The traditional approach to interactions is to imagine hos to define the system without interaction first.

 

We discussed how Newton needed to carefully imagine momentum conservation as a natural state of motion. We recognize that indeed there is no such place. Everywhere in the universe we will discover some remnants of gravity, E&M and the other forces. It is impossible to actually achieve the state of no interaction physically but one can imagine it and it plays a central role in our understanding of physics.

 

In QM this is referred to as the unperturbed system. It was discovered that in dealing with the E&M interaction one could imagine an unperturbed system and then add a small interaction in such a way that to good approximation a solution for the perturbed system could be found.

 

This approach can be applied to systems where some of the interaction is treated completely and a different part is treated at a perturbation. The hydrogen atom is a good example. Because one can mathematically find the solutions for the problem of a bound electron under the influence of a positive proton, the problem can be split neatly:

·       bound electron and the associated energy levels and wavefunctions

·       perturbing E&M field that causes a transition eg 2pè1s.

 

In order to carry out realizable predictions there is a constant struggle to isolate what one takes as the unperturbed, perturbed for both the interaction and therefore the states.

 

This lecture covered

  • Flavor mixing and the Cabbibo angle
  • QCD soft vs hard processes

 

QCD soft vs hard processes

In treating the strong interaction we need to manage the problem of the strength of the gluon exchange which doesn’t lend itself to some type of expansion into a series of terms that become less and less important.  To do this we compare intial an final states that are not quark states but bound quark states. To manage the QCD strength we require that all intial, final and virtual (intermediate states) are color singlets. For us this simple means we require quarks to move together as  or . These can be made into color singlets although at this point it will not be obvious how or why.  This requirement will restrict the way we can build Feynman diagrams to represent the strong interaction.

 

Constructing diagrams:

  1. Determine the applicable force.
    1. hadrons interact dominantly via QCD (need to build meson exchange)
    2. leptons and other charged particle interact dominantly via QED (γ)
    3. Flavor changing or parity violating interactions are weak (W+, W-, Zo)
  2. Double check conservation laws followed by the interactions and the field properties.
    1. weak interaction can be charge changing (W+, W-) neutral currents (Zo)
    2. Charge conservation always holds
    3. QCD cannot change flavor
  3. Use the currents and interaction fields to transition the intial to final state.