Allowed Reactions: Checking Rules & Mass Conservation

[genloz]

Is there an ultimate rule that can tell you what to check for to see if a reaction is allowed? I'm quite confused about what to check for in each situation? Is lepton number always conserved? How do you know whether there's enough energy to produce a given mass (eg e+e- -> tau+tau- isn't allowed due to mass conservation but how do you know how much energy is released when a particle and its antiparticle annihilate?) There seems to be too many things to check for which aren't organised logically and simplistically anywhere...

 

[malawi_glenn]

Funny, i have a table which helps me a lot to classify decays and reactions as possible or not. Plus CM energy.

So in my table i have one column for each force. I.e one for EM; one for weak, one for Strong.

Lepton and baryon # conservation is an emperical rule, and now you try to find out the lepton and baryon assymetry in the universe, since we live in a universe that has matter..

So your reaction $$e^+ + e^- \rightarrow \tau ^+ + \tau ^-$$ is possible if you have the right CM- energy, i.e CM energy > 2*restmass(tau-lepton)

 

[mjsd]

yeah, there are quite a lot to check sometimes, but the usual ones are
conservation of CM energy, charge, angular momentum (spin).
lepton and baryon number are conserved in most reactions (exceptin some non-perturbative reactions, like sphalerons)
it is probably not as difficult to decide whether something can happen, it is how likely (branching ratio) things will happen that may give you more problems.

 

[genloz]

okay, that's very useful.. thanks... But these reponses made me think of another question... how do you know when a weak interaction will violate P or CP?

 

[blechman]

okay, that's very useful.. thanks... But these reponses made me think of another question... how do you know when a weak interaction will violate P or CP?

Weak nuclear interactions (almost) always violate P. If the decay involves a W-boson, it violates it maximallly; if it involves a Z-boson, it could violate it or conserve it.

CP is much harder. The first thing that needs to happen for CP-violation is that the coupling constant must be complex (have a nontrivial phase). However, this is a necessary but not sufficient condition. The other condition is that there has to be two processes that occur that can interfere with each other, each with *different* phases. In the Standard model, this typically means that there are two Feynman diagrams (typically involving loops with W-bosons and all three generations of quarks) that contribute to the same process. This is how CP-violation in $K-\bar{K}$ and $B-\bar{B}$ mixing work, for example.