Note: I very well understand spontaneous symmetry breaking of global symmetries and the Higgs mechanism.

I want to know to what extent the Standard Model vacuum is made of a Bose-Einstein condensate of Higgs bosons and what evidence (or intuitions) we have to claim that. For example, for superconductors (typical example of Higgs mechanism in condensed matter), Feshbach resonance has been used to detect the Bose-Einstein condensation of Cooper pairs. Also, in the case of the Bose-Einstein condensation of Rubidium atoms first observed in the mid 1990s, there is a very well-known graph showing the velocity distribution of the atoms, with a peak at zero velocity. These observations make it clear that there were a large number of bosons (Cooper pairs and Rubidium atoms, respectively) occupying the ground state (this is what defines Bose-Einstein condensation). What is the theoretical argument or observation for the existence of a condensate of Higgs bosons in the Standard Model?

Also, in particle physics, one usually identifies a particle as an excitation from the vacuum state, how can the (true) vacuum be full of particles?

Note: Please, please, please, don't tell me that the W and Z bosons (and other particles) acquire mass by interacting with a Higgs condensate. I know the Higgs mechanism.

  • $\begingroup$ Feshbach resonance was not used to detect BEC of Cooper pairs, this seems like a misconception. It was a way to tune interactions between atoms, in cold atom settings. Superconductivity in metals was discovered and understood long ago before Feshbach resonance was realized experimentally, so you may ask to what extent we know there is BEC of Cooper pairs, and essentially that is the Meissner effect (or the Higgs mechanism). $\endgroup$ – Meng Cheng Sep 15 '15 at 23:56
  • $\begingroup$ @MengCheng Of course superconductivity was understood and discovered long before. I don't know how you could understand that from my question. But observing superconductivity, the Meissner effect or massive Z and W bosons doesn't imply observing the occupation of a ground state by a large number of particles. If you could elaborate it further, I could perhaps understand why you see these two phenomena as equivalents. I can see how the formation of a Bose-Einstein condensate of Cooper pairs (Higgs bosons) """implies""" the Anderson-Higgs mechanism. But this doesn't make both things equivalent. $\endgroup$ – Diego Mazón Sep 16 '15 at 0:19
  • $\begingroup$ For superconductivity, there are other evidence of the macroscopic quantum coherence, such as the Josephson effect, which in my opinion is more striking. These are not direct observation of ground state occupation (and in fact, Cooper pairs in BCS superconductors are not bosons, so the picture of a large number of bosons occupying the same state is not mathematically precise), but such highly nontrivial consequence that truly reflects the phase coherence. $\endgroup$ – Meng Cheng Sep 16 '15 at 1:35
  • $\begingroup$ For the Higgs mechanism, I would say the Meissner effect is basically defining superconductivity of charged bosons (to be more precise, charged bosons coupled to the gauge field). $\endgroup$ – Meng Cheng Sep 16 '15 at 1:35
  • $\begingroup$ @MengCheng Before we go on, let's agree on definitions. To me, the property defining a Bose-Einstein condensate of bosons is the occupation of the ground state by a large number of particles. What property defines a BE condensate to you? Don't tell me Meissner or Josephon effect because BE condensation genuinely takes place in another systems such as dilute gases, where it was first experimentally encountered. $\endgroup$ – Diego Mazón Sep 16 '15 at 2:02

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