4.44 Particle Interaction Equations

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

• Quantum numbers such as Q, B and L 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

Step 1: Determine conservation of charge Q

• • There are two protons on the left hand side
  • There are two protons on the right hand side, with a positively charged pion (Q = +1) and an antiproton (Q = –1)
  • Therefore charge is conserved, because:  

1 + 1 = 1 + 1 + 1 + (– 1)

Step 2: Determine conservation of baryon number, B

• • There are two baryons on the left hand side, each with a baryon number B = +1 (protons are baryons) 
  • On the right hand side
    • Two protons each with baryon number +1
    • One pion, with a baryon number 0 (it is a meson)
    • One anti-proton with a baryon number –1 
  • Therefore baryon number is not conserved, because:  

1 + 1 = 1 + 1 + 0 + (– 1)

Step 3: Conclude whether this reaction is permitted

• • This reaction is not permitted
  • Because baryon number is not conserved