# Weak interaction - half-lifetime of a decay

1. Jan 28, 2007

### 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?

2. Jan 30, 2007

### arivero

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.

Last edited: Jan 30, 2007