Strong versus weak interactions

[RedX]

For the process where two neutral pions turn into two charged pions, I noticed that this can occur through both the strong and weak interactions. Through the strong interaction it is a 4-pion vertex, and through the weak interaction it involves a virtual W-particle. If I were asked on a quiz what force is responsible for two neutral pions turning into two charged pions, would the answer be strong force, because the coefficient is proportional to 1/(100 MeV)^2, as opposed to 1/(80 GeV)^2 for the weak force?

Similarly, I noticed processes where a nucleon can change into another nucleon can occur through both the strong and weak interactions, with intermediary particles being either a charged pion or W-particle, respectively. So which interaction would I say is responsible for a change in the nucleon?

 

[Bob_for_short]

That which is the most probable, i.e., via the strong coupling mechanism. Just make sure that the process is not forbidden due to some conservation laws.

 

[RedX]

That which is the most probable, i.e., via the strong coupling mechanism. Just make sure that the process is not forbidden due to some conservation laws.

I have a question that is kinda of related. Take the process where a neutron turns into a proton. This can be done via the weak interaction, where there is also an electron and antineutrino that flies out. Or it can be done via the strong interaction, where the negative pion flies out.

The weak decay seems to have a very small chance, proportional to Fermi's constant. The strong decay seems to be much more probable according to the Goldberger-Treiman relation. In fact, the strong decay seems to be so ridiculously more probable than the weak decay, that there shouldn't even be talk of weak decay!

Am I correct in saying that the reason the weak decay (beta decay) is talked more about is because it happens more? And would the reason that it happens more be related to statistical mechanics, since quantum mechanics seems to favor the strong decay? The pion is a lot heavier than the neutrino and electron, so energetically does beta decay happen as opposed to pion decay because of statistical mechanics rather than quantum mechanics?

 

[Bob_for_short]

Am I correct in saying that the reason the weak decay (beta decay) is talked more about is because it happens more?

Yes, the weak decay is, in fact, the only process allowed energetically.

And would the reason that it happens more be related to statistical mechanics, since quantum mechanics seems to favor the strong decay? The pion is a lot heavier than the neutrino and electron, so energetically does beta decay happen as opposed to pion decay because of statistical mechanics rather than quantum mechanics?

No, as soon as the sum (pion mass + proton mass) exceeds the neutron (i.e., initial) mass the strong decay is forbidden by the energy conservation law. It may happen if there is a projectile of sufficient energy and there are no other conservation laws to obey, for example barion, lepton numbers to be conserved, etc.

 

[RedX]

Ah, got it. I forgot about energy conservation. I thought the pion was pretty much massless, because that is part of how the chiral Lagrangian is derived, the pion as a pseudo-goldstone boson resulting from broken SU(2) axial flavor symmetry breaking in the quark condensate. But it achieves some mass when you give the u and d quarks mass, through the Gell-Mann-Oakes-Renner relation. Evidently, this mass, although it is said to be small, is still much larger than the mass difference between the proton and the neutron, which are really close in mass.

So it looks like it'll be beneficial to memorize some masses.