Weak interaction - half-lifetime of a decay

[Soff]

Hello!
I need help with an exercise about the weak interaction:

How do the mass, the q-value and the vertices depend on the half-lifetime of a decay?

The myon decay has a half-lifetime of 0.0000015 seconds, the neutron decay has a half-lifetime of 607 seconds.

Why is there such a big difference between this two times? Is this because the q-value of a myon is 105MeV while the q-value of a neutron is 0.782MeV? Or has it maybe to do with the involved mas?

Please help me!

 

[arivero]

Hello!
I need help with an exercise about the weak interaction:

How do the mass, the q-value and the vertices depend on the half-lifetime of a decay?

The myon decay has a half-lifetime of 0.0000015 seconds, the neutron decay has a half-lifetime of 607 seconds.

Why is there such a big difference between this two times? Is this because the q-value of a myon is 105MeV while the q-value of a neutron is 0.782MeV? Or has it maybe to do with the involved mas?

Please help me!

Really good exersice. Muon decay is covered in most textbooks, and all the other weak decays except the neutron scale with the quintic power of the mass, in a first approximation. For the neutron, which has a rare decay between two quarks of similar masses in the presence of another one of the same order, the calculation is troublesome and I only know of a textbook covering it, probably Griffith's.

You can argue that the q-value is not the whole history if you consider the decay of the charged pion to muon.