Particle physics Flashcards
What are fundamental particles?
Point-like objects without any internal structure
What are intrinsic properties? (not examples)
Properties that are independent of reference frame
What are examples of intrinsic properties of particles?
Mass, spin, charge (type changes depending on the type of interaction), parity and charge conjugation
Why do we need to be careful about the mass for unstable particles?
The mass (and energy) aren’t fixed if the uncertainty in time is not infinity because of Heisenberg’s uncertainty principle
How is the width (capital gamma) related to the mean lifetime of the particle (tau)?
The mean lifetime is equal to h bar over the width
What are particles with half-integer spin?
Fermions
What are particle with integer spin?
Bosons
What is general charge?
It is the quantum number that tells us how likely a particle interacts via a particular force (ie EM, weak, strong, gravitational)
What are the extrinsic properties of a particle? (ones that do depend on the reference frame)
Four momentum and the projection of the spin onto some axis (like helicity)
What is the helicity?
Two times the projection of the spin onto the axis defined by the particle’s momentum
What is the amplitude when referring to Feynman diagrams?
A path a particle can take and the modulus squared of it gives the probability
What is the matrix element when considering Feynman diagrams and what is also known as?
It is the total complex amplitude for a transition from one initial state to a final state and also known as the transition amplitude
What is the transition rate?
It is proportional to the magnitude squared of the matrix element (for it to be equal to rather than proportional, there is a phase space term as well)
What we will be ignoring in Feynman diagrams?
Spin
What is conserved at each vertex?
Energy, momentum (including 4 momentum) and charge
What direction does time run on a Feynman diagram?
Left to right (LHS is initial state, RHS is final state and middle is how it happened)
What direction do anti-particles point on Feynman diagrams?
In the negative time direction
What does each vertex of a Feynman diagram contribute and what is it proportional to?
A coupling strength factor g and the charge of the particle (charge changes depending on the type of interaction, eg electric charge for EM etc)
In a Feynman diagram, what factor does each intermediate particle (propagator) contribute?
1 over q squared minus m squared (q = four momentum)
Is the intermediate particle in Feynman diagrams real or virtual and is it on or off shell?
Virtual and off shell
What is the contribution from a massless propagator (like a photon)?
1 over E squared minus p squared
What are 3 types of Lorentz transformations?
Rotations, shift and boosts
What do Lorentz transformations do?
They transform between two frames that have a constant velocity relative to each other
For a Lorentz transformation that is a rotation about one of the axes, what parts of the 4 component are not affected?
Time and the axis it is being rotated about
For a Lorentz transformation that is a boost in either the x, y or z direction, what does the matrix look like?
Along the diagonal it always has gamma first then the rest of the diagonal are 1 except the one that will correspond to the particular direction will be a gamma. The rest are zeros except the first one in the row and column that correspond with x (2nd row and column), y (3rd) and z (4th)
What is a shift/translation in Lorentz transformation?
dx is added to x (general)
What are four-vectors?
Objects that transform under Lorentz transformations like the differences in ct, x, y, z
What is the energy using Lorentz transformations?
gamma multiplied by mass times c squared
What is the modulus of the momentum vector using Lorentz transformations?
beta times gamma times mass times c
What is beta?
The speed of the particles
What is gamma?
1 over square root 1 minus beta squared
What is the dot products between two four vectors?
the 0th components (first part of the vector) of the vectors multiplied together minus the dot product of the 3 vector (last 3 components of the vectors)
What does Lorentz invariant mean?
Independent of reference frame/ the same in any coordinate system
Are dot products Lorentz invariant?
Yes
What is the centre of mass energy?
root s
What is tau, the proper time of the particle?
The same as the time of the particle at rest
What is time dilation?
Time intervals observed from a moving coordinate system are stretched by a factor of gamma relative to the time in the rest frame
What are the terms in the p four vector?
E is the first term, and the other three are the speed of light (c) multiplied by the momentum in that direction eg cp(x), cp(y), cp(z)
What properties are conserved quantities at any point in space and time?
Energy and momentum
What quantity is not conserved but is invariant under Lorentz transformations?
Mass
What do we change when using natural units?
The speed of light = h bar =1
What is the main problems of Schrodinger’s equation?
It does not account for relativistic effects and isn’t Lorentz invariant (looks different in different inertial frames)
What does the sum of the differential of the probability density with respect to time and the divergence of the probability current equal?
Zero
What is the Klein-Gordan equation?
It is a relativistic wave equation, related to Schrodinger’s equation
What was the problem with the Klein-Gordan equation?
The solutions to the equation can give negative probability density (and negative energy solution)
What are the gamma matric elements in the Dirac equation?
They are four 4x4 matrices that look like 2x2 matrices but each component is itself another 2x2 matrix
Is the probability density always positive positive for the Dirac equation?
Yes
The negative energy solutions to the Dirac equation are explained by Feynman and Stueckelberg as being what?
Positive energy energy anti-particles travelling backwards in time
How many solutions are there to the Dirac equation and what type of particle do they respond to?
4 and the first two correspond to particle solutions and the final 2 correspond to anti-particle solutions
The solutions to the Dirac equation are also eigenstates of what?
The Hamiltonian operator
What are the components of total angular momentum (J) which means it is conserved?
Orbital angular momentum (L) and the spin operator (sigma)
What does the spin operators look like to be suitable with the four components of the Dirac equation solutions?
4D matrices with the 2x2 Pauli matrices included in 2x2 matrices
How are the Hamiltonian, three momentum, angular momentum and spin operators for antiparticles related to that of particles?
They are the negatives of them
The Dirac equation describes particles with how much spin in the z direction?
Plus or minus half
Is the helicity quantum number conserved and what commutation relation shows this?
The Hamiltonian commutes with helicity
Is helicity Lorentz invariant?
No
What are the eigenvalues of the helicity operator for a spin-half particle?
Plus or minus one
What is the total spin operator equal to?
The spin operator multiplied by its adjoint
When is the only cases when the wavefunctions that are solutions to the Dirac equation are eigenstates of the z direction spin operator?
The particle is at rest or only carries momentum along the z- axis (not the case in general though)
Are the wavefunctions that are solutions to the Dirac equation eigenstates of the total spin operator?
Yes
What are the eigenvalues of the total spin operator with the wavefunctions that are solutions to the Dirac equation as eigenstates?
3/4 (three quarters)
Why must the force (the strong force) holding the nucleons together be short range?
Nucleons can be observed as free particles, without needing to bond into a nucleus
What did Yukawa suggest?
The force holding nucleons together must be short range and the carrier of the strong force must be massive. He predicted the mass of this particle to be 200x that of an electron and a tenth of a proton and called it a meson
What is the Yukawa meson?
A pion
What is a Yukawa interaction?
The nuclear force between nucleons mediated by pions in low energy regimes
The fact that the mass of protons is approx the same as that of neutrons and that the elastic scattering of protons and neutrons have the same coupling strengths means what?
The strong force acts the same on protons and neutrons
What is strong isospin and what are its components?
It is the quantum number related to the up and down quark content of the particle. The first is its isospin and the second is its 3rd-component isospin (I subscript 3)
What is the value of the isospin?
1/2 for protons and neutrons and 1 for pions
What is the value for the third component of isospin?
Plus 1/2 for up quarks and minus 1/2 for down quarks and 0 for other quarks
What is an isospin-doublet and what is an example of one?
Two different states with different isospins of a single isospin, like a neutron and a proton make up a nucleon
What are the isospin values of protons and neutrons?
Protons: |1/2,1/2> and neutrons: |1/2, -1/2>
What are the isospin values of the isospin-triplet made by the three types of pions?
The first value (isospin) is 1 and the third component isospin is the same as its charge (eg +1 for the positive pion, 0 for neutral etc)
If the strong force is symmetric under isospin transformation, what does this mean by Noether’s theorem?
Isospin is conserved in isospin interactions
How do we calculate the total isospin with 2 particles?
The total isospin is between the sum of the particles isospins and the modulus of the difference between the particles isospins. Also, it is constrained by the fact that the total third component has to be between the total isospin and minus the total isospin
How do we calculate the total 3rd component isospin with 2 particles?
Just the addition of both third components of each particle.
Does the strong force treat up and down quarks equally?
Yes
What is the strong isospin of up and down quarks?
Both have 1/2 as the first component with 1/2 for the third component of the up quark and -1/2 for the third component of the down quark
What are the four parts of the wavefunction?
Isospin, spin, spatial part and colour
Since quarks are fermions, what do they also have (other than isospin)?
Spin
How many isospin and spin states are there?
8 of each
Is the wavefunction of indistinguishable fermions symmetric or anti-symmetric under the exchange of any two functions?
Anti-symmetric
What is the net colour charge of baryons and mesons?
Zero
Is the colour wavefunction symmetric or antisymmetric under the exchange of any two quarks?
Antisymmetric
What are the three values of colour charge that quarks can carry and what are the three that anti-quarks can carry?
Quarks: red, blue and green. Anti-quarks: anti-red, anti-blue and anti-green
Why is there no restriction of the wavefunction being antisymmetric for mesons?
They are made up of distinguishable quarks and anti-quarks
What is the principle of colour confinement?
Only states with a total colour charge of 0 can exist as free particles
How many combinations of the colour charges are there for baryons to have 0 net colour charge?
1
Does the gluon, the massless carrier of the strong interaction, carry colour charge and if so, what type?
Yes and one colour and one anti-colour
What vertices can gluons have with itself and why can it do this?
3 or 4 gluon vertices and it can do this because it carriers a colour charge
In EM interactions, the field line density is inversely proportional to the distance squared, what is the field line density and distance relationship for strong interactions?
Approximately constant
For the strong force and in short distances, does the potential increase or decrease with distance?
Increase
How are jets formed?
2 quarks separate at high velocity and a tube of uniform energy density forms between them, and as separation increases, energy in the tube increases. When the energy surpasses the mass of two quarks, the tube breaks to form a quark and antiquark pair and process repeats
Why was the neutrino hypothesised in the first place?
In beta minus decay, the energy of the emitted electrons varied, rather than being a constant, so it violated energy conservation laws
What properties was hypothesised that the neutrino should have?
No electric charge, little to no mass, spin-half
What are the 3 vertices that we are considering with weak interactions?
All also have a weak boson in the vertex. Lepton vertices (leptons and their neutrinos), up and down vertex and up and strange vertex
What is the d’ (d primed) quark that couples with the up quark?
Cos(cabibbo angle) down quark + sin(cabibbo angle) strange quark
What is the Cabibbo angle roughly?
0.22
What is the coupling strength of the d’ (d primed), u and W vertex and what is it the same as?
g subscript W. It is the same as the lepton, neutrino, W vertex coupling strength
What is the s’ (s prime) quark equation?
-sin(cabibbo angle) down quark + cos(cabibbo angle) strange quark
What are the vertex factors for the weak interactions? (use g for g subscript W and C for cabibbo angle)
g for lepton, neutrino, W vertices, g cos(C) for up, down and W vertices, gsin(C) for up, strange and W vertices
What are the weak eigenstates and what are the mass eigenstates for weak interactions?
The weak eigenstates are d’ and s’, whilst the mass eigenstates are d and s
How many parameters are there for to describe the coupling of weak interactions and what are they?
2, one coupling constant (g subscript W) and one angle (the cabibbo angle)
Why are there no allowed vertices for the s, d and W in the weak interaction? (keep in mind these are the same charge)
There are no tree-level flavour changing neutral currents (FCNC) in the standard model
The observations made in decays of kaons, which links to the GIM mechanism, lead to the prediction of what particles?
Charm quarks
What are flavour changing neutral currents (FCNC) transitions?
Transitions where the quark flavour changes but not the charge
In the weak interaction, in the same way that the u quark couples with the d’ quark, what does the s’ quark couple with?
The charm quark
What is the GIM mechanism?
The mechanism through which flavour changing neutral currents (FCNC) are suppressed
Why does the s’ quark coupling with the charm quark via the W have an effect of cancelling FCNC? (GIM mechanism)
The -sin(C)d contribution in the s’ cancels the +sin(C)s contribution of the d quark
Can you have FCNC in loop level processes and if so, how common are they (weak interaction)? hint: GIM mechanism
Yes, but they are still highly suppressed so they are rare (low probability)
The probability of flavour changing neutral currents (FCNCs) occurring is proportional to what mass equation? (GIM mechanism)
The mass of the up quark squared minus the the mass of the charm quark squared
What is parity?
The operation of replacing all space coordinates x, y, z with -x, -y, -z, which is the same as a mirror reflection followed by a 180 degree rotation
What does it mean by parity symmetry?
The laws of physics should be symmetric
Is parity a discrete or continuous symmetry and what does this mean?
Discrete and continuous symmetry operations are built up by a succession of infinitesimally small steps, but discrete ones can’t, like in mirror images
Which is the only symmetry that breaks parity?
Weak interaction
Which of these quantities turn into the negative of themselves under parity: position, velocity, mass, momentum, energy, angular momentum, electric field and magnetic field
Position, velocity, momentum, electric field
Which of these quantities stay the same under parity: position, velocity, mass, momentum, energy, angular momentum, electric field and magnetic field
Mass, energy, angular momentum, magnetic field
What is an axial vector and what is it also called?
It is the cross product of vectors and resembles a normal vector. It is also called a pseudovector
What are examples of axial vector and what is one of their properties regarding parity?
Angular momentum and magnetic field. They remain the same under parity
How is the absolute squared of the wavefunction affected under parity?
It equals itself
How is the wavefunction affected under parity?
It is the wavefunction multiplied either 1 or -1
What does it mean for a particle wavefunction to have either even or odd intrinsic parity?
If it equals itself under parity it is parity even, if it is the negative of itself under parity, it is parity odd
On formula sheets, the particles are listed with J superscript PC, what does J and P stand for? (C not currently learnt)
J is the spin of the particles and P is the parity
Since fermions always have the opposite parity of their antiparticles, what is the combined intrinsic parity of fermion anti-fermion pairs?
It is negative (-1)
For any two body system, the parity eigenvalue is equal to what?
(-1) to the power of L, the angular momentum quantum number, multiplied by the intrinsic parity of each particle (sometimes you know the intrinsic parity of the 2 particles as a pair or them individually)
How do you calculate the parity of three or more-body systems?
Break down the problem into successive 2 body problems spin
If the parity operator commute with the Hamiltonian, what does this mean?
It means parity is a good symmetry and parity is conserved in these cases, so it will remain the same parity over time, including before and after a decay
What experiment shows that parity is violated in weak interactions?
Wu’s experiment
How is chirality defined relative to helicity?
It is equivalent to helicity for zero-mass particles, but different for massive particles
Is chirality and helicity Lorentz invariant?
Chirality is, helicity isn’t
Which is the only type of chirality particles that take part in the weak interactions?
Chirality left-handed particles
When is helicity and chirality the same (eg both left-handed or both right-handed) and when is it different (eg one is left-handed and one is right-handed)?
They are the same for matter particles and different for antimatter particles when they are massless only
For massless particles, what type of helicity particles take part in weak interactions?
Helicity left-handed matter particles and helicity right-handed antimatter particles
What is the formal sentence for saying that weak interactions violate parity symmetry?
Parity is maximally violated in the weak interaction
What values does helicity need to be to be right or left handed?
+1 for right-handed and -1 for left-handed
What makes the helicity of a particle positive or negative?
Positive if the direction of the spin is in the same direction as its motion and negative if the are in opposite directions
What is chirality?
When something is not identical to its mirror image
What happens to chirality and helicity under parity and what does this mean?
They change sign, so parity is violated under weak interactions because a massless particle that is subject to the weak interaction is, after applying the parity, not subject to it at all (since weak force only affects left handed chirality particles)
What is the branching fraction?
The number of decays into one particular state divided by the overall number of decays is equal to the partial width of the decay into that particular state divided by the overall decay width
What is the phase space density?
The magnitude of the three-momentum of the daughter particles in the rest frame of the mother (after the mother decays)
What does Fermi’s golden rule relate together?
The matrix element and decays rates (like partial width) for two-body decays
Does the phase space density in Fermi’s golden rule favour decays to lighter or heavier particles?
Lighter
When do we consider a particle in the ‘wrong’ or suppressed helicity state?
A massive particle with definite chirality can be found in either helicity state but the favoured state is the same as when its massless and its suppressed state is the opposite one and can be in it
What do pions usually decay into and why?
A muon and muon antineutrino because of helicity suppression leading to the chance of it being the electron version a lot smaller
Helicity suppression is a direct result of what type fo violation?
Parity
What does charge conjugation do?
It takes matter to antimatter
What are the eigenvalues of charge conjugation?
Plus or minus one
What type of particles are able to be charge conjugation eigenstates?
Neutral particles
What is CP?
The product of charge conjugation and parity
CP violation is equivalent to what type of violation?
Time reversal
Does an up-type quark to a down-type quark use the original or complex version of the mixing matrix element (CKM)?
Complex
Does an down-type quark to a up-type quark use the original or complex version of the mixing matrix element (CKM)?
Original
What type of matrix is the Cabibbo/CKM matrix?
Unitary
The fact that the CKM matrix is unitary gives rise to what?
A set of 6 equations and 6 unitarity triangles
Why is the unitarity triangle given top us in the formula sheet special and called ‘the’ unitarity triangle?
It is one of out only 2 of the unitarity relations that give a triangle with sides of the same order of magnitude
What is neutral meson mixing and what is it also called?
It is when neutral mesons can turn into their own antiparticles and back. It is also called oscillations
What is the oscillating frequency of B mesons?
The mass difference between the two mass eigenstates (mass between B meson particle and antiparticle) divided by 2 pi
What is the heavy and light B meson mass eigenstates?
They are both 1 over root 2 times by the either the difference (for heavy) or sum (for light) of the B meson particle and antiparticle
Out of the B meson heavy and light state, which one is CP odd and which one is CP even?
The heavy state is odd whilst the light state is even
For box diagrams where the choice of internal quarks are up-type quarks, which type dominates and why?
Top because its heaviest (GIM suppression)
For box diagrams with the internal quarks being bottom-type quarks, which one dominates?
None do as their masses are similar to each other and GIM cancellation works better
All CP violation measurements are what type of experiments?
Interference experiments where we have more than one path from an initial state to a final state
What are the 3 types of CP violation?
Indirect (in the mixing), direct (in the decay) and CP violation in the interference between mixing and decay
What is CP violation in the mixing (indirect)?
The mass/width eigenstates do not match the CP eigenstates
What is CP violation in the decay (direct)?
The decay rates for some initial state i to final state f are not the same as for the CP-conjugate decay
Is the strong phase CP symmetric and what does this mean between two CP conjugate decays?
Yes (so it stays the same under CP) and it means there will be no phase difference between the two
What interferes with what for indirect CP violation (violation in the mixing) (paths)?
The path of a neutral particle to itself with the path of a neutral particle oscillating to its antiparticle and back again
What interferes with what for direct CP violation? (violation in the decay (paths)?
Two paths with the same initial and final state but with a different middle state
Direct CP violation requires what type/types of phase differences between two interfering processes?
Strong and weak separately
What interferes with what for CP violation in the interference between mixing and decay (paths)?
A neutral particle going to its final state and the neutral particle going to its antiparticle (oscillating) then going to its final state
What phase difference matters in the CP violation in the interference between mixing and decay?
Overall together
How is the weak phase of the CP-conjugate process related to the weak phase of the original process?
The negative of it
For the strong interaction, are all symmetries conserved and if not, which ones are violated?
All are
For the electromagnetic interaction, are all symmetries conserved and if not, which ones are violated?
All except isospin
For the weak interaction, are all symmetries conserved and if not, which ones are violated?
All except charge conjugation, parity, CP, flavour and isospin
What are the two modes of accelerator that can achieve particle collisions?
Fixed target and collider. Fixed target is with a non-moving target, whilst collider is two moving beams shot at each other
When would you use each mode of accelerator (fixed target or collider)?
For max energy, use a collider, for max luminosity, (but energy not as important) fixed target. Fixed target always involve protons
What is the positives and negatives of circular vs linear accelerators?
Circular ones can give the particles a kick every time they come round but they lose energy when it bends electrons or positrons around a circle (synchrotron radiation), but protons do not lose as much energy from this
What is the advantages of an electron-positron collider over a proton-proton collider?
The initial state is very well known, unlike in proton-proton colliders (partons of unknown energy will interact) and they work well for precision studies
How do you detect invisible particles in electron-positron colliders?
Look for missing momentum and energy as the momentum and energy of the initial state and the other particles are known
How do you detect invisible particles in proton-proton colliders?
Look for missing transverse momentum (often called transverse energy), as there should be no transverse momentum (magnitude of the vector sum of the momenta transverse to beam direction equals zero), so if it is non-zero, there is an undetected particle
What sections make up a detector, starting from the inner most part?
Vertex detectors, tracking detectors, RICH detectors, electronic calorimeter (ECAL), hadronic calorimeter (HCAL) and then muon detectors
What do calorimeters do in detectors and why is this important?
They initiate particle showers and the energies can be measured. This is needed to make neutral particles into charged particles so that electromagnetic signals can be recorded
The coupling strength of the Higgs boson to other particles is proportional to what?
The mass of the particle the Higgs couples to
What is the probability that a Higgs will decay to a particular particle proportional to?
The mass of the particle the Higgs couples to squared
How do Higgs bosons decay into a pair of photons? (this is how it was discovered)
Loop-processes involving either W bosons or top quarks as intermediate particles
In proton-proton colliders, what actually collides when colliding protons at high energies?
Primarily gluons, as well as quarks/antiquarks
How can Higgs bosons be produced in hadron colliders with proton-proton collisions?
Gluon fusion is most dominant but there are others involving quarks and bosons
How can a Higgs boson be produced in electron-positron colliders?
After electron and positron collision, which emits an off-shell Z boson decaying to an on-shell Z boson and a Higgs
What are some problems with the standard model that show that there are discrepancies of it with reality?
Baryon asymmetry of the universe (more matter than antimatter), dark matter (strong evidence for it but no candidate for it) and gravity is missing from the SM
What are the problems with the standard model which are ones that we find unsatisfactory but not necessarily wrong?
Why are the masses between the particles so different? Also, the SM has too many free parameters
What problems does supersymmetry (SUSY) solve?
Hierarchy/finetuning problem and gives a candidate for dark matter
Why must supersymmetry (SUSY) be a broken symmetry?
Otherwise SUSY particles will have the same masses as their SM partners
Describe the two types of approaches for looking for physics beyond the standard model
Direct search approach - using colliders to search for ‘missing’ mass. Precision approach - suppressed transitions that have no current reason to be suppressed, look at transitions that can be precisely measured and if it deviates from prediction then there is more physics going on
Where are we looking for new physics?
Production of new heavy particles at LHC (esp heavy neutral ones for dark matter), Higgs decay to invisible particles, and ‘flavour physics’ (new particles discovered as virtual particles)
