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Methods of Experimental Particle Physics

Alexei Safonov

Lecture #10

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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

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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

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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)

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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

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• 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

Multiple Scattering

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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

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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

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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)

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Electrons: Low Energy• Electron losses as a function of Energy

• Note the new variable in the Y-axis label: X0

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Radiation Length• Length over which an electron loses all

but 1/e of it’s energy due to Bremsstrahlung

• a=aZ

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Electrons: Higher Energy• At high energy: Bremsstrahlung

• k – energy of the photon produced by “Bremming” electron

• Y-axis: photons per radiation length

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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

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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?

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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

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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

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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)

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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

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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