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Exams Summer 2022 > Particle Physics > Flashcards

Particle Physics Flashcards

1
Q

What is the higgs coupling to fermions?

A

sqrt(2) * g_w * (m_f / m_w)

so probability ~ m_f^2

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2
Q

What is asymptotic freedom?

A

Quarks are ~independent at small distance / high energy scales.

Potential is ~ 1/r i.e: analogous to the coulomb potential.

Dimensionless coupling is ~ 0.1

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3
Q

What is parton-hadron duality?

A

The total momentum of the hadrons in a jet should be approximately equal to the momentum of the initial QCD particle.

However, some energy will be stored internally in the hadrons, and some energy is lost to soft gluons at wide angles.

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4
Q

What is the primary production channel for the higgs at the LHC?

A

Gluon-gluon fusion via a t-loop

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5
Q

What is detector acceptance?

What about detector efficiency?

A

Acceptance is the % of particles that are detectable/reconstructable. (e.g: incident on detectors, detectable by the detectors, pass the trigger)

Efficiency is the % acceptable particles that are missed.

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6
Q

How can the cross section for a particular decay mode be related to that for the general decay?

A

Cross section(specific channel) = Cross section(general) * BR(specific channel)

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7
Q

What does the sqrt of S usually refer to?

A

The COM energy of a collision.

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8
Q

What is the relation between decay rate (width in natural units) and the lifetime?
What about between decay rate and cross section?

A

width = hbar / tau

Width (rate) is proportional to cross section

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9
Q

What is the (approximate) mass of the bottom and top quarks?

A

Bottom : 4.2GeV

Top : 173 GeV

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10
Q

Why do we expect a longer lifetime from K_long?

A

Decays to CP odd final state of 3 pions -> “smaller phase space” due to decreased mass difference, so we expect slower “rate”.

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11
Q

How does the dimensionless coupling relate to coupling strength?

A

dimensionless coupling is proportional to g^2

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12
Q

How can the range of a force be estimated?

A

1 / the mass of the force carrier

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13
Q

How are weak eigenstate s’ and d’ states expressed in terms of their strong eigenstate counterparts?
(in the cabibbo model)

A 
d' = d cos(theta) + s sin(theta)
s' = -d sin(theta) + s cos(theta)
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14
Q

How many times larger is the integrated luminosity of proton collision compared to lead collisions at the LHC?

A

10^10

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15
Q

What is the (approximate) mass of the tau particle?

A

1.7 GeV

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16
Q

For the decay of a particle at rest, what is the constant K in the relation between width and (matrix element squared) proportional to?

A

Proportional to mass ^ 5

Can be shown using dimensional analysis

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17
Q

What plane are hadron supermultiplets represented in?

A

The Y - I_3 plane.

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18
Q

What are the Sakharov conditions?

A

Sufficient and necessary conditions for the matter/antimatter asymmetry we see in the universe.

1: Baryon number violation
2: C and CP violation
3: Interactions out of thermal equilibrium

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19
Q

What is the expression for the matrix element?

A

m-element = - g^2 / ( q^2 - m^2)

g is the coupling strength
q is the 4-momentum transfer
m is the mass of the force carrier

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20
Q

What is it important to remember when estimating the matrix element for a process?

A

The coupling constant g is for EACH VERTICE
i.e: for a two-vertice interaction, the matrix element will have two g factors in.

The coupling constant g is equal to charge, for the EM coupling.

The dimensionless coupling is effectively g^2 for charge e.

The cross section is proportional to the m-element squared.

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21
Q

What is the probability for the weak force to couple to a LH antiparticle or a RH particle?

A

Proportional to the mass of the particle squared.

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22
Q

What is colour confinement?

A

Inter-quark potential ~ r at large distance / low energy scales.
At some separation it becomes energetically favourable to create a quark-antiquark pair.
–> quarks cannot exist in isolation

Dimensionless coupling is ~ 1 at 1fm separation

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23
Q

What is thrust?

A

An event shape observable to help distinguish jets from one another.
Defined as the vector for which the fraction : [(sum of jet momenta dot the vector) / (sum of jet momenta)] is at a maximum.

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24
Q

What does high rapidity correspond to?

A

A particle being very forward-boosted in the detector.

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25
Q

What are the possible decay chains of a muon?

A

There is ONLY ONE!

Via a W boson to an electron/electron neutrino state (and muon neutrino).

The muon mass is not large enough to produce quarks.

(and obviously not large enough to produce a tau particle)

26
Q

What is an equation for the interaction length of a neutrino travelling through neutrons?

What does the interaction length mean?

A

The distance over which there is a 1/e probability of interaction.

1 / (cross section * neutron number density)

27
Q

What is the characteristic differential cross section of a spin-1/2 particle?

A

proportional to (1 + cos^2(theta))

28
Q

What interaction is used to detect neutrinos?

A

Charged current interaction converting neutrons into protons, the resultant electron can be detected via cherenkov radiation or in EM calorimeters.

29
Q

What is the dominant source of neutrinos on the earth, and what are it’s characteristics?

A

From the sun.

2:1 ratio of muon : electron neutrinos due to production from pi-

30
Q

How is the weinberg angle related to the mass of the W and Z bosons?

A

Cos(theta) = M_w / M_z

31
Q

What is the relation between isospin component and hypercharge?

A

I_3 = Q - Y/2

32
Q

What key relation is obeyed by all real particles?

A

E^2 = p^2 + m^2

33
Q

What is hypercharge?

A

Baryon number + all quark flavour numbers (but not isospin).

34
Q

How can the rate (width) for a specific channel be related to the total width?

A

Multiply the total width (rate) by the branching ratio, just as for cross section.

35
Q

Why does a threshold scan method not work for hadron colliders?

A

The parton distribution means that there is effectively a range of COM energies for the interacting quarks.

36
Q

What is the benefit of calculating rate/cross section ratios for decays with the same final state?

A

There is a large cancellation of systematic uncertainties.

37
Q

Why do interesting collisions usually result in products with high transverse momentum?

A

Heavy particles produced from a collision will not be boosted, so the decay products are far more likely to have large transverse momentum.

Light decay products would be heavily boosted.

38
Q

What is the dimensionless coupling of the weak force?

A

effectively 10 ^ -6 at normal energies

but really on the scale of EM coupling

39
Q

What is an equation for the interaction rate for neutrinos travelling through a detector?

A

Interaction rate = particle flux * cross section * # target particles

40
Q

What is an effect of the Vtb term in the CKM matrix being ~ 1?

A

The third generation hardly mixes with the first two.

  • > b quarks have surprisingly long lifetime.
  • —-> b mesons have long lifetime
  • ———-> gap between primary and secondary vertices in detectors producing b meson.
41
Q

What is a hadron supermultiplet?

A

A set of particles with the same B (baryon number) and J^pi state.

42
Q

What is the form of the yukawa potential?

What does it represent?

A
  • g^2 / 4pi * { e ^( -mr) / r}

Describes the wavefunction of the force carrier.
m is the mass of the force carrier

43
Q

Which particles have weak isospin?

A

RH particles have T = 0
LH (neutrinos and +charged quarks) have +1/2 (component)
LH (leptons and -charged quarks) have -1/2 (component)

W and Z form a triplet state with T= 1

44
Q

What is the range of values for the dimensionless coupling of the strong force?

A
  1. 1 minimum (asymptotic freedom)
    - > 1 at 1fm

-> infinity (colour confinement)

45
Q

What is the experimental value of the cabibbo angle?

How could this be measured?

A

13.1 degrees.

Find the ratio of decay rates of pi- and K- mesons.

46
Q

What is one of the key predictions of GUT?

A

Proton decay

47
Q

What is the ratio baryons/photons in the modern universe?

What does this suggest about the asymmetry of matter/antimatter?

A

10^-9

Asymmetry 1 + 10^-9

48
Q

What two signals gave evidence of CP violation in K_long decay?

A

Pi+ pi- momentum angle with K_long momentum peak at 0degrees. (we expect missing pi0 momentum)

Some pi+ pi- events have K_long invariant mass.

49
Q

What is the dimensionless coupling of the EM force?

A

alpha (the fine structure constant)

However, it increases at smaller distances (higher energy scale) as there is reduced charge screening.

50
Q

How can we find the probability of a process involving cabibbo mixing?

A

Find all possible intermediate states.
Find the amplitude of each intermediate state (product of cabibbo amplitude at each vertex), and sum them.
Square the amplitude to find the probability.

51
Q

What is the dominant top quark decay mode?

A

t -> q qbar and b

52
Q

What is the form of the breit-wigner distribution?

What would we actually see in experiment?

A

cross section ~ 1 / [ (E - pole mass)^2 + width^2 / 4]

The width is effectively a damping term preventing infinite resonance.
E is the COM energy of the interaction.
The pole mass is the mass of the mediating particle (resonance).

In experiment, we would see this distribution convolved with some resolution distribution.

53
Q

What are the possible decay chains of a tau particle?

A

Via a W boson:

electron/neutrino pair
muon/neutrino pair
quark pair
Enough energy to produce multiple quarks

54
Q

What is the approximate range of lifetimes for light hadrons decaying via the three forces?

A

Strong : e-22 -> e-24

EM : e-16 -> e-21

Weak : e-7 -> e-13
(very virtual W/Z bosons)

(s)

55
Q

How come EM and weak couplings become comparable at high energy?

A

They actually have ~ the same coupling, but the weak interaction appears weak at low energies due to the large mass of the W/Z compared to the massless photon.

56
Q

How many gluon states are there?

A

8

57
Q

Why is the decay of a pion to electron state so heavily supressed?

What extra factor is included in the ratio of branching ratios?

A

Due to angular momentum conservation, the lepton must be RH, so the muon channel is far more likely due to the larger muon mass.

Due to phase space, there is a factor of (M_pi^2 - m_e^2)^2 as well as the m_e^2 factor. (for both the electron and muon).

58
Q

How is the cross section for an event related to the matrix element?

A

proportional to the m-element squared

59
Q

What two effects contribute to the running of the strong coupling?

A

Quantum quark fluctuations (screens colour charge) [decreases effective colour charge]

DOMINANT EFFECT:
Quantum gluon self-interaction (antiscreening effect) [increases effective colour charge]

60
Q

What is the equation for the number of events seen in an experiment?

A

Equal to the cross-section * the luminosity

Luminosity can be integrated or instantaneous.

61
Q

By convention, what is the result of the charge conjugation operator on a neutral meson?

A

Gives the charge conjugate meson with a factor of -1.

62
Q

What must be considered for possible baryon supermultiplets that we don’t have to worry about for mesons?

A

Baryons can contain identical quarks, so the pauli exclusion principle must be considered.

The quarks will always be in an antisymmetric colour state, so they must have ALIGNED SPIN.

Exams Summer 2022 (5 decks)

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