the Goldstone boson
/ GOLD-stohn /
Go back to the marble resting in the circular trough of the Mexican hat. Once it has settled at one spot, there are two very different ways to disturb it. Push it up the steep inner wall of the trough and it costs real energy, and it rolls back — that is a 'stiff' direction. But nudge it sideways, around the flat bottom of the trough, and it costs almost no energy at all, because every point on the ring is equally low. Those two directions correspond to two different particles. The effortless, flat sideways direction corresponds to a massless particle, and that is the Goldstone boson.
The general rule, called Goldstone's theorem, says that whenever a continuous symmetry is spontaneously broken, you automatically get one massless particle for each 'flat direction' that the breaking opens up. These massless particles are Goldstone bosons. In some physical systems they are real, observable particles — for example, pions in nuclear physics behave approximately like Goldstone bosons of a nearly-broken symmetry of the strong interaction. So Goldstone's theorem is not a mere curiosity; it has direct experimental signatures in the hadron world.
But in the Higgs case something special happens. The broken symmetry there is a gauge symmetry, not an ordinary global one, and for gauge symmetries the would-be Goldstone bosons are not left as free massless particles. Instead each one is absorbed — 'eaten' — by a force-carrying boson, becoming the extra third polarization that a massive W or Z needs. So in the Standard Model the three Goldstone bosons that would have appeared never show up as separate particles at all; they are exactly what turn the massless W and Z into massive ones. The phrase 'would-be Goldstone boson' captures this: they are real in the mathematics but never seen on their own.
In the electroweak theory the Higgs field has four parts. Three of them are would-be Goldstone bosons; when the symmetry breaks they are eaten by the W+, W-, and Z to become heavy. The fourth part is the stiff, costly direction up the wall of the hat — and that is the physical Higgs boson, which does have mass and which we can detect.
Three flat directions get eaten by the W/Z; the one steep direction is the Higgs boson.
When a gauge symmetry breaks, the Goldstone bosons are not seen as free particles — they become the longitudinal polarization of massive gauge bosons. They appear as separate particles only when a global (non-gauge) symmetry breaks.