Frontiers of Particle Physics 1 Flashcards
What is the EM photon-fermion-antifermion coupling?
sqrt(alpha)
*i.e: for an extra loop: extra factor of alpha (1/137)
In what case can we make perturbative calculations for QCD processes?
Because gluons carry colour charge there is a self-interaction: this leads to running of the coupling (decreases at higher energy due to gluon anti-shielding).
This is called asymptotic freedom and allows us to make perturbative calculations a high energy.
What kind of colliders were LEP and Fermilab?
LEP was an e+e- collider
Fermilab was a proton-antiproton collider
What are the dominant and subdominant production methods for the Higgs boson at the LHC?
What was the discovery decay mode for the Higgs?
Gluon-gluon fusion via a top quark.
subdominant: vector boson fusion
Higgs -> gamma gamma was the discovery channel, despite having an extremely low cross-section compared to other decay modes.
How many free parameters does the standard model have?
How can we constrain these and test the standard model?
18 (couplings, masses, CKM mixing angles)
+7 in the neutrino sector
=25
Loop corrections result in predictions for the relationships between these parameters.
What are some limitations of the Standard Model?
Dark Matter
Dark Energy
CP asymmetry problem
Fine-tuning
Why 3 generations?
Higgs mechanism for neutrinos (no RH neutrinos)
Gravity
Grand Unification
What are the “Three Frontiers” of particle physics?
Energy frontier
-new heavy particles
Intensity frontier
-precision measurement / BSM behaviour
-neutrino interactions/proton decay
Cosmic Frontier (non-accelerator)
-neutrino/dark matter detectors
-dark energy
What are some examples of different experiments working on the three frontiers of particle physics?
Energy: LHC (ILC,FCC in future)
Intensity: LHCb, DUNE
Cosmic: IceCube, DUNE
What are the natural units of cross-section?
E^-2
How are bubble chamber images created?
Charged particles pass through a medium, ionising atoms.
Vapour condenses onto these ions, creating a path of tiny liquid drops.
What describes energy loss via ionization?
The Bethe Bloch formula gives an equation for energy loss per unit path length.
What extra terms does the QM form of the Bethe-Bloch formula contain?
The ionization energy of the atoms in the medium.
A dielectric screening term (only important at high energy)
QM shell corrections related to the frequency of electron atomic orbitals (only relevant at low energy)
What is “specific energy loss”?
What about “mass stopping power”?
For energy loss via ionization:
1: Energy loss per unit path length
2: specific energy loss / mass density of medium
What dependence does the Bethe-Bloch formula have on the medium?
Linearly dependent on mass density.
Linearly dependent on Z/A
Also dependent on ionization energy
What is the main dependence of the Bethe-Bloch formula on the incident particle?
Strong dependence on velocity
proportional to 1/ beta^2
proportional to ln(gamma^2)
Proportional to charge squared
What does “minimum ionization” refer to?
What is the rate of energy loss for a minimim ionizing particle?
The momentum of an incident particle such that the rate of energy loss in a medium is minimized.
This is at around beta*gamma = 3-4 for all particles.
MIP’s lose energy with stopping power 2 MeV / g cm^-2
Describe the full stopping power regime.
What does “critical energy” refer to in this context?
Check notes!!!!!
Critical energy refers to the momentum scale where energy loss to ionization is equal to energy loss to bremsstrahlung.
How is the energy loss of a particle in a medium distributed?
*as well as distribution based on incident particle and medium parameters, ionisation is a stochastic process, so is described by some p.d.f.
*energy straggling and range straggling
Landau distribution for charged particles that easily escape the medium.
Bragg curve for particles that do not easily traverse the medium (speed is significantly reduced) –> bragg peak
What is specific ionization?
The average number of electron-ion pairs created per unit path length.
What would be the ideal range - energy loss distribution for radiation used for tumor therapy?
Very sharp bragg peak –> majority of dose deposited at a precise depth.
How does a scintillation detector work?
What are their benefits?
Lost energy is converted to light (usually visible - good for photomultipliers) in the scintillating medium via excitation/de-excitation.
Cheap, efficient, good time resolution
What is the difference between organic and inorganic scintillators?
Organic scintillators work via the excitation of electron states in atoms.
-better time resolution (~1ns)
Inorganic scintillators work via excitation of “excitons” from a valence band to a conduction band.
-worse time resolution (~500ns)
-higher stopping power
–>more compact
–>better energy resolution (more light yield)
What is Cherenkov radiation and when does it happen?
Occurs when a charged particle moves faster than light through a medium. v > c/n
-particles in the medium polarize creating EM pulses that spread out uniformly from the position of the particle.
-once the particle speed is faster than the EM pulse propagation, there is constructive interference between the wavefronts.
- this light is usually in the blue / UV range: good for photomultipliers
How can Cherenkov radiation be used to calculate particle velocity?
What is the relevant formula?
The angle of cherenkov emission is dependent on the velocity of the particle.
theta = arccos(1/ beta * n)
How can Cherenkov radiation be used for particle ID?
e.g: electrons will result in a shower so there will be multiple cherenkov emission cones –> diffuse ring
muons will produce a well defined ring as they do not easily interact
How does a photomultiplier tube work?
Detects photons in the near infrared - UV range
-Scintillator photocathode produces photoelectrons.
-Photoelectron is amplified via multiplication - passes between multiple dynodes with increasing voltage.
What is transition radiation?
Radiation emitted when a relativistic charged particle passes between two homogenous materials with different dielectric constants.
-intensity (E) proportional to gamma*m
-emission at small angle proportional to 1/gamma
-photons emitted in the X-ray range
What does a transition radiation tracker look like?
Layers of foam and straws.
-foam allows for lots of transitions - lots of transition radition
-straws detect the transition radiation.
Describe the distribution of photon attenutation at different energy scales.
Check notes
-photoelectric effect (+rayleigh scattering)
-compton scattering
-pair production
Describe an EM shower
Shower develops via bremsstrahlung and pair production.
Until at an energy where compton/photoelectric effects dominate (<10MeV) and the shower stops branching.
Energy described by E_0 * [e ^ (-x / L_R)]
-for high initial energy only
-L_R is radiation length
How is the attenuation of photon intensity via pair production described?
exponential distribution:
I_0 * e^(- 7x / 9L_R)
L_R is the radiation length describing electron energy attenuation
How can we judge the energy of the initial particle from a shower process?
The shower multiplicity is directly proportional to the incident energy.
What is the moliere radius?
The radius of a cylinder that contains 90% of the shower energy.
R ~ 0.0265 * L_R * (Z + 1.2)
What are some differences between hadronic and EM showers?
Length scales generally larger for hadronic
Broader transverse profiles for hadronic
Larger variability (more complex) for hadronic due to more allowed interactions.
–>more missing energy
–>worse resolution than EM calorimeters
How do we define nuclear interaction length?
The mean distance a single hadron travels before initiating an INELASTIC interaction.
How does a silicon tracking detector work?
What is the main benefit?
Incident charged particle deposits electrons/holes in the detector medium along the track.
These charges drift (separate) due to EM field.
This drift induces a current which is detected.
Gives very good position resolution.
What are some challenges and solutions faced by silicon tracking detectors?
Cooling
Radiation hardness
-use radiation hard materials (e.g: diamond)
-use 3D electrode arrangement
–>decreases drift path limiting the negative effect of radiation damage
What is primary vertex resolution?
The resolution in the position of the primary vertices for each bunch crossing.
What are some common trigger requirements?
Isolated leptons
Central and forward jets
Higher transverse energy
Large missing energy
What is the difference between the (approximate) way in which statistical and systematic uncertainties scale?
stat ~ 1/ sqrt(N)
sys ~ C + 1/sqrt(N)
*there will be a point at which sys uncertainties become dominant: no longer advantageous to take more data
What is a nuisance parameter?
An additional confounding parameter that is added to account for imperfect accounting for systematic uncertainties.
These are usually gaussian or log-normal distributed.
O(100) nuisance parameters will be used for a single analysis.
What is a p-value?
The probability we will measure a value within some RANGE given the null hypothesis.
What is significance level is deemed “evidence” and “discovery”?
3sig: evidence
5sig: discovery
What is the “Look-Elsewhere” effect?
The probability of finding some fluctuation within your dataset scales with the size of the phase space.
i.e: the p-value must be renormalised (using the size of the phase space) to a local p-value
What is the use of MC methods in particle physics?
calculating phase space factors
simulating processes for specific matrix elements
simulating trigger/detector response and efficiencies
simulating experimental outcomes - limit setting
What are the processes involved in an MC simulation of a particle physics experiment?
Physics process (prompt process + decay)
Detector medium
Interactions with detector
Signal output from detector
Trigger function
What are some of the positives and negatives of lepton/hadron colliders?
Lepton
+high precision (initial state known precisely)
+allows full reconstruction (not just transverse plane)
+beams can be polarised
-large energy loss to synchrotron radiation
-fixed COM energy so not ideal for searching for unknown particles
Hadron
+wide COM range due to PDF’s -> good for searching
-less energy loss to synchrotron (due to higher mass)
-messy environment -> hard to do precision measurements
What are pdf’s?
How are they determined?
Parton distribution functions
-Partons (constituents of hadrons) have a range of momenta due to gluon self-interaction and virtual particles.
-Determined using deep inelastic electron-proton scattering
*cannot be derived from QCD as we cannot make perturbative calculations
How do PDF’s scale with Q^2 (momentum transfer)?
PDF’s at large x (large momentum fraction) decrease as Q^2 increases. This is because at higher Q^2 re resolve more detail - gluon emission has removed some quark momentum.
PDF’s at low x (small momentum fraction) increase as Q^2 increases, as more low-x partons can now be resolved.
What do the DGLAP equations describe?
Describe the evolution of parton distribution functions with ln(Q^2) from first principles of QCD.
Terms include probabilities of quarks (or gluons) emitting a gluon/quark, reducing it’s momentum.
What can we determine about PDF’s from ep colliders?
Find PDF’s for up/down quarks. (quarks and antiquarks combined)
Can therefore determine approximate gluon PDF as missing.
How can we determine PDF’s for quarks/antiquarks?
What about for gluons?
Use neutrino-nucleon scattering (fixed target)
Use hadron-hadron collisions for gluons.
What are the Lorentz transformations for energy and momentum?
E’/c = gamma(E/c - beta * p_x)
p_x’ = gamma(p_x - beta * E/c)
What is the difference between flux and luminosity?
What about rate?
Flux is the rate of particle incidence per unit area.
Luminosity is flux * target particles.
Rate is luminosity * cross-section.
By how many radiation lengths are EM showers usually extended?
~10
What equation can we use to find momentum given the radius of a particle helix in a magnetic field?
p_T = 0.3 z B R
p_T is momentum transverse to magnetic field
z is particle charge (units e)
B is magnetic field strength
R is helix radius
What are the rough scalings and values for calorimeters and trackers at ATLAS?
Calorimeter:
sigma_E / E ~ 1 / sqrt(E) ~1%
(much worse for hadronic calorimeters ~ 50%)
*scaling as is a counting measurement
Tracker
sigma_p / p ~ p ~5%
*scaling as is measurement of curvature
What is the final event rate at ATLAS required to be after (hardware+software) triggers?
~ 1kHz
x10 more is allowed at LHCb
How is pile-up distributed?
The number of interaction vertices in one bunch crossing is poisson distributed.
Currently with expectation value of ~50 at ATLAS/CMS, this will increase for highlumi LHC.
What is the gamma factor?
1/sqrt[ 1 - beta^2 ]
How can we work out the energy threshold for a cherenkov detector?
Work out the threshold gamma value by setting v=c/n.
From this we can work out the threshold energy gamma * m * c^2
What is hbar c equal to?
197 MeV fm
Describe a cross-section of the ATLAS detector.
Pixel detector
SCT (SemiConductor Tracker)
TRT (Transition Radiation Tracker)
Solenoid magnet
EM Calorimeter
Hadronic Calorimeter
Toroid magnet
Muon Systems
Considering a MIP losing energy to ionisation, how will the rate of energy loss change?
Rate of energy loss will go as:
( 1/ beta^2 ) * MIP rate
Why might there be a discrepancy between the peak of a inv mass distribution expected and observed?
Initial state radiation can shift the peak up.
Final state radiation / missing energy can shift the peak down.
Why is it more difficult to measure W boson mass than Z boson mass?
Z mass can be found using e+e- collider scan (LEP1), as we have e+e- -> Z -> ff’
W bosons do not have the same interaction, instead:
e+e- -> W+W- -> quarks/leptons+neutrinos
We must therefore reconstruct masses from decay products.
Why does the value of W mass obtained experimentally not agree with that obtained from Z mass and weinberg angle?
This value of mass includes contributions from virtual loops.
We can therefore use the discrepancy to learn about the properties of particles involved in virtual loops.
What are 4 leading-order diagrams for ttbar production at the LHC?
Which is dominant at the LHC?
Check notes
(gluon fusion dominant at LHC)
Why can we not search for top decays the same way as we do for charm and bottom?
Charm and bottom hadronise forming resonances, which can be identified.
Top quarks decay before they hadronise.
What are the main decay channels for ttbar events?
What are some pros and cons?
**in addition to these, there will be 2 b-tagged jets and secondary vertices
Dilepton
+pure: easy to tag two leptons
-low BR
-2 neutrinos: poor reconstruction
All hadronic
+large BR
+no missing energy
-large background (MJBG)
l+jets
+easy to tag lepton and MET
+good BR
What are singletop events used to study?
What is the issue with studying these events?
To measure the top-bottom element of the CKM matrix
They have a large background from W+jets events.
How do top quark events allow us to study quark spin structure?
As they decay before hadronisation, we can directly study spin structure.
Unfortunately, at hadron colliders the resultant ttbar are unpolarised. However, they have correlated spin!
What role does the Higgs field play?
Gives mass to W, Z, fermions.
(Gauge fields are massless in the SM)
W+W- –> W+W-
has a unitarity violation without higgs diagrams
How does the Higgs boson couple to other particles?
Couples to fermions proportional to their mass.
Couples to W and Z proportional to mass^2.
Only couples to left-handed fermions.
What is the dominant Higgs production channel at the LHC?
What about for an e+e- collider?
Production via a top loop.
For an e+e- collider: production of virtual Z boson which decays to Z and H
What spin states of the Higgs can we rule out?
Higgs to gamma gamma rules out Higgs spin = 1
(Higgs spin = 0 in the SM)
What does a metastable universe refer to?
The vacuum state is not a global minimum: any switch to true minimum will start a chain reaction
The SM currently predicts a metastable universe. (3sigma)
What are some failures of the SM?
Matter-antimatter asymmetry
Dark matter
Dark energy
Gravity
Unification of forces?
Hierarchy problem (fine-tuning)
What are the benefits / issues with SuSy?
+Can solve hierarchy problem by introducing new cancellations.
+Neutralinos can be candidates for dark matter.
+Introduces many new CP-violating effects.
+Can lead to unification at high energy.
No SuSy particles found so far.
–> The ideal masses have now been ruled out
MANY new free parameters introduced.
What is MSSM?
Minimal Supersymmetric Model
-minimises the number of extra particles
What is R-Parity?
An additional discrete symmetry introduced by some SuSy theories.
+1 for SM particles
-1 for SuSy particles
Supresses interaction between SM and SuSy
Lightest SuSy particle is then stable: DM candidate
What is the benefit of searching for BSM behaviour using loop contributions?
Allows sensitivity to contributions from particles heavier than our mass scale.
What is the WIMP miracle?
Under the assumption of thermal equilibrium between matter and DM in the early universe, simulation with DM as WIMPs gives correct prediction for the current amount of DM in the universe.
What is the ADD model?
How could we test it?
Extra dimensions in which gravity can propagate but not other particles, explains weakness of gravity compared to other forces.
Leads to an extra 1/r term in gravitational force for each additional dimension.
Need to measure gravitational force on very short scales, n=1,2 are already ruled out.
What is s (COM energy squared) equal to for fixed target and collider experiments?
2 E_b m_t for fixed target
(2 E_b)^2 for collider
How does a linear accelerator work?
Drift tubes of increasing length arranged in a line.
RF generator oscillates electric field.
This causes particle to be attracted/repelled: acceleration.
*Particles only pass through once so energy is limited by length of the accelerator.
How does a cyclotron accelerator work?
Charged particle trapped in circular motion by a perpendicular magnetic field.
A region of electric field (oscillating) drives the motion.
->the circle get larger as energy increases
*limited by the size of the device
What is an equation for cyclotron frequency?
gamma m omega^2 r = q v B = q omega r B
=> omega = q B / gamma m
How does a synchrotron accelerator work?
A variable magnetic field allows particles to be contained in a ring of fixed radius, at different speeds.
Particles can be accelerated using RF cavities (basically embedded linacc’s) [perfectly timed]
What does betatron oscillation refer to?
Oscillation in synchrotron orbits around the central orbit.
This must be minimised in order to avoid orbits becoming unstable.
How will High-Lumi LHC improve on the current LHC?
Luminosity increase of 5-7x
-larger pileup
-crab cavities increase effective bunch crossing region
What is limiting the COM energy of the LHC?
We need either stronger magnetic fields to contain higher velocity particles, or a larger tunnel (wider radius).
What are the double angle identities?
Check wall note
What is the relationship between width and lifetime?
Width = hbar / lifetime
What is the higgs mass?
What about W?
Z?
Pions?
Higgs: 125GeV
W: 80GeV
Z: 91GeV
Pion: ~ 140MeV
(muon and tau stored in calculator in grams)
What are four dominant diagrams for higgs production? (hadron collider)
Check notes
How can we find the max # particles created in an EM shower?
What about shower depth?
We can calculate the approx critical energy as 600MeV / Z
The max # particles is then E_incident / E_critical
The number of particles created ~ 2^t where t is the number of radiation lengths. We can use this to estimate the shower depth.
What is the master formula to calculate a differential cross-section w.r.t. variable X for a hadronic process?
Check notes / Past Paper
Sum over partons (two summations)
Integral over X
PDF’s x2 (dependent on Qi^2 and respective x)
Differential partonic cross-section (Qi^2, Qf^2)
Transition to observables function (Qi^2, Qf^2)
Why is sign mis-identification a significant problem for electrons but not muons?
Electrons undergo far greater bremsstrahlung.
this leads to situations in which a high energy photon is emitted which decays into e+e- collinear, so the wrong charge may be reconstructed if most of the energy is taken by the positron.
What are three light-emitting processes used for particle detection?
Cherenkov radiation
Transition radiation
Scintillation (ionisation)
What is the relation between attenuation length and radiation length?
L_attenuation = 9/7 * L_R
Describe the relationship between momentum resolution and momentum.
Constant and then linear
(constant due to multiple scattering)
(linear due to decrease in curvature)
*remember that for electrons we also use calorimetry for momentum measurement.
How do pi_0 mesons decay?
Usually two photons
In what units must we measure angles when carrying out error propagation?
radians
