Particle Conservation Laws (DP IB Physics: HL)

Charge

• Electric charge must be conserved during particle interactions
  • This means charge must have the same value overall before and after the interaction

• Charge is found in quarks, leptons and exchange particles and their anti-matter counterparts

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

• Baryon number is a quantum number and is conserved in all interactions
  • This is one of the indicators for whether an interaction is able to occur or not

Lepton 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 one of the indicators for whether an interaction is able to occur or not

Conservation Laws

• All particle interactions must obey a set of conservation laws. These are conservation of:
  • Charge, Q
  • Baryon number, B
  • Lepton Number, L
  • Strangeness, S
  • Energy (or mass-energy)
  • Momentum

• However, strangeness does not need to be conserved in weak interactions. It can change by either 0, +1 or –1
• Quantum numbers such as Q, B, L and S can only take discrete values (ie. 0, +1, –1, 1/2)
• To know whether a particle interaction can occur, check whether each quantum number is equal on both sides of the equation
  • If even one of them, apart from strangeness in weak interactions, is not conserved then the interaction cannot occur

Example of a working out what is conserved in Kaon decay. This decay must be through the weak interaction since S is not conserved

Strangeness

• Strangeness, S, like baryon and lepton number, is a quantum number
• Strangeness is conserved in every interaction except the weak interaction
• This means that strange particles are always produced in pairs (e.g. K+ and K–)
• S depends on whether the particle contains a strange quark, anti-strange quark, or no strange quarks
  • Particles with an anti-strange quark have S = +1
  • Particle with a strange quark have S = –1
  • Particles with no strange quark have S = 0

Only particles with a strange or anti-strange quark have a strangeness of +1 or –1

• Strangeness can change by 0, +1 or –1 in weak interactions

Strange Particles

• Strange particles are particles that include a strange or anti-strange quark
• An example of these are kaons
• Strange particles always:
  • Are produced through the strong interaction
  • Decay through the weak interaction

• An example of a kaon production could be:

Kaons are produced through the strong interaction. This is shown by the gluon exchange particle.

• An example of kaon decay could be:

Kaons decay via the weak interaction. This is shown by the W⁺ boson.

Step 1: Determine conservation of charge, Q

• • The Λ⁰ has a charge of 0
  • The pion π^– has a charge of –1
  • The positron e⁺ has a charge of +1
  • The electron neutrino ν_e has a charge of 0

0 = –1 + 1 + 0

• • Therefore, charge is conserved

Step 2: Determine conservation of strangeness, S

• • Λ⁰ has an s quark, so must have a strangeness of –1
  • None of the particles on the right hand side of the decay has a strange quark

–1 = 0 + 0 + 0

• • Therefore, strangeness is not conserved

Step 3: Determine conservation of baryon number, B

• • Λ⁰ is a baryon since it has 3 quarks, so must have a baryon number of +1
  • The pion π^– is a meson so has a baryon number 0
  • The positron is a lepton so has a baryon number 0
  • The electron neutrino ν_e is a lepton so has a baryon number 0

+1 = 0 + 0 + 0

• • Therefore, baryon number is not conserved

Step 4: Determine conservation of lepton number, L

• • Λ⁰ is a baryon, so must have a lepton number of 0
  • The pion π^– is a meson so has a lepton number of 0
  • The positron e⁺ is an anti-lepton so has a lepton number of –1
  • The electron neutrino ν_e is a lepton so has a lepton number of +1

0 = 0 + (–1) + 1

• • Therefore, lepton number is conserved

Step 5: Conclusion

• • Since the baryon number is not conserved, this interaction is not permitted

Step 1: Determine the strangeness, S of each particle

• • Since sigma baryon has one s quark, it has S = –1
  • The proton and pion has no strange particles, so they have S = 0

Step 2: Determine strangeness, S on both sides of the equation

• • The sigma baryon has a S = –1 but the meson and proton have a S = 0

–1 = 0 + 0

Step 3: Comment on the conservation of strangeness

• • Since S is not conserved on both sides of the decay equation (only changed by –1), this decay is via the weak interaction
  • This is because S is conserved in all other types of interaction (strong and EM), but isn't always conserved in weak interactions