Unraveling Hadronization: Understanding Particle Decay and Feynman Diagrams

[simon96c]

Hello everyone,
I've been wondering for a while how is it possible to determine which decays are possible from a particle or, given a decay be sure that the given decay is possible and hence draw a Feynman diagram of it.
I know I have to take into account conservation charge, energy conservation, baryon and lepton number etc.. but I feel like I'm missing something, as I'm not too sure about it.

(this is technically for homework, but I posted it here because I'm trying to understand the topic rather than get the work done)

Thanks to everyone who answers, sorry if the question is a bit silly :)

 

[mfb]

Conservation of angular momentum
Landau-Yang theorem for uncharged spin 1 particles

If all those things are conserved, the decay is possible.

 

[simon96c]

This may seem really silly from me, so I apologise in advance: how do I confirm that the energy-momentum is conserved? I clearly can't consider the rest mass only as there must some energy "used" to create the bonds to form the particles.

Plus, I don't get why for particles such as the neutral pion or rho meson only part of the quarks seem to be considered in the diagrams!

Thanks for the reply :)

 

[mfb]

Which bonds to form particles?

The sum of masses of the decay products has to be smaller than the mass of the decaying particle. That is all. The mass of hadrons includes their binding energy already.
If you care about angular distributions and so on, you also have to consider the energies and momenta in the lab frame, but that is a different topic.

Plus, I don't get why for particles such as the neutral pion or rho meson only part of the quarks seem to be considered in the diagrams!

The particles are superpositions of different quark contents, for illustrative purposes one of them is picked.

 

[simon96c]

Ok, I think I get it now!
By bonds I meant the binding energy, it's just that I think I have to clear my mind on the subject on a more general basis.
Would you be able to suggest me a good introductory book for particle physics? Everything I have found right now it's either too simple (as in popular science book) or too advanced for what I need.
I'm a first year undergrad, but never did particle physics in high school (which is the case for many of the students of my course)

 

[mfb]

Would you be able to suggest me a good introductory book for particle physics?

I know a good German one. English: no idea. There are some standard textbooks, of course, but usually they require knowledge about quantum mechanics and classical mechanics (Lagrange/Hamilton formalism and so on).

 

[simon96c]

I see.
Just one last question:
Why isn't a decay like W⁺ → π⁺π⁰ allowed? If I have considered all the quantities that need to be conserved correctly (which could easily not be the case) it should work, but still we know that it isn't allowed and I cannot find trace of it among the possible decays.

Sorry for all the silly questions ^^"

 

[mfb]

It is allowed, but it is very unlikely. The decay would be $W^+ \to u \bar d$, those quarks then hadronize. The production of exactly two pions is not impossible, but really rare.

 

[simon96c]

Wouldn't I need two pairs of quark-antiquarks (one for each particle)? Or am I missing something?

 

[mfb]

That is the hadronization part.

 

[vanhees71]

I think it's fair to say that we don't understand hadronization from first principles. The first sentence in the above cited Wikipedia article is already at least sloppy. If you could create "free quarks or gluons" there were no confinement and quarks and gluons could be observed as asymptotic states. To the best of our knowledge that's not true.

There are of course some effective models to describe what's going on in hard reactions involving hadrons. You define "parton distribution functions", which can only be measured and describe the hard part of the reaction with "quasi free quarks and/or gluons (partons)" with perturbative quantum chromodynamics (pQCD). Then you use "fragmentation functions" (in heavy-ion collisions also coalescence or kinetic recombination models) to describe the hadronization of the "quasi free partons". The parton distribution functions and fragmentation function depend on the treatment of the hard pQCD part and are only empirically given. They are not derivable from first principles of QCD. What, however can be derived are certain dependences on the energy-momentum scale of the hard collision with renormaliation-group methods (DGLAP, BFKL equations).