# Why in general speaking the mass of gauge boson is zero?

## Main Question or Discussion Point

Why in general speaking the mass of gauge boson particle is zero(except W,Z bosons)?Because if we consider the self-energy of the bosons,we might think of the mass of gauge bosons.
Thank you very much for your kind helping.

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Why in general speaking the mass of gauge boson particle is zero(except W,Z bosons)?Because if we consider the self-energy of the bosons,we might think of the mass of gauge bosons.
Thank you very much for your kind helping.
Well, both EM and gravitational radiation propagates at the speed of light; that means that their force carrying vector bosons must travel at the speed of light, therefore their rest mass must vanish. There are other, deeper, more mathematical reasons as well, but this I think is the simplest and most straightfoward explanation.

But how about gluon and why we know the speed of graviton is c(meaning speed of the propagation of gravity interaction is c)?

tom.stoer
But how about gluon and why we know the speed of graviton is c(meaning speed of the propagation of gravity interaction is c)?
We can analyse the classical, linearized field equations and we find a standard wave equation with

$$\partial_0^2 - \nabla^2$$

This is interpreted as a free, massless field propagating with c (plus interaction terms which have been neglected due to linearization)

I think the better way to think of it is 'why do the W and Z bosons have mass'? Gauge bosons are always massless unless something special happens to give them mass.

The reason guage bosons are massless is exactly because they are GUAGE bosons. That is they obey a guage symmetry which forbids mass terms in the Lagrangian (since we require the action to be guage invariant - not change under guage transformations).

However the mass terms in the Lagrangian only represent tree level masses. It is, as the question asks, not so obvious that self energy diagrams would not contribute to the guage boson masses. The fact that they don't is again down to guage invariance but is more subtle and is seen via the Ward identities (themselves a result of guage invariance). This is all nicely explained on pages 20-23 of Willenbrock's excellent review of "Symmetries of the Standard Model".

The fact that the Ws and Z can have masses is because the guage symmetry is spontaneously broken by the Higgs vev, but that is a whole other story...