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EXAMS January 2022 > Particle Physics equations and more > Flashcards

Particle Physics equations and more Flashcards

1
Q

Which quantities are conserved in all interactions?

A 
Energy/Momentum
Angular momentum J
Individual Lepton number
Baryon number B (1/3 * total quark number)
Charge Q
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2
Q

Which quantities are conserved by EM/Strong interactions but not Weak?

A 
Quark flavour (although conserved by the Z coupling)
Isospin and Isospin component I and I3

Parity, Charge Parity and Time reversal symmetry

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3
Q

What is the meaning of range?

A

Particles have a lifetime corresponding to hbar / their energy width.
The maximal range corresponds to c * the lifetime.

As energy width ~ mc^2. Maximal range ~ hbar / (mc)

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4
Q

What has lepton number?

A

One lepton number for each generation of leptons (electrons/quarks).
Particles have positive lepton number and antiparticles have negative lepton number.

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5
Q

What has baryon number?

A

Baryon number = total quark number/3
Quarks have +1/3 and antiquarks have -1/3.

i.e: baryons have B = 1 or -1, mesons have B = 0

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6
Q

What is hypercharge Y?

A

Baryon number + strangeness, charmness, bottomness, topness

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7
Q

Which particles have isospin?

A

Up quark has +1/2

Down quark has -1/2

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8
Q

What is an isospin multiplet?

Give some examples.

A

Isospin is an additive quantum number just like spin, so for a given isospin I there is a multiplet of 2I+1 states.

e.g: up/down quark is a multiplet with I = 1/2
proton/neutron is a multiplet with I = 1/2
pi+, pi0, pi- is a multiplet with I = 1

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9
Q

What kind of quantum number is parity?
What is the intrinsic parity of fermions, antifermions, photons, gluons?
What is the orbital angular momentum component of parity?

A 
Parity is a multiplicative quantum number.
Fermions have P = 1
Antifermions have P = -1
Photons have P = -1
Gluons have P = -1

P(orbital angular momentum) = (-1)^L

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10
Q

What is a charge parity transformation?

A

Transforming all particles to their anti-particle.

i.e: neutral particles are eigensates of C

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11
Q

What kind of quantum number is charge parity?

What is the intrinsic charge parity of a photon?

A

Multiplicative quantum number

Photons have intrinsic C= -1

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12
Q

When can charged particles be eigenstates of a charge parity transformation?
What is the value of charge parity in this case?

A

Particles with distinct anti-particles can only be eigenstates of C if there is a particle-antiparticle pair.

In this case C = (-1)^(L+S)

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13
Q

In what interactions is colour charge important?

A

Colour charge is conserved in all strong interactions.

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14
Q

What particles carry colour charge?

A

Quarks can be red, green or blue.
Antiquarks anti-red, anti-green or anti-blue.
Only particles with zero colour charge can be observed.
Gluons carry colour-anticolour pair (including superpositions).

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15
Q

What is the particle exchange symmetry for two identical bosons or fermions?

A

Fermions must be in an antisymmetric state overall.
Bosons must be in a symmetric state overall.

i.e: two identical bosons must be in a symmetric angular momentum state (even L) as the rest of the state is symmetric.

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16
Q

What is helicity? How is it different from chirality?

A

The projection of spin in the direction of momentum, divided by the spin magnitude. If spin vector and and momentum vector are aligned, the particle has +1 helicity (right-handed).

Helicity is not an inherent property of massive particles, as you can just Lorentz boost into a frame with a different momentum.
For ~massless particles (photons, neutrinos) helicity is equal to chirality.

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17
Q

What is chirality? What is its interaction with the weak sector?

A

An inherent property of particles.
The weak force only couples to left-handed fermions and right-handed antifermions.

**only left-handed neutrinos have been observed in nature.

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18
Q

Which three quarks have positive charge? What is the value of this charge? What special properties do these have?

A

up, charm, strange Q = +2/3
up has +1/2 isospin
charm has charmness 1
top has topness 1 (and does not form hadrons)

19
Q

Which three quarks have negative charge? What is the value of this charge? What special properties do these have?

A

down, strange, bottom Q = -1/3
down has -1/2 isospin
strange has -1 strangeness
bottom has -1 bottomness

20
Q

What spin do quarks and leptons have?

A

1/2

21
Q

What are the three charged leptons?

A

electron, muon, tau

Q = -1

22
Q

What are the three neutral leptons?

A

electron neutrino, muon neutrino, tau neutrino

negligible mass

23
Q

Which fundamental bosons have spin 1?

A

Photon, gluon, Z, W+-

24
Q

Which bosons have zero mass?

A

photon, gluon

25
Q

Which bosons have charge?

A

W+- only

gluons carry colour charge

26
Q

Which fundamental boson has spin 0?

A

The Higgs boson

27
Q

Which fundamental bosons have defined parity?

Charge parity?

A

Photons and gluons have P = -1
Higgs boson has P = 1
Photons have C = -1

28
Q

What spin do pions have?
What kind of particle are they?
What is their intrinsic parity?

A

Pions have spin 0
They are mesons (quark antiquark pair)
Pions have intrinsic parity -1
**neutral pion has intrinsic charge parity +1

29
Q

What is the intrinsic parity of nucleons?

A

Neutrons and protons both have P = +1

30
Q

What are the purely EM vertices?

A

Photon coupled to an identical charged lepton pair, or an identical quark pair.

31
Q

What is the approximate maximal range of a gluon?

A

10^-15m (one femtometre)

32
Q

How does the weak interaction couple in the leptonic sector?

A

W+ and W- can couple to a charged lepton and neutrino pair, within the same family. (conserving lepton number)
**remember, the weak interaction only couples to left-handed fermions and right handed anti-fermions.

33
Q

How does the weak interaction couple in the quark sector?

A

Quark flavour is not conserved.
Quark family is not conserved (“quark mixing” as per the cabbibo hypothesis).
**the further away, familialy, the more cabbibo supressed.

34
Q

How does the “electroweak” Z boson couple to fermions?

A

Couples to all fermions, conserves flavour.

i. e: only couples to identical fermion pairs.
* cannot decay to top anti-top as the combined mass is greater than the Z boson mass.

35
Q

How does the Higgs interaction couple in the fermionic and bosonic sectors?

A

Couples to all fermions excluding neutrinos, conserving flavour.

1 or 2 H can couple to:

  • H pair
  • W+ W-
  • Z pair
36
Q

What is the basic concept of the Cabbibo Hypothesis?

A

Quarks exist as a linear superposition of quark states, that can be:

  • weak eigenstates (couple with the weak force)
  • mass eigenstates (conventional quark states)
37
Q

What process was used to show parity violation by the weak force in the Wu experiment?

A

The preferred electron emission direction in beta- decay was observed. The nuclear spin orientation was kept polarised using a solenoid.

Switching the polarisation direction resulted in electrons emitted in the opposite direction, violating parity conservation.

We now realise this is necessary due to the chirality condition.

38
Q

What (CP invariant) process was used to show C parity violation by the weak force?

A

The decay of polarised muons, observed in the rest frame.

The chirality condition results in the charge parity transformed system being forbidden.

39
Q

What process was used to show CP parity violation by the weak force?

A

The decay of long-lived neutral Kaons into either 3 neutral pions or 2 neutral pions.

The 2 pion decay chain does not conserve CP, but is observed with small branching fraction.

**CP violation can be mathematically incorporated into the CKM matrix.

40
Q

What is the weighting of right-handed and left-handed states for a massive lepton with velocity v in a frame where it is left-handed?

A

0.5(1-v/c)[right-handed] + 0.5(1+v/c)[left-handed]

**these coefficients will give the suppression factor for a weak interaction.

41
Q

What is the CPT theorem?

A

CPT symmetry is always invariant.

-> the weak interaction must break T-symmetry in some interactions (not yet observed).

42
Q

Which bosons can couple to themselves?

A

Gluons, Higgs, W+-

43
Q

What is a parity transformation in spherical polar coordinates?

A

r -> r
theta -> pi - theta
phi -> pi + phi

44
Q

What are the approximate maximal ranges of the strong and weak interactions?

A

Strong ~ 10^-15 m (1 fm)

Weak ~ 10^-18 m (10^-3 fm)

EXAMS January 2022 (7 decks)

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