number of target particles. Multiply (1) by (2).
Question: how do we calculate the number of protons in the target ?

16. Fermi’s Golden rule Bettini p.15 Reaction rate per target particle
Phase space volume available in the final state
Quantum mechanical matrix element between initial and final state.
Should be Lorentz invariant.
Do you see the mistake on the blackboard ? Alpha = k e^2/(hbar c) in cgs or (1/4pi epsilon_0) e^2/hbar c in MKS ~ 1/137
On p.16-17, Bettini applies this and the phase space calculation to obtain the case of two-body phase space
ac +d (please study this calculation).
Is there something terribly wrong with this picture ?
Why is there only one momenta in the result ?

17. Differential scattering cross-section
Total cross section-Differential cross-section, which depends on solid angle or other parameters.

18. In QM, if a particle has spin s there are (2 s + 1) spin states 
Now let’s look at the result for a + b c + d in the center of mass frame. (picture on the right)
Bettinip.18
Question: Why are there only two momenta here ?
One subtlety for particles with spin: the beams are not polarized and the final state polarizations are not measured.
So one must average over initial polarizations of the
spins (notice the bar) and sum over polarization of final state spins (notice the summation).
In QM, if a particle has spin s there are (2 s + 1) spin states 

19. One subtle point for particles with spin: the beams are not polarized and the final state polarizations are not measured.
So one must average over initial polarizations of the
spins and sum over polarization of final state spins.
Remember In QM, if a particle has spin s there are (2 s + 1) spin states

20. Rutherford scattering
Bettini p.22
Rutherford scattering
Question: Who were the graduate students sitting in the dark and counting rare flashes on the screen through a microscope?
Ans: Hans Geiger
and Ernest Marsden
Apparatus
The beam consisted of alpha particles charge z scattering on gold (Z=79).
What is the z for alpha’s ?

21. The Rutherford scattering result was non-relativistic and neglected spin.
Sir Neville Mott gave the expression including spin and for the case of zero recoil of the nucleus.
The text (p.23) notes that the Mott cross-section goes to zero at 180 degrees ?
Why might this happen ?
Ans: Must flip the relativistic electron spin (or helicity) (more on this in Chapter 3).

22. Figure 1.6 (Subatomic Particles are waves)
And hence can interfere and diffract
Take the Fourier transform of the slit distribution for diffraction or the Fourier transform of the charge density for particle diffraction. (Please study p.21)

23. Ionization loss for “heavy” charged particles
Hans Bethe
Some features to note:
energy loss per unit length ~1/β2
energy loss grows logarithmically at large β (relativistic rise)
A minimum ionizing particle (“a mip” ~ MeV m2 kg-1 ρ)
Figure: PDG
Should be called the Bethe formula.
Felix Bloch was a great man but had nothing to do with it

24. Energy loss data from a TPC detector
Bettini, Fig 1.10
TPC stands for “Time Projection Chamber”, a type of detector that measures three-D track segments and energy loss information.
The Bethe formula gives the average energy loss; there are large fluctuations called “straggling”
Question: Why did I write “heavy charged particles” on the previous slide ?
Aihara, H. et al. (1988); Phys. Rev. Lett
Note that dE/dx can be used to identify particles (distinguish pions from kaons, for example).

25. Question: What is the d band ? Why is it so far to the right ?
Question: What do the colors mean ?
ALICE heavy ion/nuclear physics TPC at the LHC.