4.43 Conservation Laws in Particle Physics

• When particles interact, they must obey a set of laws associated to the type of particles involved
  • These laws are governed by numbers called quantum numbers

• Quantum numbers that are always conserved (i.e., they are the same before and after an interaction) are:
  • Charge, Q
  • Baryon number, B
  • Lepton number, L

• Using these quantum numbers, physicists are able to determine whether certain interactions are possible or not
  • In other words, an interaction that does not conserve charge, baryon or lepton number is not allowed by the laws of physics

Conservation of Charge

• The charge of a particle Q, is the charge carried by that particle
  
  • Protons have a charge Q = +1
  • Electrons have a charge Q = –1
  • Up quarks have a charge Q = +2/3
  • Neutral particles, like photons and neutrinos, have a charge Q = 0

Conservation of Baryon Number

• The baryon number, B, is the number of baryons in an interaction
• B depends on whether the particle is a baryon, anti-baryon or neither
  • Baryons have a baryon number B = +1
  • Anti-baryons have a baryon number B = –1
  • Particles that are not baryons have a baryon number B = 0

The baryon number of a particle depends if it is a baryon, anti–baryon or neither 

• The up (u), down (d) and strange (s) quark have a baryon number of 1/3 each
• This means that the anti–up, anti–down and anti–strange quarks have a baryon number of –1/3 each
• Note: The baryon number of each quark is provided on the datasheet

• The implication of this is that baryons are made up of all quarks and anti-baryons are made up of all anti-quarks
• There are no baryons (yet) that have a combination of quarks and anti-quarks e.g. up, anti-down, down
• The reason being that this would equate to a baryon number that is not a whole number (integer)

Conservation of Lepton Number

• Similar to baryon number, the lepton number, L is the number of leptons in an interaction
• L depends on whether the particle is a lepton, anti-lepton or neither
  • Leptons have a lepton number L = +1
  • Anti-leptons have a lepton number L = –1
  • Particles that are not leptons have a lepton number L = 0

• Lepton number is a quantum number and is conserved in all interactions
• This is helpful for knowing whether an interaction is able to happen

The lepton number depends on if the particle is a lepton, anti-lepton, or neither

Step 1: Determine the lepton number of all the particles on both sides of the equation

• • 0 + (–1) = 0 + X

Step 2: Identify the lepton number of X

• • If the lepton number must be conserved, X must also have a lepton number of –1

Step 3: State the identity of particle X

• • Particle X is an anti-neutrino