Method to know if a reaction is allowed

[Xico Sim]

Hi guys. This is my first post here. Here it goes.

I'm attending an introductory course on particle physics.
By now, I'm supposed to know how to find out if a given reaction, say
ν_μ+p→μ⁺+n
(for example) is possible or not.
Unfortunately, the rules by which a reaction must abide are still foggy for me. I can't find anywhere a complete set of steps which I can follow to find out if a reaction is allowed or not.
This is what I'm asking: I'm asking for a method which leads me to the answer to the question: "Is the reaction possible?". Ideally, the method should be written in the form:

1. Are the quantities A, B and C conserved? If they are not, skip to point 5. If they are, go to the next point.
2. Are the quantities D and E conserved? If not, the reaction is impossible. If they are, go to the next point.
3. ...
4. ...
5. ...
6. ...

And so on.
Thank you in advance!

EDIT: I also want to know what type of interaction (strong, weak or EM) is predominant.

 

[mfb]

Charge, baryon number and lepton number conservation are the important things. Energy and momentum conservation for particle decays (=a single particle on the left side) or if you know the total initial energy. If all those work out, the reaction is probably possible. It can be unlikely, but it should be possible.

One notable exception: a massive spin 1 particle cannot decay to an even number of massless spin 1 particles.

 

[Xico Sim]

Charge, baryon number and lepton number conservation are the important things. Energy and momentum conservation for particle decays (=a single particle on the left side) or if you know the total initial energy. If all those work out, the reaction is probably possible. It can be unlikely, but it should be possible.

One notable exception: a massive spin 1 particle cannot decay to an even number of massless spin 1 particles.

I believe this list of conserved quantities is too incomplete for my interests... For example, there are quantities which are conserved in one type of interaction but are not conserved in another type of interaction. This is where it gets messy, I think. And I do need to know these subtleties... I've edited my question to include them.

 

[mfb]

Well, if you ask for specific interactions then you have more conservation laws for the strong and electromagnetic interaction, but that is a different question.

Those two interactions don't change particle types, so the number of particles of each type (minus the number of antiparticles) is conserved. Parity and charge conjugation come up as additional conservation laws. If anything appears/disappears that is not a quark, it cannot be the strong interaction alone. If neutrinos appear/disappear, it has to be the weak interaction.

The strong interaction is much stronger than the electromagnetic interaction, which is stronger than the weak interaction. If something is possible via the strong interaction, it will be dominant. Same for things that are impossible via the strong interaction but possible via the electromagnetic interaction.
That rule has an exception again: the decays of a some charmonium and bottomonium states have some significant contribution from the electromagnetic interaction.

 

[Xico Sim]

Thank you, I think I'm starting to understand.
Let me try to write down a set of steps to find if a reaction is possible and what is the predominant type of interaction. I'll start in this post and then try to complete it:

1. Check if the charge Q, the lepton numbers L_e, L_μ, L_τ and the baryon number are conserved. If at least one of these aren't conserved, then the reaction is not possible.
2. If it is a decay, check if the linear momentum and the energy are conserved. If not, the reaction is impossible.
   
3. Check if the Strangeness S is conserved. If not, the reaction cannot have a contribution from the strong interaction --> it is "at most" electromagnetic.
4. Are there photons involved? If there are, it is certainly EM.
5. Are there neutrinos involved? If there are, it is certainly weak.
6. If leptons are present, it cannot be Strong.

Can you please help me complete this list of steps? I'm not aiming for the most general case, here: I'm sure that would be full of subtleties.

 

[mfb]

Check if the Strangeness S is conserved. If not, the reaction cannot have a contribution from the strong interaction --> it is "at most" electromagnetic.

It is not just strangeness. And the electromagnetic interaction cannot change strangeness.

Are there photons involved? If there are, it is certainly EM.

Can be EM+weak together.

 

[ChrisVer]

My list:
1. check Q conservation
2. check Baryon number conservation
3. check Lepton numbers conservation
4. Check energy/momentum conservation if you have 1 particle decay.
If all of the 4 above are conserved the process is possible..

Once the process is found to be possible, you can start thinking of what it might be... but on this stage, there can be ambiguities; there can be more than 1 interactions responsible for some process. One example is the following:
$e^- e^+ \rightarrow \mu^+ \mu^-$
Which can happen from both the electromagnetic (via a photon) and the weak (via a Z boson) interactions.

However indeed; there are some cases which by definitions can rule out certain interactions... leptons by definition are the fermions that cannot feel the strong interactions. So if you see leptons you know that you had at least one EM or Weak interaction (however there can still be strong interactions but they have nothing to do with the leptons)... these are in loop processes [like gluon penguins].
Neutrinos also show you that there is at least 1 W (weak interaction)...the other way around is not true... the above example of the electron/positron interaction is such...Also the Ws don't have to decay into a lepton (+neutrino), but they can decay to quarks/hadrons.
Also an additional rule can come from checking the Parity and CP... if they are not conserved, it's a weak interaction.

 

[Xico Sim]

Thank you for your clear answer! One question:

Once the process is found to be possible, you can start thinking of what it might be... but on this stage, there can be ambiguities; there can be more than 1 interactions responsible for some process. One example is the following:
$e^- e^+ \rightarrow \mu^+ \mu^-$
Which can happen from both the electromagnetic (via a photon) and the weak (via a Z boson) interactions.

If I'm only interested in the dominant interaction, in this case I only consider the EM force, right?

 

[mfb]

However indeed; there are some cases which by definitions can rule out certain interactions... leptons by definition are the fermions that cannot feel the strong interactions. So if you see leptons you know that you had at least one EM or Weak interaction (however there can still be strong interactions but they have nothing to do with the leptons)... these are in loop processes [like gluon penguins].

Not necessarily loop processes. Consider $D^+ \to K^- \pi^+ \mu^+ \nu_\mu$ (~4% branching fraction). It is a tree-level diagram that needs the strong interaction to produce an up/antiup quark pair.

If I'm only interested in the dominant interaction, in this case I only consider the EM force, right?

The electromagnetic interaction, unless the center of mass energy is close to the Z mass of 90 GeV, then the Z is dominant.

 

[Xico Sim]

Ok, so I'm going to try to organize a list of steps to find out if a reaction is allowed, and what is the dominant interaction. If anyone sees somthing wrong or incomplete, please tell me!

Steps to find out if a reaction is allowed

1. Check if the charge Q is conserved.
   
2. Check if the lepton numbers L_e , L_μ , L_τ are (separately) conserved.
   
3. Check if the baryon number A is conserved.
   
4. [usually relevant only for decays] Check if the energy E and linear momentum p are conserved.

The above-mentioned quantities are conserved if and only if the reaction occurs.

Finding the predominant type of interaction
Having determined that a certain reaction occurs using the steps above, we may want to know what is the predominant interaction.
If the process can happen through the strong interaction, the dominant process is strong.
If the strong interaction plays no role but the EM interaction does, then the dominant process is electromagnetic.
The dominant process is weak iff both strong and EM processes are forbidden.
Here is a method to determine what is the dominant process. Answer these questions:

1. Are there leptons involved?
   
2. Are there photons involved?
   
3. Are there neutrinos involved?
   
4. Is parity violated (not conserved)?
   
5. Is charge conjugation violated?
   
6. Do quarks change flavour?

We now interpret our answers:

• If all of the questions got “No” for an answer, then the process is predominantly strong. (If at least one got “Yes” as the answer, strong processes are not allowed)
• If 3., 4., 5. or 6. got “Yes” as the answer, then the dominant process is weak.
• If these two facts (bullets) above did not give you an answer, then the dominant process is EM.

 

[mfb]

The quark numbers got lost somewhere, e.g. if we have a transition b-quark -> something without b-quark it is always weak.

 

[Xico Sim]

The quark numbers got lost somewhere, e.g. if we have a transition b-quark -> something without b-quark it is always weak.

I've edited the last bullet list to include that case. I think it's correct now.

 

[Xico Sim]

And what about isospin? I'm not shure what we can do about it... If the total isospin I is not conserved, then the interaction is not strong? But I_z need not be conserved for the strong interaction, right?

 

[ChrisVer]

Procceed to add any further information and you will create a monster... I believe things as they are now, are fine [and maybe it can become less complicated]...afterall I don't like too many ifs...
In fact if you want to get used to which process is possible or not, I'd recommend not to learn parrot-like a huge list but rather start drawing Feynman diagrams of possible processes and see what you need to put in order to achieve the desired result... try doing the same with a process that violates for example the electric charge and you will see that you can't come up with a Feynman diagram for them...
Then the only thing you have to know is that photons couple to charged particles, gluons couple to quarks, and W,Z bosons couple to all the fermions; W can change the quark flavors (this is coming from charge conservation for example, an u is positively charged and if it goes to a d that is negatively charged it should "shoot away",not physically but on the sketch, a W+ ..)...since Zs are neutral they are like the photons in most of the diagrams meaning they can have a fermion+antifermion on the vertex [in contrast to Ws that have a fermion+another antifermion ] , with the addition that Zs can couple to neutrinos.
The only thing you can't see by following the flow in a Feynman Diagram and you have to rethink everytime is the possibility to violate energy/momentum... for example you can easily make a FD that shows a $\pi^0 \rightarrow K^+ K^-$ transition even with a gluon, but that's impossible to happen because the pion is too light (it's the lightest of mesons)...

 

[Xico Sim]

Procceed to add any further information and you will create a monster... I believe things as they are now, are fine [and maybe it can become less complicated]...afterall I don't like too many ifs...
In fact if you want to get used to which process is possible or not, I'd recommend not to learn parrot-like a huge list but rather start drawing Feynman diagrams of possible processes and see what you need to put in order to achieve the desired result...

I agree. I'm studying Feynman diagrams now, and I see what you mean.