How are the probabilites derived for the outcome of electron and positron high energy collisions using the Alpha Em constant, is the same method used with Alpha S e.g to find the probability of the emission of a gluon ?

For the first part of the question you will have to go read a textbook or attend a course, because it is far too complicated.

 

For the second but, yes, it is calculated in pretty much the same way. There are some subtleties though: for example, the quarks and gluons are representations of SU(3) rather than U(1) so the maths is a wee bit more complex. Also you have to be careful to ensure you are at a high enough energy - since alpha_s changes with energy, it is too large to use perturbation theory below about 1 GeV.

For the first part of the question you will have to go read a textbook or attend a course, because it is far too complicated.

 

Ok, thanks Severian, my current course pretty much said the same thing. I just wasn't content with not knowing the method, I'm sure it's covered in later courses...a couple of years from now, so I'll just have to wait.

If you think you can handle the maths, this course gets as far as cross-sections without using Quantum Field Theory. (It is a bit hand wavey but it gives you the idea.)

Thanks Severian, the maths is a bit beyond my scope for now, but I've saved the course on my hard drive for future reference.