10. Leptons and Quarks Flashcards
What is a Feynman diagram?
A convenient way to represent particle interactions.
What are the 3 conventions/requirements for a Feynman diagram?
- Time runs from left to right.
- An arrow directed towards the right is a particle, one directed towards the left is an anti-particle.
- At each vertex, momentum and charge are conserved (along with other quantum numbers). This means that arrows should be continuous at each vertex.
______-vertex interactions violate energy conservation.
Single
Describe the Feynman diagram for e- photon emission
Describe the Feynman diagram for e+ photon emission
Describe the Feynman diagram for e- photon absorption
Describe the Feynman diagram for e+ photon absorption
Describe the Feynman diagram for e+, e- annihilation
Describe the Feynman diagram for e+, e- creation
_________ is conserved at each vertex of a Feynman diagram.
Momentum
State the full relativistic expression for energy
E = energy
p = momentum
c = speed of light
m = mass
Why can’t exchange particles occur in isolation?
Because energy is not conserved for a single vertex interaction involving an exchange particle, hence, another vertex is required so that energy conservation is only violated for a short period.
What is a lowest order Feynman diagram?
A Feynman diagram containing two vertices. It is the lowest amplitude real process.
What is the difference between these two electron scattering lowest order diagrams?
The time ordering is different for the two.
Why are Feynman diagrams drawn with implied time orderings rather than drawing all the possible time orderings?
Because it is inconvenient to draw all variations so the time orderings are suppressed.
When is it not possible to suppress the time-ordering of a Feynman diagram?
When W± exhange particles are involved as the time ordering fixes the charge.
Describe the basic vertex Feynman diagram resulting from electromagnetic interactions for all leptons in the standard model
What is lepton universality?
The coupling constant is the same for each of the 3 generations of lepton because there isn’t much difference between each of the lepton generations apart from their mass.
Give the equation for the electron lepton number
Give the equation for the muon lepton number
Give the equation for the tau lepton number
Are lepton numbers conserved in the standard model?
Yes
Are lepton numbers conserved at each vertex of a Feynman diagram?
Yes
Is there any experimental evidence for the violation of lepton number?
No
Give the equation for the experimental probability of lepton number violation
P = probability
The limit is based on the number of observed decays experimentally.
Describe the basic vertex Feynman diagram resulting from weak Z0 interactions for all leptons in the standard model
These interactions conserve charge and lepton number at each vertex.
Describe the basic vertex Feynman diagram resulting from weak W± interactions for all leptons in the standard model
The time ordering has been left implied as it specifies the charge. If the diagrams contained W+ it would have to be incoming to the vertex. If the diagrams contained W- it would have to be outgoing from the vertex.
Lepton number and charge are conserved at each vertex.
Describe the lowest order Feynman diagram for muon decay
This interaction is purely leptonic.
What can the strength of the weak interactions be approximated as at low energies?
How does the Fermi coupling constant change low energy Feynman diagrams?
Diagrams involving W and Z can be approximated by a single vertex with the Fermi coupling constant in the middle.
Give the equation for the relation between the Fermi coupling constant and the mass of an exchange particle, M_W
G_F = Fermi coupling constant
c = speed of light
α_W = coupling strength constant
M_W = exchange particle mass
Why is the weak interaction comparable to the electromagnetic interaction?
They both have a constant that determines the coupling strength. The only difference is that the electromagnetic interaction is stronger.
α_W = weak interaction coupling constant
α = electromagnetic interaction coupling constant
Give the equation for the strangeness of a particle
Give the equation for the charm of a particle
Give the equation for the beauty of a particle
The tilde distinguishes beauty from the baryon number.
Give the equation for the truth of a particle
How are the conservation laws for up and down quarks defined?
As a linear combination of the individual quark flavours.
Give the equation for baryon number
What is the baryon number of a baryon (3 quarks)?
1
What is the baryon number of an anti-baryon (3 anti-quarks)?
-1
What is the baryon number of a mason (quark and anti-quark)?
0
Give the equation for the baryon number in terms of individual quark flavours
B = baryon number
N_u = number of up quarks
N_d = number of down quarks
N_s = number of strange quarks
N_c = number of charm quarks
N_b = number of bottom quarks
N_t = number of top quarks
Give the equation for the charge of a particle in terms of individual quark flavours
Q = charge
N_u = number of up quarks
N_d = number of down quarks
N_s = number of strange quarks
N_c = number of charm quarks
N_b = number of bottom quarks
N_t = number of top quarks
Which interactions conserve individual quark flavour numbers?
Strong and electromagnetic interactions
Which interactions do not conserve individual quark flavour numbers?
Weak interactions: they only conserve baryon number and charge
Describe the basic vertex of a Feynman diagram for charged current interactions with leptons
The charge on W is left unspecified because it depends on the time ordering.
g_W is the coupling strength constant for W exchange.
State the relationship between the W exchange coupling constant and the coupling strength of a charged current interaction
α_W = coupling strength of a charged current interaction
g_W = exchange coupling constant
Describe the zero-range approximation for muon decay
What are natural units?
When ℏ = c = 1 so that all quantities can be expressed as a power of energy E.
Give the equation for dimensional analysis
What are the dimension of the Fermi coupling constant?
What are the dimensions of the decay rate (inverse time)?
What are the dimensions of mass?
Give the equation for muon decay
Give the equation for tau decay
How can lepton universality be proven?
By showing that the ratio between muon and tau decay is equal to unity as K is the same for both decays. This is experimentally shown to be true to high precision.
What quark is the lepton v_e identical to?
Up
What quark is the lepton e- identical to?
Down
What quark is the lepton v_µ identical to?
Charm
What quark is the lepton µ- identical to?
Strange
What is the quark structure of π-?
Give the equation for π- decay
Why is the π- decay vertex theoretically allowed?
Because the equivalent quarks of the lepton decay products are from the same generation.
What is the quark structure of K-?
Give the equation for K- decay
Why is the K- decay vertex theoretically forbidden?
Because the equivalent quarks of the lepton decay products are from different generations.
Can quark mixing occur?
Yes: it causes quark-lepton symmetry to be conserved
For a previously allowed decay (before considerations of quark mixing), what is the coupling strength modified to?
θ_c = Cabibbo angle
For a previously forbidden decay (before considerations of quark mixing), what is the coupling strength modified to?
θ_c = Cabibbo angle
What happens if the Cabibbo angle equal 0?
There is no quark-mixing
How can the Cabibbo angle be measured experimentally?
By comparing the decay rate for pion and kaon decays by taking the ratio of the coupling squared.
What is the experimental value of the Cabibbo angle?
13.1 degrees
What is the quark mixing matrix?
The mixing of quark states between all three generations. It is called the Cabibbo-Kobayashi-Maskawa (CKM) matrix.
Is the 3x3 CKM metric real or complex?
Complex
Describe the two basic neutral current interaction vertices (those involving Z0)
Are there flavour changing vertices for Z0 interactions?
No
