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276 Cards in this Set
- Front
- Back
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Which particles interact via the weak interaction?
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All particles |
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Which particles interact via the EM interaction |
All particles except neutrinos |
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Which particles interact via the strong interaction |
Quarks |
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How can antiparticles detected in a magnetic field |
They'll curve the opposite way to normal matter |
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What spin does the gluon, photon, W+, W-, Z and Higgs boson have? |
All have spin 1 except Higgs which has spin 0 |
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What is a fermi in SI
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10^-15 m |
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What are the SI units for hbar? |
Js |
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Give a value for hbarc |
0.197GeVfm
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Electron mass |
0.5 MeV/c^2 |
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Down quark mass |
3 MeV/c^2
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Up quark mass |
5 MeV/c^2 |
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Strange quark mass |
100 MeV/c^2 |
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Muon mass |
106 MeV/c^2 |
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Charm quark mass |
1300 MeV/c^2 |
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Tau mass |
1780 MeV/c^2 |
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Bottom quark mass |
4500 MeV/c^2
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Top quark mass |
173000 MeV/c^2 |
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W boson mass |
80 GeV/c^2 |
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Z boson mass |
91 GeV/c^2 |
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Higgs mass |
125000 MeV/c^2
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Why does particle physics require high energies? |
De Broglie wavelength: lamda=h/p If we want to resolve the smallest distances we need the largest possible momenta and hence energies |
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What does the rate of decay mode depend on? |
The strength of the interaction |
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Which type of decays are fastest and which are slowest?
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Strong decays are fastest and weak decays are slowest |
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Which particles are stable? |
Electron, positron, lightest neutrino, photon and proton |
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Why is the photon stable? |
It's massless so conservation of energy and momentum ensure its stable |
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Why is the electron stable |
To conserve charge, it's decay products would have to include a charged particle, but it is the lightest charged particle, hence it is stable |
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What is elastic scattering? |
The initial and final state particles are the same |
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What is inelastic scattering? |
The initial and final state particles are different |
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What is the coupling of a photon proportional to |
The charge and sqrt(alpha) |
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What is the probability of a process occuring, in terms of the number of vertices in its Feynman diagram? |
Probability is proportional to e^2n n=# of vertices |
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What is neutral current? |
No charge exchange |
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What is charged current? |
Charge exchanged between scattered particles |
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What is the centre of mass frame? |
The frame in which the total momentum is 0 |
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What is the probability for a particle to be scattered by potential V proportional to? |
The modulus of the scattering amplitude squared |
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What is the cross section and what are its units? |
Characterises the probability for a certain process. Independent of all beam parameters except energy [area] |
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What is instantaneous luminosity and what is its units? |
Number of particles per unit time per unit area [barns^-1 seconds^-1] |
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What does the instantaneous luminosity depend on in modern colliders which employ bunched beams? |
The number of colliding bunches, the number of particles in each beam, cross-sectional area of the beam, frequency with which the beams circulate the ring |
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Why do we often measure differential cross-sections? |
Our detectors don't provide full coverage so we can't access all angular directions |
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What are virtual particles? |
Exchanged particles, don't obey Einstein's energy-momentum relationship, off mass shell i.e. can be produced with different masses and only exist for a short period of time |
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Explain the divergence in the scattering amplitude |
Divergence when p^2=Mx^2c^4 because propagator (denominator) doesn't account for particles being unstable |
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What are the two types of fundamental matter particles? |
Leptons and quarks |
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What is the spin of fermions? |
Half integer |
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What is the spin of bosons? |
Integer |
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Why are neutrinos stable? |
They're the lightest leptons so they're decay would violate lepton number |
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What is lepton universality? |
The coupling of W boson to any lepton doublet is the same for all 3 generations (applies to all bosons?) |
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What kind of a decay does a long lifetime imply?
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Weak decay |
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What are the units of decay width Gamma? |
[mass] |
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How is energy conservation restored in nuclear beta decay? |
Through the emission of an additional particles, the neutrino |
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What are neutrino oscillations and under what condition are they possible? |
Neutrinos can oscillate between flavours Only possible if the neutrinos have mass |
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Under what condition does neutrinoless double beta decay become possible? |
If the neutrinos have mass |
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Why are very large detectors required to detect electron neutrinos? |
Because they have very long mean free lengths |
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Evidence for neutrino oscillations |
Solar neutrino deficit - nuclear reactions that power the sun produce electron neutrinos. Flux recorded on Earth showed a deficit compared to calculations - some of the electron neutrinos had oscillated to different flavours |
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Which angle do solar neutrino experiments, atmospheric neutrons and the Daya-Bay experiment measure? |
Solar: theta_12 Atmospheric: theta_23 Daya-Bay: theta_13 |
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Where do atmospheric neutrinos originate from? |
The decay of pions and muons produced by cosmic rays in the atmosphere |
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How are electron neutrinos detected in the Daya-bay experiment? |
Liquid scintillator |
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Describe the reactor set up for studying neutrino oscillations |
Several different detectors at different distances from the source - near and far detectors |
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How can the uncertainty of incoming neutrino flux be reduced? |
Using near and far detectors and measuring the nearly unmixed flux at the near detector end, close to the reactor |
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What is the advantage of using near and far detectors in neutrino oscillation experiments? |
Only meed to measure a ratio rather than an absolute neutrino rate |
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What information on mass do neutrino oscillation experiments provide? |
They only tell us the mass difference between neutrino species, they don't provide an absolute mass scale |
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List 3 ways of measuring an absolute neutrino mass scale |
End point of the beta decay spectrum Structure formation in the early universe Neutrinoless double decay |
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Explain how an absolute neutrino mass scale can be measured using the end point of the beta decay spectrum |
The end point of the beta decay spectrum shifts to lower energies with increasing mass of the electron neutrino. Can use the electron spectrum from tritium decay; the energy available to the electron from tritium is very small |
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Explain how an absolute neutrino mass scale can be measured using structure formation in the early universe |
Structure formation in the early universe depends on the gravitational pull of the mass density of relic neutrinos, so measurements of density fluctuations allow us to put limits on the sum of neutrino masses. |
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Explain how an absolute neutrino mass scale can be measured using neutrinoless double beta decay experiments |
If neutrinos are majorana particles, (they're their own antiparticles), they can annihilate with themselves and neutrinoless double beta decay can occur. Double beta decay is rare and neutrinoless double beta decay is even rarer. The decay rate for neutrinoless double beta decay is proportional to the mass of the neutrino squared |
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What are dirac particles? |
Particles with distinct anti particles |
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What are majorana particles? |
Particles which are their own antiparticle |
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Are double beta decay and neutrinoless double beta decay allowed in the standard model? |
Double decay is allowed Neutrinoless is forbidden due to lepton number violation |
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How do we know there's only 3 neutrinos with mass< half Z boson mass, and what effect would another neutrino species have? |
From measurements of the decay width. Another species would increase its decay width |
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Explain lepton number violation by neutrino oscillations |
Violated macroscopically, but conserved microscopically |
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Evidence for quarks |
Electron-nucleon scattering shows point like constituents in the nucleon Hadron production/spectroscopy consistent with quark content Jet formation |
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Where does the notion of different quark types come from? |
The increase in cross section at electron-positron colliders. When passing the threshold for a new quark-antiquark pair, R is increased by step of size N_colour * Q^2_quark |
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What is the value of N_colour? |
3 |
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What are the different colour charges? |
Red, blue, green |
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Why do gluons self interact? |
They carry colour charge so they can couple to themselves |
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What are hadrons? |
Strongly interacting particles made of quarks, colourless |
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What are the two ways of forming a colourless object? |
Combine colour and anti-colour Combine 3 colours (or 3 anticolours) |
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What are mesons? |
Hadrons made of a quark and an antiquark |
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What are baryons? |
Hadrons made of three quarks |
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What is the baryon number of baryons, antibaryons and mesons? |
Baryon: 1 Antibaryon: -1 Meson: 0 |
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What spin do baryons have? |
half integer |
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Which interactions conserve individual quark flavour? |
Strong and EM and Z boson interactions |
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What kind of a decay do we deal with if flavour changes? |
Weak |
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What is the quark content of the 3 pi mesons? |
Pi- : d anti-u Pi+ : u anti-d Pi0 : u anti-u OR d anti-d |
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What is the only stable hadron and why is it stable? |
Proton, stable because it's the lightest baryon so it's decay would violate baryon number |
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What kind of a decay does a short lifetime imply? |
Strong decay |
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What is the quark content of the 3 kaons? |
K+ : u anti-s K- : s anti-u K0 : d anti-s |
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How does a neutral pion decay? |
Electromagnetically to a pair of photons |
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How does a pi+ decay? |
To an anti-muon and anti-muon neutrino |
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List some sources of high energy particles |
Cosmic rays Natural radioactivity Nuclear reactors Particle accelerators |
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How do all particle accelerators increase particle energy?
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Use the Coulomb force |
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What are the two types of particle accelarator |
Linear and circular |
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Describe how a circular accelerator works and state the disadvantages and advantages |
Uses magnets to bend charged particles into an orbit. The magnetic field strength is increased synchronously with the energy, allowing for constant bending radius Adv. - energy can be increased in several revolutions, reducing the size of the accelerator Disadv. - Suffer from energy losses due to synchotron radiation which is proportional to 1/m^4 so it limits the acceleration of light particles such as electrons |
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Describe the interaction between hadrons and atoms |
Hadrons interact strongly with atomic nuclei |
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What is the most important mechanism for particle detection? |
ionisation |
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How can charged particles heavier than electrons lose energy? (in particle accelerators) |
lose energy through EM interactions with electrons in atoms |
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What does energy loss of a particle in a material depend on? |
speed and charge |
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At low energies, do slower of faster particles lose more energy? (inside a material?) |
Slower |
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What are minimum ionising particles? |
particles which lose the least energy around the minimum of beta*gamma~4 |
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Explain the Bragg peak |
A particle loses most energy when it is slowest. As a particle gets stopped in a medium, it will deposit most of its energy at the end of its path |
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Describe the photoelectric effect and its probability of occurence |
Photon hits electron in atom, photon is absorbed and electron is freed from its shell and emitted. Probability ~ Z^5/E^(3/2) |
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Describe Compton scattering and its probability of occurence |
Photon scatters off an electron, gets deflected and transfers some of its energy (inelastic scattering) Probability ~ (ZlnE)/E |
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Describe pair production and its probability of occurence |
Dominant method of energy loss at high energies, E>2m_e to produce and electron-positron pair Probability ~ Z^2 |
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What is Bremsstrahlung? Give an example |
EM radiation produced by deceleration of a charged particle when deflected by another charged particle Electrons being deflected by atomic nucleus |
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How does an electromagnetic shower develop? |
When high energy photon/electron enters a material, an EM shower develops through continuous repetition of bremsstrahlung and pair production |
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When does an electromagnetic shower stop? |
Shower process stops when bremsstrahlung is not the dominating process any more. For electrons this is at the critical energy Ec when energy losses from ionisation and bremsstrahlung are equal |
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How are hadron showers formed? Describe them |
When hadrons are stopped in a material they shower. In the shower, pi0 are produced which decay into 2 photons leading to an EM component of hadronic showers |
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Describe cosmic ray air showers |
Primary cosmic rays hitting atomic nuclei in the top of the atmosphere create hadronic showers - these are cosmic ray air showers. Due to their larger depth, more of the produced particles can decay. These decays produce electromagnetic showers and muons. Mainly muons survive to ground level. Fluorescence and Cherenkov light is emitted from showers. |
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What properties of interest do particle detectors measure |
Position Momentum Energy |
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Describe scintillators |
Indicate the passing of a charged particle by emitting light - passing particles excite atoms/molecules which decay from their excited states and emit light. Two types: organic and an-organic crystal Scintillators are coupled to light sensitive detectors to enable electronic readout - photomultiplier tubes. PMT - photocathode, light frees electrons via the photoelectric effect. These are accelerated by a high voltage towards a dynode, the impact frees more electrons, and a chain of dynodes leads to a cascade of free electrons which create an amplified electric pulse on an anode. More modern photodetectors use semiconductor detectors |
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What are gas detectors? Explain the three types |
Basic counters which record particle passing. Simplest form: wire inside a gas volume, high voltage applied to create a potential difference between wire and outer wall Ionisation counters: at lower voltage, only the charge carriers initially created in the ionisation process drift to the anode and cathode Proportional counters: At moderate voltages, the electrons created in the initial ionisation process are accelerated enough so they themselves can ionise the medium. The resulting avalanche leads to gas multiplication and the initial pulse is amplified. The resulting pulse height is proportional to the initial ionisation pulse Geiger-muller counters: at high voltage, gas multiplication saturates and the created pulse becomes independent of the initial ionisation These three differ in their gas multiplication created by the acceleration of the electrons in the applied electric field. |
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Describe semiconductors |
Semiconductors have energy gap between valence and conduction band of the electrons. They can be doped with other atoms, creating an excess of n or p carriers. Semiconductor acts as a reverse-biased diode, creating a depletion zone on the border between n- and p-doped material. Particles passing through depletion zone create charge carriers through ionisation. Very low energy is needed to create a pair of charge carriers. |
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How do tracking detectors work? |
They use several position measurements to reconstruct the trajectory of a particle. They operate inside a magnetic field; charged particles have a curved trajectory in a magnetic field. Can measure the radius, and the B field is known, so the momentum can be calculated
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Briefly explain the multiwire proportional chamber, and the advantage of drift chambers. |
MWPC are proportional counters (tracking detectors) which use an array of wires inside a gas volume. Drift chambers allow a more precise measurement of position by measuring the time between the passing of the particles and the arrival of the drifting ionisation electrons. If the drift velocity is known, the distance to the wire can be calculated. |
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List some tracking detectors |
Multiwire proportional chamber Drift chambers Semiconductor detectors Pixel detectors Scintillating fibre tracker |
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What makes semiconductors detectors good trackers? Describe this in a semiconductor microstrip detector |
They can be finely segmented so they make good trackers Semiconductor microstrip detectors are only segmented in 1D, consist of a strips separated by a few micrometres |
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Describe pixel detectors and how they can be used as trackers |
Similar to digital cameras, use tiny pixel dimensions. They're etched and doped. A tracker consists of several layers of these detectors, passing particle leaves a hit in each layer. Algorithms used to reconstruct particle trajectory from these hits |
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Describe scintillating fibre trackers |
Use thin fibres made of plastic scintillator grouped together in bundles |
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What are calorimeters? Describe the two main classes? |
Calorimeters stop particles and measure their energy. When particles enter material, they shower. 1) Sampling/sandwich calorimeter - actively sample only parts of the shower. A dense, passive absorber layer is interspersed with an active layer. Used to detect both EM and hadronic showers 2) Homogenous - absorber is the detector. Mainly used to detect EM showers |
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What is the main contribution to the resolution of calorimeters? |
Statistical fluctuations in the shower development. The measured energy is proportional to the number of final particles recorded |
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Describe an electromagnetic calorimeter (ECAL). What resolutions can they reach? |
Radiation length depends on Z, high X0 -> large Z ECAL stops photons and electrons. Other charged paticles deposit some energy and pass through the ECAL. |
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Describe hadronic calorimeters. What resolutions can they reach and why? |
Placed after the ECAL. Hadrons shower and get stopped in the HCAL. High nuclear interaction length lamda0 -> heavy absorber. The low resolutions is due to the complexity of hadron interactions and large fluctuations. |
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What kind of particles can normal detectors not distinguish between? |
Different types of semi-stable charged hadrons |
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What is the general principle behind particle identification (PID)? |
Find mass of the particle by measuring momentum and velocity simultaneously |
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Describe the time of flight method, its limitations and what its used for |
To measure velocity beta, measure time to cross a known distance L. Required time resolutions limit the separation capabilities of TOF. TOF effective for beta*gamma < 3 Used to separate pions, kaons and protons |
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Explain how dE/dX is used for particle identification (PID) |
Energy loss varies with beta*gamma and hence can be used for PID Used to separate kaons and pions in region beta*gamma > 3 Minimum and lower rise of Bethe-Bloch curve shifted with mass when plotted vs momentum. Relativistic rise also allows PID for 100 < beta*gamma < 1000 |
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Explain the use of Cherenkov radiation for PID and explain Threshold Cherenkov detectors an Ring Imaging Cherenkov detectors (RICH) and how RICH are used in neutrino detectors |
Cherenkov radiation emitted when speed of charged particle passing through a medium with refractive index n is > speed of light in that medium. Threshold - employed for PID for 3 < beta*gamma < 14. The Cherenkov light is emitted in a cone with certain opening angle around direction of particle. RICH - the light of the emitted Cherenkov cone is reflected and recorded as a projected ring. Diameter of ring is proportional to opening angle. RICH detectors operate for 14 < beta*gamma < 140. Large scale neutrino detectors can distinguish between electrons and muons because lighter electrons scatter more and create fuzzy edges on the Cherenkov rings. |
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Explain transition radiation detectors for PID |
Transition radiation emitted when particles above a certain velocity pass through the boundary of 2 materials with different dielectric constants. Transition radiation detectors can be used up to beta*gamma < 1000 Help identify electrons |
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Summarise in which ranges the different methods of PID can be used |
gamma*beta < 3 TOF, dE/dX 3 < gamma*beta < 14 Threshold Cherenkov 14 < gamma*beta < 140 RICH 100 < gamma*beta < 1000 dE/dX relativistic rise gamma*beta < 1000 Transition radiation |
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List the compononents of a multi purpose detector from closest to the collisions outwards |
Vertex and tracking detectors (inside magnetic field) ECAL HCAL Muon detector |
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Describe a photon's path through a multi purpose detector |
Deposit energy in ECAL, leaves no trace in tracker |
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Describe an electron's and positron's path through a multi purpose detector |
Electrons deposit energy in ECAL with associated track in tracker Positrons the same as electrons but track curved in opposite direction |
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Describe a neutral and charged hadron's path through a multi purpose detector |
Neutral: deposit energy in HCAL but leave no track in tracker Charged: deposit energy in HCAL and leave a track in tracker |
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Describe jets in a multi purpose detector |
quarks produce jets of particles that contain hadrons which are identified by their tracks and energy deposits in calorimeters |
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Describe b-jets in a multipurpose detector |
Jets originating from a bottom quark contain longer lived b-hadrons. B-jets identified by reconstructing the displaced secondary vertex. c*tau~450 micrometres so they decay a few mm away due to boost |
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Describe a muon's path through a multi purpose detector |
Muons can tranverse the whole detector and are measured in the outermost muon detector |
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Describe a neutrino's path through a multi purpose detector |
Neutrinos escape. The sum of all momenta in plane transverse to beam=0 so the missing momenta is attributed to neutrinos
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How can short lived particles be identified in a multi purpose detector? |
Identified by reconstructing the invariant mass of the decay products |
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What is a trigger? |
Signals an interesting event in a detector. In first trigger stage, fast electronic signals for example a muon candidate that passes through the muon chambers. Events with large deposits in the calorimeter or with large missing energy are selected. In later trigger stages, the information from all sub detectors is readout, passed to a computer and further reconstructed |
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What holds atomic nuclei together? |
The strong force |
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What does the strong force conserve? |
electric charge, baryon number, lepton number, quark flavour (c,s,t,b) parity, isospin, charge parity, colour charge |
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What is deep inelastic scattering? |
Scatter high-energy leptons off nucleons. Directions and energies of the scattered leptons depend on what they interact with within the nucleon. Deep because momentum transfer of scattering is high so distances much smaller than nucleon size are probed Inelastic because nucleon breaks up |
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State the process used to find evidence for quarks |
Deep inelastic scattering |
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What are partons? |
Quarks and gluons |
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Proton substructure evidence |
20GeV electron beam fired at stationary protons. Detectors measured differential cross-sections vs Q^2=-q^2 where q is the 4 momentum transfer. Experiments found more high Q^2 scattering than expected; high Q^2 -> large scattering angle -> expected for proton consisting of smaller constituents |
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What is a space-like interaction? |
The momentum/space part of 4 vector is larger than the energy/time part -> negative 4-momentum squared |
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What is a parton distribution function? |
number of partons of a certain type in the proton with momentum fraction between x and x+dx |
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For EM interaction between electron and quark, what is cross section for each quark flavour proportional to? |
(Quark charge)^2 |
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How are parton distribution functions (PDFs) obtained? |
measured experimentally |
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What are scaling violations? |
Structure functions should not be dependent on 4-momentum transfer. Plot structure function vs x^2 and Q^2. For x~0.1, there's litte dependence of structure function on Q^2 as expeced -> Bjorken structure For small values of x, there's an increase in structure function with Q^2 -> number of partons in proton depend on how energetically it's probed -> scaling violations |
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What are the causes of scaling violations? What are valence quarks? |
Simple of model of nucleon made of 3 quarks is incorrect. Nucleon is a sea of quarks. Quarks are continuously interacting via exchange of gluons which can split momentarily into a quark-antiquark pair then recombine to a gluon -> quantum fluctuations (allowed by uncertainty principle). Struck quark radiating numerous gluons as it collides with the lepton leads to a Q^2 dependence to the structure functions. Valence quarks are the 3 quarks that describe the contents of baryons, gives the baryon its quantum numbers. Emitted from these are gluons -> q(antiq) pair -> 'sea' quarks -> increases PDF at low x High Q^2-> structure of proton probed to higher resolution -> more sea quarks seen |
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Why was colour charge introduced? |
Quarks could be in the same spatial and spin state which appeared to violate Pauli's exclusion principle |
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How many colour states are there and what are they?
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3 Red, blue, green |
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What are the 2 conserved colour charges and what kind of quantum numbers are they? |
Colour isospin charge Colour hypercharge They are additive quantum numbers |
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What are the colour isospin and hypercharge values for the three colour states? |
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What is the colour isospin, colour hypercharge and total colour charge for a hadron? |
0 for all 3 |
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What are pentaquarks? |
qqqq(antiq) |
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What colour do gluons carry? |
Colour and an anti-colour |
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What is asymptotic freedom? |
The statement that the strong interaction gets weaker at high energies and short distances. |
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What is the strength of interaction given by? |
the coupling of the force carrying particle to the charge of the interaction |
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What is the strength of the EM interaction at each vertex given by? |
The EM coupling constant |
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Explain the 'running' of coupling constant in QED |
Coupling constant depends on 4-momentum transfer. Electrons continuously emit photons which fluctuate into electron-positron pairs. The positrons (electrons) are attracted to (repelled by) the original electron. The measured electric charge of electron is screened by the quantum fluctuations and reduces with distance -> vacuum polarisation effect |
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Explain the 'running' of coupling constant in QCD |
Quarks emit gluons which fluctuate into quark-antiquark pairs which have a screening effect on the colour charge of the original quark. Reduces the size of the coupling constant at lower momentum or larger distances. Gluons self interact so can form a gluon loop which has the opposite effect - antiscreening. Size of coupling constant increased at low momentum transfer or high distances |
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Explain colour confinement |
Strong interaction is confining, coloured quarks and gluons are confined to colourless hadrons. Potential energy between two coloured objects that increases with distance, so pulling two quarks apart eg would require an infinite amount of energy, hence we never see free quarks. |
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Explain quark jets |
Consider e+e- -> q(antiq) In CM frame, the quarks are produced back to back, they move apart at high velocity, force from the colour field between them is constant, energy in the colour field increases linearly with distance until it becomes energetically favourable for a q(antiq) pair to form in between, leading to the production of jets of hadrons |
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What was the first direct evidence for gluons? |
e+e- -> q(antiq) with 3 distinct jets Third jet is a high momentum, non-collinear gluon being emitted from one of the quarks |
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Explain what QCD is and isn't used for today |
Predicts rate of interactions at colliders Successful at predicting rates of jets at high momentum Cannot be used at low momentum |
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What symmetry does the conservation of momentum come from?
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Symmetry under a spatial translation |
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What symmetry does the conservation of angular momentum come from? |
Symmetry under a rotation |
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What symmetry does the conservation of energy come from? |
Symmetry under a time translation |
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What symmetry does parity come from? |
Symmetry under a space inversion |
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How does position (r), momentum (p) and angular momentum (L) change under a space inversion? |
r -> -r p -> -p L=r x p so is unchanged |
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What parity does a fermion and its antiparticle have? |
Opposite parity to eachother |
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What parity does a boson and its antiparticle have? |
They both have the same parity |
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How do the spherical polar coordinates change with a space inversion transformation? |
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What does conservation of parity imply? |
Interaction is invariant under a space-inversion transformation Total parity before interaction = total parity after |
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What is the tau-theta puzzle? |
theta+, tau+, two weakly decaying particles found in cosmic rays. Thought to be the same particle but their 2 decay modes had different parities. It was suggested that parity isn't conserved in weak interactions |
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Explain parity violation in weak decay using the beta decay of cobalt-60 and how it solves the tau-theta problem |
Consider beta decay of polarised cobalt 60 (all spins are aligned). Electron is one of the decay products. It was measured that electrons are more likely to be travelling in the direction opposite the nuclear spin. A space inversion would leave the nucleus spin unchanged, but the emitted electrons would be in the opposite direction - this is less likely meaning that parity isn't conserved in weak interactions This solves the theta-tau problem, they are both the same particle |
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Which interactions conserve parity? |
Strong and EM |
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What does the charge conjugation operator do? |
Switch particles with their antiparticles |
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When is psi_a an eigenstate of the charge conjugation operator? |
If particle a is its own antiparticles |
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When is total C-parity of an interaction conserved? |
If the interaction is symmetric under particle-antiparticle exchange. |
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Describe C, P and CP conservation/violation in muon decay |
Experiments measured angular distribution of electron (positrons) from (anti)muon decay. If C was conserved these would have the same form, i.e. the +/- wouldn't be there - C is violated Parity also violated as theta -> pi-theta so the sign in the bracket changes CP is conserved though |
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What is helicity? |
projection of a particle's spin on its direction of motion |
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Are neutrinos and antineutrinos left or right handed? |
Neutrinos are left handed Anti neutrinos are right handed |
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Describe what happens to a left handed neutrino when it undergoes a P, C and CP tranformation
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P: -> right handed neutrino, doesn't exist so parity violated C: -> left handed antineutrino, doesn't exist so charge conjugation violated CP: -> right handed antineutrino, allowed, CP conserved |
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Explain why, in the beta decay of Cobalt-60, electrons are preferentially emitted in the direction opposite to the nuclear spin |
Cobalt has spin 5, Ni (a decay product) has spin 4, so the electron and antineutrino, which both have spin 1/2, must have their spin aligned with the nuclear spin. To conserve momentum, the electron and antineutrino are travelling in opposite directions. If antineutrino is travelling in direction of nuclear spin, it will be right handed, electron will be left handed -> allowed If electron travelling in direction of nuclear spin, it will be right handed and antineutrino will be left handed -> forbidden |
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Explain why electrons from muon decay are emitted in the direction opposite the muon spin (and vice versa for positrons and antimuons) |
Consider decays with highest energy electrons, electron will travel in opposite direction to the neutrino and antineutrino. Neutrino must be left handed, antineutrino right handed In top pic, electron must have negative helicity to conserve ang mom - allowed In bottom pic, electron will have positive helicity - suppressed in the relativistic limit |
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Explain the different branching ratios in pion decay |
Can decay to muon or electron, muon far more likely. In pion rest frame, l and v produced back to back. Pion has spin 0 so l and v must have antialigned spins so they can either both be left handed, or both be right handed. Can't both be right handed because right handed neutrinos are forbidden. Both left handed, but left handed l+ is suppressed. Electron is lighter and therefore can use relativistic case, so decay to electron will be far more suppressed |
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Explain the GIM mechanism |
Certain kaon decays which proceeded through a us and sd transition were not observed. Suppression of these could be explained if a 4th quark was involved - destructive interference between the two diagrams |
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Why was electroweak theory introduced? |
Initial weak theory only had W bosons, resulted in infinites for cross sections of processes with more than 1 W boson. Electroweak and Z boson were introduced |
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If the EM and weak forces have the same intrinsic strengths, why do they have different interaction strengths? |
Bosons have different masses |
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How was the Z boson discovered? |
Neutral currents seen at CERN, required a massless boson but not photon because it couple to charge - > Z boson |
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Why was the SppS, used to produce W and Z, built with a CM energy much larger than the W and Z masses? |
Because the interaction quarks only carry a fraction of the protons mass |
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How can Z and W bosons be observed at the SppS? |
They decay almost instantly to a pair of fermions. Electrons and muons are easiest to observe. For Z: The invariant mass of the decay products would peak at the mass of the boson For W: decay involves weakly interaction neutrinos which can't be detected, their existence is inferred from an imbalance in momentum in the plane transverse to the colliding beams. |
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What is a gauge theory? |
The equations of the theory are invariant under local gauge transformations of the wavefunction |
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Explain the Higg's mechanism |
Idea: spontaneously break the symmetry to allow the gauge bosons to have mass without destroying the theory Expectation value of the Higgs field in vacuum is non-zero. Our universe takes a minimum value of the potential, this choice spontaneously breaks the symmetry. Masses arise from interactions of gauge bosons with the non-zero expectation value of the field. The value of the field is not gauge invariant but the interactions are. |
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What is the dominant production method of the Higgs? |
gluon-gluon fusion |
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What is the second most likely mechanism for Higgs production? |
Weak boson fusion V=W+/_ or Z |
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What is the third most likely mechanism for HIggs production? |
W/Z boson associated production Virtual V (W/Z) must be produced with invariant mass larger than W or Z so there's enough energy left over for the Higgs |
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What is the dominant decay of Higgs boson and why? |
Coupling depends on mass so likely to decay to the heaviest particle it can. Top quark is too heavy so dominant decay is b(antib) |
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How can a Higgs decay to a W+W- pair? |
One of the W bosons can be produced with mass less than Mw (allowed for virtual particles) |
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How does the decay of Higgs to two photons occur and why? |
Photon is massless so doesn't couple directly to Higgs. Decay occurs via a top quark loop |
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What does the branching fraction of Higgs decays depend on? |
The mass of the Higgs |
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What are background processes? |
Processes that have similar of the same final-state particles |
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Describe how the Higgs can be discovered and some of the challenges of the Higgs discovery? |
Higgs only produced once in every 10 billion pp interactions Need to look in Higg's decay channels that have low background Invariant mass of the Higgs decay products will peak at the mass of the Higgs. Need good resolution of energy and momentum so peak doesn't get smeared away |
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Describe the discovery of the Higgs in the H->ZZ channel
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ZZ decays almost instantaneously to a pair of fermions, easiest to detect e+e- or muon pairs. Plot invariant mass of the decay products - peak at Higgs mass |
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Describe the discovery of the Higgs in the H->2photons channel |
Photons from the decay identified in calorimeters Large background of diphoton production but resolution of photons is good so a little bump could be seen in the invariant mass |
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Describe the discovery of the Higgs in the H->W+W- channel |
Second largest decay channel but harder to detect. Leptonic decays of W involve neutrinos that can be detected at LHC so the invariant mass of the decay products can't be constructed Can plot a quantity similar to the invariant mass which doesn't have a peak as clear |
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Describe the discovery of the Higgs in the H->tau+tau- channel |
Tau decays to neutrinos so invariant mass can't be reconstructed. Variable close to invariant mass was plotted but it has worse resolution than in ZZ and photon channel.s To enhance the Higgs events over background processes, the weak boson fusion process is used as it leads to additional identifying features eg high energy jets from the final state quarks |
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Describe the discovery of the Higgs in the H->b(antib) channel |
Has not been discovered in this channel Most dominant decay but extremely large background due to QCD production of b(antib) Poor resolution of jets coming from the bottom quarks making a peak in the dijet invariant mass difficult to resolve Can be searched for via associated W+/_ or Z production mechanisms which have distinctive features from the leptonic decays which hugely reduce the background. |
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What are isotopes? |
Have same Z |
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What are isobars? |
Have same A |
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What are isotones? |
Have same N |
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What is the unified atomic mass? |
1/12 of the mass of carbon-12 |
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How is the form factor related to the charge distribution? |
It's the fourier transform of the charge distribution |
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What does the liquid drop model assume? |
Interior densities are constant |
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Explain the volume term in the SEMF |
Assumes that nucleons bind to their neighbours. Binding energy proportional to volume of nucleus. Increases the binding energy. |
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Explain the surface term in the SEMF |
Nucleons on the surface have fewer binding partners. Binding reduced by amount proportional to surface area. Decreases binding energy |
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Explain the Coulomb term in the SEMF |
Protons are positive and hence repel eachother. Reduces binding energy |
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Explain the asymmetry term in the SEMF |
For unequal numbers of protons or neutrons, need to fill higher energy levels. Energy penalty for excess protons and neutrons. Decreases the binding energy
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Explain the pairing term in the SEMF |
Nucleons are tighter bound if they can be paired, so even-even nuclei are most tightly bound and have increased binding energy. Odd-odd nuclei are less tightly bound, decrease the binding energy |
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Which observations are not explained by the SEMF? |
Shells, magic numbers |
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What is activity? |
Number of decays in a given time |
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What is the half life? |
THe time after which half the nuclei have decayed |
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What is a becquerel? |
1 decay/s |
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What is exposure measured in? |
Roentgen |
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What is absorbed dose measured in? |
Rad or Gy |
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When is beta- decay allowed? |
M(Z,A)>M(Z+1, A) |
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When is beta+ decay allowed? |
M(Z,A)>M(Z-1, A) + 2m_e |
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When is electron capture allowed? |
M(Z,A) > M(Z-1, A) +excitation energy of atomic shell of captured nucleus |
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When is emitting an alpha particle energetically favourable? |
B(2, 4) > B(Z,A) - B(Z-2, A-4) |
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Describe gamma decay |
Following a decay, nuclei are often left in an excited state. They deexcite emitting a photon in the process |
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What are some assumptions of the Fermi gas model? |
Assume a 3D potential well in which the nucleons can move freely like a gas The potential that each nucleon experiences is the superposition of the potentials of other nuclei |
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In the Fermi gas model, why do heavy nuclei have a surplus of neutrons and what effect does this have on their potential well?
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Coulomb repulsion between protons decreases the binding energy leading to a surplus of neutrons. Potential well for neutrons is deeper than for protons because protons are less tightly bound due to the Coulomb repulsion |
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What states are occupied in the nuclear ground state? |
All states up to a maximum momentum, the Fermi momentum |
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Why does the Fermi momentum of protons and neutrons differ? |
Due to differences in their potentials cause by Coulomb repulsion felt my protons |
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What is the Fermi energy? |
The energy of the highest occupied state |
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Why do heavy nuclei have an excess of neutrons even though the asymmetry term prefers Z=N? |
Coloumb repulsion reduces binding energy for protons and dominates for heavier nuclei |
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What are magic numbers? List them |
Nuclides with a certain number of protons or neutrons are particularly tightly bound 2, 8, 20, 28, 50, 82, 126, 184 |
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What does the existence of magic nuclei suggest? |
The existance of shells, magic numbers indicate closed shells |
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What is the degeneracy of a state with J? |
2J+1 |
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What is the pairing hypothesis? |
In a filled shell, for every nucleon with J, there is +mj and -mj, so the total angular momentum is 0 when these nucleons pair up
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What is the spin of a nucleus with fully filled shells? |
0 |
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What is the spin of an even-even nucleus? |
0 |
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What is the intrinsic parity of protons and neutrons |
+1 |
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What is the parity of even-even nuclei? |
+1 |
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What is the collective model? |
Combines the shell and liquid drop model |
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How to permanent deformations of potential occur? |
Interactions between nucleons |
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What do deformations represent? |
Collective motion of nucleons |
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What are the two major types of deformation? |
Vibration: surface oscillations Rotation: rotation of a deformed shape |
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What is the screening factor used for? |
Account for the fact that electrons and positrons are deflected differently in the Coulomb potential of the nucleus |
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Explain these two graphs |
positrons repelled by protons electrons attracted beta- shifted towards lower momentum and beta+ shifted to higher momemtum The effect increases with charge and hence Z |
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At which nucleus does the binding energy reach a maximum |
56-Fe |
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What is nuclear fission? |
splitting of heavy nuclei into two lighter nuclei -> larger total binding energy -> negative so results in a smaller total energy -> leftover energy released as kinetic energy |
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What is nuclear fusion? |
Two light nuclei fuse together to form a heavier nucleus -> total binding energy is larger (negative) -> total energy is smaller -> release KE |
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At what mass number does it become energetically favourable for nuclei to undergo fission? |
Mass number > 100
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What are delayed neutrons? |
The decay products of fission will themselves decay and emit neutrons, these are released much later to the neutrons emitted from the initial decay |
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What is spontaneous fission? |
fission process occurs without external action |
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Explain how spontaneous fission can occur, and for what values of Z and A |
Imagine nucleus deforms before it splits. As nucleus elongates, surface term increase -> Coulomb term decreases If change in Coulomb term > change in surface term, the deformed shape is energetically favourable so the nucleus is unstable and undergoes spontaneous fission For Z>116, A>=270 |
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How can fission occur for lighter nuclei? |
Quantum tunnelling |
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What is induced fission? |
Supply energy in the form of neutrons to overcome barrier. Neutrons are neutral, so they approach nuclei are attracted by the strong force. When a nucleus absorbs a neutron, some energy is released due to binding energy of that neutron. If this energy is as large as the activation energy, fission is induced |
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Why can fission be induced in U-235 by neutrons with zero kinetic energy, but not in U-238? |
U235 is even-odd - looser bound. By supplying a neutron it becomes U236 which is even-even, tigher bound, so the energy released is greater than the activation energy U238 is even-even - tightly bound. Neutron turns it into U239 which is even-odd and more loosely bound so the energy released is less than the activation energy |
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What is the most common element used in fission reactors? |
Uranium |
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What is the U235 cross section dominated by at low energies and high energies? |
fission at low energies elastic scattering and excitation of the nucleus at higher energies |
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What is the cross section of U238 dominated by? |
Scattering, fission only becomes relevant above the activation energy |
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How does a fission chain reaction occur? |
Neutrons induce fission and fission produces neutrons |
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What are the 3 possible scenarios in a fission chain reactor? |
subcritical: nq<1, N(t) decreases exponentially and reaction will soon die out critical: nq=1, N(t)=constant, conditions right for sustained, controlled reaction supercritical: nq>1, N(t) increase exponentially, energy grows rapidly -> explosion |
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What is the key determining factor in a fission bomb? |
Size of metal - if small enough that neutrons are likely to reach the edge before t_p, the reaction will die out |
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Why does a fission bomb need a slightly larger radius than the distance a neutron can travel in time t_p? |
Neutron doesn't travel in straight line due to collisions, not all neutrons induce fission, some escape or are captured by nuclei without inducing fission, radius of bomb needs to be slightly larger to ensure a supercritical reaction |
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Explain the two ways of ensuring a critical reaction in a nuclear fission reactor |
Enrich uranium so it contains more U-235, more likely that neutrons will induce fission in U-235 Surround natural uranium fuel in a large volume of moderator material, which slows down the fast moving neutrons produced in fission, making them more likely to induce fusion in U-235 |
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Why are slower neutrons more likely to induce fission in U-235? |
Cross section is higher for fission at low energies in U-235 |
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What are control rods? |
Rods that are mechanically inserted in fission reactor when reaction needs to be reduced |
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Why are delayed neutrons important in fission reactors? |
Need to keep nq=1 for critical reaction, however tiny increases to nq leads to explosive reactions far quicker than control rods can be inserted. Idea is to have (n_prompt + n_delayed)q=1 for critical reaction, but keep n_promptq << 1 so tiny variations don't cause explosions. Timescale of delayed neutrons is ~13s which is manageable for insertion of control rods |
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What is the difficulty with nuclear fusion? |
Two positively charged nuclei will repel, stopping them getting close enough for strong force to take over and allow them to fuse - Coulomb barrier High temperatures are required |
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Why can fusion happen at a slightly lower temperature than calculated? |
Quantum tunnelling - effect increases with energy Nuclei have maxwell distribution of energies - effect decreases with energy |
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What is the difficulty with fusion reactors, and what are suggested solutions? |
How to contain plasma at such high temperature, container would vaporise. Contain using: 1) magnetic confinement - charged particles in plasma follow a helix path as they curve around in a magnetic field 2) inertial confinement - pulsed lasers bombard pellets of tritium-deuterium mixture in many directions at the same time at very high energies |
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What is Lawson criteria for nuclear fusion reactors? |
Energy ouptut/energy input > 1This ratio is larger for high particle density/long confinement time
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