Weak Decay of Hyperon: Explained!

[vertices]

I attach a solution to a problem. I don't understand the highlighted bit:

I mean, firstly why can we assume that qc (where q is the momentum transfer) is of the order of the hyperons rest mass energy?

And secondly, why is the rest mass energy of the W boson MORE than the rest mass energy of the hyperon. Erm, does this not violate energy conservation? (doesn't the hyperon 'decay' to a W- boson AND a proton?)

Thanks:)

 

[nrqed]

I attach a solution to a problem. I don't understand the highlighted bit:

I mean, firstly why can we assume that qc (where q is the momentum transfer) is of the order of the hyperons rest mass energy?

This is an order of magnitude type of problem. The only energy scale you have at your disposal is th erest mass energy of the hyperon so the momentum transfer must of that order. You would not expect it to be 100 times larger or 100 times smaller.

And secondly, why is the rest mass energy of the W boson MORE than the rest mass energy of the hyperon.

I am not sure I understand.

Erm, does this not violate energy conservation? (doesn't the hyperon 'decay' to a W- boson AND a proton?)

Thanks:)

The W boson is a virtual particle. Energy is conserved at the vertices but it does not mean that the energy of the W boson must be equal to its rest mass energy since it is virtual. I am not sure I understand the problem, sorry.

 

[vertices]

thanks nrqed:)

I am not sure I understand.
The W boson is a virtual particle. Energy is conserved at the vertices but it does not mean that the energy of the W boson must be equal to its rest mass energy since it is virtual. I am not sure I understand the problem, sorry.

Yes, ofcourse, it's virtual so it can violate energy conservation for a little bit as long as it satisfies HUP. I can be really silly sometimes:(

 

[vertices]

Actually, I'm goint to backtrack on this one.

The question is can we really neglect qc? The hyperon could be going ultra relativistically, in which case, it must transfer way more more momentum than its mass*c because it has way more momentum to start off with (this kind of makes sense intuitivly, but I'm not sure how to prove it) - so the qc term in the propagator could exceed the M_x^2c^2 term (could it not?) and hence it would not make sense to neglect it..

 

[Vanadium 50]

The hyperon could be going ultra relativistically, in which case, it must transfer way more more momentum than its mass*c because it has way more momentum to start off with

Whoa!

It helps to study relativistic kinematics before studying particle physics. Making the hyperon go faster is the same as observing an at-rest hyperon from a fast-moving frame. That can't change the underlying physics of the decay.

The same thing happens in elementary physics. Imagine two cars colliding. Observers moving at different non-relativistic velocities will disagree with how much kinetic energy each car has, but they will not disagree on how much energy is transferred during the collision.

 

[vertices]

It helps to study relativistic kinematics before studying particle physics. Making the hyperon go faster is the same as observing an at-rest hyperon from a fast-moving frame. That can't change the underlying physics of the decay.

Yes, ofcourse!

I forgot it was a decay!