# How do W and Z particles conserve energy?

I have been looking at the Beta decay process and can't see how energy is conserved. The W boson, for example, is many times more massive than all of the other particles together. But how does that additional mass/energy come about and where does it go to? I'm guessing that it gets its mass from the Higgs field and or that it borrows its mass in accordance with the uncertainty principle.
I have found loads of sources describing Beta decay but none addressing energy conservation when the event is described in terms of Bosons. Thanks to anyone who replies.

## Answers and Replies

The_Duck
The W boson involved in beta decay is "virtual." Virtual particles can have any mass. The mass of the virtual W in beta decay is not 80 GeV but is determined by the requirement that energy be conserved.

However, the probability per unit time of producing a virtual W boson of a given mass is smaller the farther that mass is from 80 GeV. The mass of the virtual W boson in beta decay is quite far from 80 GeV, so the probability per unit time of beta decay is thus very small. All low-energy processes involving W bosons are suppressed in this way. This is why interactions mediated by W (and Z) bosons were named the "weak interaction."

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dauto
The mass doesn't even have to be a real number. It can be an imaginary number as well

Thank you but let me get this clear.If I'm understanding this correctly the W takes a mass such that energy is conserved, so it can have different masses for different events ( I can't think of other events involving Ws or Zs but I will do a search). Why then do the data tables quote a single value for the mass of each particle?

RGevo
These are on shell masses. Or pole masses. For real particles

If you look at the data group you will actually see many mass definitions. For example you may see the MSbar mass etc.

So not only can particles not have their pole mass in an interaction (when they are virtual) but their mass also depends on the theoretical treatment.

RGevo
An example is Higgs (126 GeV) which decays to two z bosons (91 GeV) which was one of the discovery channels (4 charged leptons).
One of the z bosons has to be off shell, so more like 35 GeV for example. This is fine since it can be virtual and produce two real charged leptons which are detected.

Hope this helps

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