Particle Physics equations and more Flashcards
Which quantities are conserved in all interactions?
Energy/Momentum Angular momentum J Individual Lepton number Baryon number B (1/3 * total quark number) Charge Q
Which quantities are conserved by EM/Strong interactions but not Weak?
Quark flavour (although conserved by the Z coupling) Isospin and Isospin component I and I3
Parity, Charge Parity and Time reversal symmetry
What is the meaning of range?
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)
What has lepton number?
One lepton number for each generation of leptons (electrons/quarks).
Particles have positive lepton number and antiparticles have negative lepton number.
What has baryon number?
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
What is hypercharge Y?
Baryon number + strangeness, charmness, bottomness, topness
Which particles have isospin?
Up quark has +1/2
Down quark has -1/2
What is an isospin multiplet?
Give some examples.
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
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?
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
What is a charge parity transformation?
Transforming all particles to their anti-particle.
i.e: neutral particles are eigensates of C
What kind of quantum number is charge parity?
What is the intrinsic charge parity of a photon?
Multiplicative quantum number
Photons have intrinsic C= -1
When can charged particles be eigenstates of a charge parity transformation?
What is the value of charge parity in this case?
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)
In what interactions is colour charge important?
Colour charge is conserved in all strong interactions.
What particles carry colour charge?
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).
What is the particle exchange symmetry for two identical bosons or fermions?
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.
What is helicity? How is it different from chirality?
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.
What is chirality? What is its interaction with the weak sector?
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.
Which three quarks have positive charge? What is the value of this charge? What special properties do these have?
up, charm, strange Q = +2/3
up has +1/2 isospin
charm has charmness 1
top has topness 1 (and does not form hadrons)
Which three quarks have negative charge? What is the value of this charge? What special properties do these have?
down, strange, bottom Q = -1/3
down has -1/2 isospin
strange has -1 strangeness
bottom has -1 bottomness
What spin do quarks and leptons have?
1/2
What are the three charged leptons?
electron, muon, tau
Q = -1
What are the three neutral leptons?
electron neutrino, muon neutrino, tau neutrino
negligible mass
Which fundamental bosons have spin 1?
Photon, gluon, Z, W+-
Which bosons have zero mass?
photon, gluon
Which bosons have charge?
W+- only
gluons carry colour charge
Which fundamental boson has spin 0?
The Higgs boson
Which fundamental bosons have defined parity?
Charge parity?
Photons and gluons have P = -1
Higgs boson has P = 1
Photons have C = -1
What spin do pions have?
What kind of particle are they?
What is their intrinsic parity?
Pions have spin 0
They are mesons (quark antiquark pair)
Pions have intrinsic parity -1
**neutral pion has intrinsic charge parity +1
What is the intrinsic parity of nucleons?
Neutrons and protons both have P = +1
What are the purely EM vertices?
Photon coupled to an identical charged lepton pair, or an identical quark pair.
What is the approximate maximal range of a gluon?
10^-15m (one femtometre)
How does the weak interaction couple in the leptonic sector?
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.
How does the weak interaction couple in the quark sector?
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.
How does the “electroweak” Z boson couple to fermions?
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.
How does the Higgs interaction couple in the fermionic and bosonic sectors?
Couples to all fermions excluding neutrinos, conserving flavour.
1 or 2 H can couple to:
- H pair
- W+ W-
- Z pair
What is the basic concept of the Cabbibo Hypothesis?
Quarks exist as a linear superposition of quark states, that can be:
- weak eigenstates (couple with the weak force)
- mass eigenstates (conventional quark states)
What process was used to show parity violation by the weak force in the Wu experiment?
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.
What (CP invariant) process was used to show C parity violation by the weak force?
The decay of polarised muons, observed in the rest frame.
The chirality condition results in the charge parity transformed system being forbidden.
What process was used to show CP parity violation by the weak force?
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.
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?
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.
What is the CPT theorem?
CPT symmetry is always invariant.
-> the weak interaction must break T-symmetry in some interactions (not yet observed).
Which bosons can couple to themselves?
Gluons, Higgs, W+-
What is a parity transformation in spherical polar coordinates?
r -> r
theta -> pi - theta
phi -> pi + phi
What are the approximate maximal ranges of the strong and weak interactions?
Strong ~ 10^-15 m (1 fm)
Weak ~ 10^-18 m (10^-3 fm)
