The Standard Model of Particle Physics

1. The Standard Model of Particle Physics EM STRONG WEAK

2. Interactions and Decays Forces are responsible for: • Interactions • Decays • Decays are really a type ofinteraction though…

3. 4 1 1 2 2 1 2 4 4 BAM 4 3 3 3 3 1 2 What do I mean by an Interaction? 1 + 2  3 + 4

4. 4 4 4 4 3 BAM 1 1 1 3 3 3 What do I mean by a Decay ? 1  3 + 4 1

5. Conservation Laws Conservation Laws, or alternately, conserved quantities, allow you to place constraints on what types of interactions and decays can or cannot occur.

6. Conserved Quantities Consider the process where two particles A and B collide, and produceparticles C and D: A + B C + D By conserved, we simply mean that the value on the left hand sidemust equal the value on the right hand side. • Some of the most important examples are: • Total energy is ALWAYS conserved – energy cannot be created nor destroyed, only transformed • Total momentum is ALWAYS conserved • Total charge is ALWAYS conserved - cannot simply create net charge

7. Energy conservation means: Energy of particle “A” + Energy of particle “B” =Energy of particle “C” + Energy of particle “D” • Or, in simpler notation, EA + EB= EC + ED Energy Conservation (I) A + B C + D If you knew any 3 of the energies, you could compute the fourth!  So, in such a reaction, you only need to measure 3 particles, andenergy conservation allows you to compute the fourth!

8. Energy Conservation (II) A + B C + D

9. B D A A EB=MBc2 EA=MAc2 ED=MDc2 Energy Conservation (III) A  B + D If particle A has non-zero mass (mA> 0), then: mB < mA mD < mA This must be true, otherwise energy would not be conserved ! This can’thappen ifMB>MA, orMD>MA

10. Energy Conservation (IV) So, energy conservation helps in 2 ways: 1. It allows you to predict the energy of particles which you do not, or cannot measure.2. It may tell you that a process cannot occur, since energy conservation cannot be violated!

11. Momentum Conservation (I) • Momentum conservation is used just as frequently as energy conservation • The classic scenario is the case of neutron decay: p n mP me e neutron at rest decays to a proton + electron

12. Momentum Conservation (II) neutron at rest appears todecay to a proton + electron p n mP me e Total Momentum Before Decay = Total Momentum after Decay P(neutron) = P(proton) + P(electron) 0 = P(proton) + P(electron) We don’t know what the value is, but we know it is NOT zero. In other words the proton and electrons momentum cannot cancel, because they are in the same direction!

13. n This is precisely what lead to the conjecture that there must bean undetected particle, called the neutrino! Momentum Conservation (III) neutron at rest appears todecay to a proton + electron p n mP me e Since both the electron and proton are both moving off to theright, their total momentum cannot be zero.  In other words, this reaction cannot occur, since itwould violate momentum conservation.

14. Charge Conservation (I) Again, let’s consider the process: A + B C + D • Charge conservation implies that: Charge of particle “A” + Charge of particle “B” =Charge of particle “C” + Charge of particle “D” So, if you know the charge of any 3 of the particles, you canimmediately say what the charge of the 4th MUST BE!

15. Charge Conservation (II) A + B C + D

16. Other conserved quantities Baryon Number Conservation When we collide particles together, we find that the number ofbaryons is conserved. A + B C + D • For each baryon, we simply assign B = +1(protons, neutrons,for example) • For each anti-baryon ,we assign B = -1(antiprotons, antineutrons,for example) • Compute the total baryon number on each side and they must be equal!

17. Assume the only particles we know about are: • p, n, p, n, p+, p-, and p0. Baryon Number Conservation (I) A + B C + D

18. Lepton Number Conservation (I) Electron, Muon and Tau Lepton Number We find that Le , Lm and Lt are each conserved quantities

19. m+ e+ + ne +nm  Lm -1 0 0 -1 Le 0 -1 +1 0  Lm -1 0 0 X X Le 0 -1 0 Lepton Number Conservation (II) Let’s look at how this works: p+ m+ + nm  Lm 0 -1 +1 m+ e+ + g

20. n  p + e-+ne Le 0 0 +1 -1  B +1 +1 0 0  Lm 0 -1 0 X X Le 0 0 -1 Lepton Number Conservation (III) More examples: g e+ + e-  Le 0 -1 +1 p+ m+ + ne

21. There is no such thing as“Meson Number CONSERVATION”

22. Summary of Conservation Laws • Conservation of Total Energy • Conservation of Total Momentum • Conservation of Baryon Number • Conservation of Lepton Number • These conservation laws always apply • There are other conservation laws, but they only apply to certain forces. I will expound upon this later…