Rabu, 14 Maret 2012

Higgs or BEEEH boson?

Most of you must have noticed a certain curious occurrence at the Moriond conference:
during the session featuring the latest experimental results on the Higgs boson searches the name Higgs did not appear at all. Instead, the speakers were discussing a mysterious SM scalar boson (?) or on a BEEEH boson (???), the latter name apparently inspired by a herd of sheep grazing outside the conference room. The most logical explanation is that the Moriond attendants have been collectively hypnotized and conditioned to say BEEEH every time they meant Higgs (I saw a similar trick at a hypnosis show in Las Vegas). That theory would also explain why only the strongest characters continued referring to the Higgs. The alternative explanation -- that someone at the conference had an idea to rename the Higgs boson into a BEEEH boson and talked to it so many otherwise reasonable scientists -- sounds utterly implausible. That's because the idea
  1. is obviously silly,
  2. betrays ignorance.
I guess there's no need to elaborate too long on why it's silly. In physics and mathematics communication heavily relies on established conventions. Like, we all agree the result of adding 2 and 2 should be called 4, although there is no deep reason for it; we could call 11 or 666 depending on the moon phase, and that would be perfectly consistent as long as we were careful to preserve the axioms of the addition group. However calling it 4 at all times makes our life easier and helps avoiding confusion. By similarly established conventions, spontaneous breaking of a local symmetry in a quantum field theory is referred to (somewhat unfairly) as the Higgs mechanism, while a spin-0 particle excitation often associated with that breaking is called (deservedly) the Higgs boson. This is how it's been for the last 40 years and this is how it'll remain.

The ignorance count deserves a bit longer explanation, as it is related to a misunderstanding that is not so uncommon. The main point is that one should clearly distinguish the Higgs mechanism from the Higgs boson; the two are often intricately related but formally they are distinct concepts, in particular the former may well exist without the latter.

The Higgs mechanism, or spontaneous gauge symmetry breaking, occurs when a Lorentz-invariant Lagrangian is also invariant under a local symmetry group with the corresponding set of gauge bosons, however some or all of these gauge bosons are massive. Such a theory still obeys a local symmetry, albeit non-linearly realized. We can describe it in a gauge invariant way with the help of a set of unphysical scalar particles called the Goldstone bosons who have a derivative mixing with the massive gauge bosons. For the public, we say that each massive gauge boson eats a Goldstone boson so as to acquire mass and another internal degree of freedom associated with it. For example, the W and Z boson must eat a triplet of Goldstone bosons. The ensemble of these phenomena is referred to as the Higgs mechanism, although more properly it should be called the Anderson-Nambu mechanism (who grasped the general idea, inspired by the related phenomenon of superconductivity in condensed matter physics), or the Brout-Englert-Higgs mechanism (who first understood its workings in the context of Lorentz invariant quantum field theories). However, the name of Higgs somehow stuck, probably because it's cute, or maybe because we all hate Anderson for cutting the throat of the SSC.

One important point is that a confirmation of the Higgs mechanism is not what the LHC is now after. Indeed, the fact that the fundamental interactions obey to a very good precision the local SU(2)xU(1) symmetry which is spontaneously broken to the electromagnetic U(1) was firmly established by the LEP experiment back in the 90s.

The LHC is now after the Higgs boson, which is something else. It turns out that in spontaneously broken gauge theories certain amplitudes, in particular those of the massive gauge bosons, grow with the center-of-mass energy. As a consequence, the theory cannot remain perturbative up to an arbitrarily high energy scale. In the Standard Model without the Higgs boson the loss of perturbativity would happen already at 1 TeV. Thus, there must be something that regulates the high-energy behavior of the W and Z scattering amplitudes. Out of several possibilities, the simplest one is to introduce an isospin-0 scalar resonance with the coupling to the W and Z bosons proportional to their masses. Voila the Higgs boson. It's not a unique possibility, but it's the one that is clearly favored by current experimental data.

Now, the Higgs boson first appeared in the paper of, surprise, Higgs in 1964, while it was completely missed in the earlier paper of Brout and Englert, and swept under the carpet in the paper by Guralnik, Hagen, and Kibble. In fact, the importance of that degree of freedom was not realized until a few years later, thanks to the papers of Higgs and Kibble, and ultimately thanks to papa Weinberg who incorporated it in the Standard Model in 1967.

In summary, if you hear someone speaking about the Brout-Englert-Higgs mechanism, that's fine, he's just trying to be fancy (and has a grudge against condensed matter). However, if you hear him talking about the BEEEH boson, that not only sounds funny but is also a good indicator that he has little idea about the subject.

Update: I see that I should clarify that this post is not about who should get the Nobel prize; that's a longer discussion. I just think that both esthetic reasons and historical truth dictate that we should continue to call the particle the Higgs boson.

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