Where does the mass of a W boson come from in beta decay?

[Dario]

TL;DR Summary

In beta decay an electron and neutrino are shot out of an atom. I was under the assumption that those particles decay from a w boson, but if that were the case, the atom would have to produce a lot of mass and then the mass would have to be converted into energy and carried away by the electron and neutrino. I am very confused.

During beta decay an electron and neutrino are emitted at very high speeds. I thought that the electron and neutrino were the product of w boson decay but I recently learned w bosons are over 80 GeV worth of energy. My question is, where does this mass come from? I know that atoms get enough excess energy from decay to create an electron and neutrino but how could they have enough energy to create a w boson? And this only gets worse with w+ decay

 

[Orodruin]

The W boson exchanged in the process is a virtual particle. It is never actually produced.

In some ways this is similar to quantum tunneling, where a particle can cross an energy barrier even if its energy is not high enough.

 

[haushofer]

As mentioned, the W-particle is "virtual" in this Feynman diagram. It also shows how deceiving these Feynman diagrams can be. If you see such a decay, as here,

https://nl.wikipedia.org/wiki/W-boson

you only see the leading term in an infinite series, not a physical process which can be directly measured. Of course, the in- and outstates are fixed, but in between there are infinitely many contributions.

 

[ohwilleke]

To be slightly more explicit, in quantum mechanics, as a general rule, conservation of mass-energy must only be satisfied by the end state relative to the beginning state. What we consider to be a necessary intermediate part of the process (even though it isn't directly observable) can "borrow" mass-energy, so long as it is "repaid" by the time that the process ends without being impossible. In a particle physics context, we call intermediate particles that don't persist into the end state that require such a borrowing "virtual particles."

Closely related are the concepts of "on shell" and "off shell":

In physics, particularly in quantum field theory, configurations of a physical system that satisfy classical equations of motion are called "on the mass shell" or simply more often on shell; while those that do not are called "off the mass shell", or off shell. In quantum field theory, virtual particles are termed off shell because they do not satisfy the energy–momentum relation; real exchange particles do satisfy this relation and are termed on shell (mass shell).

The mass of virtual particles is not irrelevant, however. The probability of a possible quantum interaction happening is impacted by the masses of the virtual particles involved in the interaction.