Methods of Experimental Particle Physics

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

Methods of Experimental Particle Physics