Methods of Experimental Particle Physics Alexei Safonov Lecture #10

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

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

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)

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

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

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

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

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)

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

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

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

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

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?

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

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

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)

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

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