Relation strength interaction and decay time

[da_willem]

There is this characteristic time associated with the decay of particles; ~10^-16s for electromagnetic decay, ~10^-23s for strong decay and >10^-13s for weak decay. Now I know that the decay time is to first order inversely proportional to the coupling constant squared (from a first order Feynman diagram with only a vertex contribution). So from this point of view I 'understand' why decay via strong interactions go faster than via weak interactions, but how can one see this physically?

Short times for virtual particles correspond to high energies by the hup, and I've seen the relation between the virtual particle mass and the interaction range, but why do interactions with exchange of virtual massless gluons go faster than those with exchange of photons which goes faster than the exchange of massive intermediate vector bosons?!

 

[Meir Achuz]

why do interactions with exchange of virtual massless gluons go faster than those with exchange of photons which goes faster than the exchange of massive intermediate vector bosons?!

1. $$\alpha(EM)$$, and $$\alpha(QCD)$$ each vary with energy.
At energies for typical decays (~100 MeV)
$$\alpha(QCD)\sim 100\alpha(EM)$$.

2. The effective weak coupling for typical decays
$$\sim \alpha(EM)(M_p/M_W)^2$$.

 

[sir-pinski]

The reason for the different decay times for different types of interactions lies in the strength of the interaction and the particles involved in the decay process.

Firstly, the strength of an interaction is determined by the coupling constant, which is a measure of how strongly particles interact with each other. The stronger the interaction, the larger the coupling constant. This means that interactions with a larger coupling constant will happen more frequently and therefore have a shorter decay time.

In the case of strong interactions, the coupling constant is very large, which means that the interaction is very strong and happens very frequently. This is due to the fact that the strong force is mediated by massless gluons, which can travel over large distances without losing energy. This allows for a very strong and fast interaction between particles, resulting in a short decay time.

On the other hand, weak interactions have a much smaller coupling constant, which means that they are much weaker and happen less frequently. This is because weak interactions are mediated by massive particles, such as the W and Z bosons, which have a much shorter range compared to massless particles like gluons and photons. This results in a weaker and slower interaction, leading to a longer decay time.

The difference in decay times between strong and weak interactions can also be understood from a quantum mechanical perspective. According to the Heisenberg uncertainty principle, there is an inherent uncertainty in the energy and time of a particle. This means that particles with a shorter lifetime will have a larger uncertainty in their energy, which corresponds to a higher energy state. This is why particles that decay via strong interactions have higher energies compared to those that decay via weak interactions.

In summary, the shorter decay time for strong interactions compared to weak interactions can be attributed to the larger coupling constant, the massless nature of the particles involved, and the inherent uncertainty in energy and time at the quantum level.