1. Methods of Experimental Particle Physics
Alexei Safonov
Lecture #10

2. PDG: Passage of Particles Through Matter
Section 30 of the “PDG Book” (using 2012 edition) provides a very detailed review
We will only walk over some of it, please see PDG and references therein for further details

3. Ionization: “Heavy” Charged Particles
Heavy (much heavier than electron) charged particles
Scattering on free electrons: Rutherford scattering
Account that electrons are not free (Bethe’s formula):
Energy losses: from moments of
Ne is in “electrons per gram”
J=0: mean number of collisions
J=1: average energy loss – interesting one

4. Energy Losses
Energy loss (MeV per cm of path length) depends both on the material and density (and of course on momentum)
Convenient to divide by density [g/cm3] for “standard plots”
If you need to know actual energy loss, you should multiply what you see in the plot by density (rho)

5. Different Materials and Particles
Energy loss (Bethe’s equation:
Note that dE/dx depends on bg
The same energy loss in gas (or liquid gas, e.g. in a bubble chamber) for 10 GeV muon and 100 GeV proton
Can possibly use to distinguish particle types if you can measure these losses as the particle goes through gas and know their momentum
E.g. CDF tracker, a drift chamber, could do that

6. Multiple Scattering
In more dense media (or thick layers of material), charged particles can encounter many single scatters
Multiple scattering
The distribution of the q scatter is ~gaussain with width
In applications, mostly important for muons, we will talk about this in more detail when discussing muon detectors

7. Higher Momentum: Energy Losses
At a few hundred GeV, a new contribution for muons and pions: radiative losses
Radiating muons is something one has to remember at LHC
100 GeV is not all that much at LHC

8. More Material
What we talked about until now is relevant for small amounts of material (like gases)
Most interactions are radiative in nature
If there is a lot of material, pions and muons will interact differently with it:
Pions and protons can undergo nuclear interactions
This is because they have quarks inside, which can interact with quarks and gluons in the atoms of the media
Muons can’t
They interact weakly or electromagentically only
We will talk about nuclear interactions closer to the end of today lecture

9. Energy Losses by Electron
What we discussed before works for “heavy” charged particles, but what about electrons?
Ionization at very low energy, but then Bremsstrahlung (electrons are light, easy to emit a photon)

10. Electrons: Low Energy Electron losses as a function of Energy
Note the new variable in the Y-axis label: X0

11. Radiation Length
Length over which an electron loses all but 1/e of it’s energy due to Bremsstrahlung
a=aZ

12. Electrons: Higher Energy
At high energy: Bremsstrahlung
k – energy of the photon produced by “Bremming” electron
Y-axis: photons per radiation length

13. Radiation Length Take steel:
r=8g/cm3
X0=14/8=2 cm
A 100 GeV electron will loose 63 GeV of energy over just 2 cm
It’s easy to stop an electron

14. Passage of Photons Through Matter
It’s easy to stop a photon
A little harder at high energies
On the left: cross-sections for photon interactions in carbon and lead
Great, but how do you read it – is it big or small?

15. Photons: Attenuation Length
A.L. is basically the average distance traveled by a photon before it interacts
Above 1 GeV ~100% of the time it’s convertion into an electron pair)
Divide by density of the material to get it in cm
Steel:
r=8g/cm3
A 100 GeV photon on average travels mere 10/8~1cm
Then you get a pair of electrons
Go back a couple of slides to see how much those will travel

16. Electromagnetic Showers
Because both electrons and photons interact almost immediately producing photons or electron pairs, our calculations are a little silly
You always have a cascade of these electrons and photons, so these probabilities somehow interplay
Simulation of a cascade produced by a 30 GeV electron:
Shower maximum somewhere near 6X0
A useful number to remember

17. Lateral Profile
We discussed the longitudinal profile of an “EM shower”, but what about lateral?
90% of the shower energy is within a cylinder of radius
Called Moliere radius
ES=21 MeV
EC is critical energy (plot on the right)

18. Nuclear Interactions
Nuclear Interaction length is defined very similar to radiation length
But refers to the probability for a hadron to interact with a nuclei in the material
In this case it is also makes more sense to talk about showers than just single particles
More when we talk about calorimeters

19. Next Time We mostly covered the basics of particle interactions
But so far we cared about what happens with the particle (energy losses, stopping power etc.)
Next time we will talk about effects on the media from passing particle
Cherenkov radiation
Scintillation
Transitional radiation
And some reminders of basics:
Measurement of the momentum for a particle in magnetic field
Then we will talk about actual detectors
Types, characteristics