*125 GeV particle*, sometimes a

*scalar boson*(as opposed to scalar fermions), and most often a

*Higgs-like boson*. This caution was understandable at the early stage, given the fresh memory of faster-than-light neutrinos. However, since it's been walking and quacking like a duck for more than half a year now, there's a discussion among experimenters when they will be allowed to drop the derogatory "-like" suffix.

So, at which point a particle becomes to a Higgs?

One issue discussed at length in this context is the spin. This is however moot as we already know with great certainty that the answer is

So we're left with a spin-0 particle as the only reasonable option. But zero spin is still not equivalent to a Higgs boson. In particular, a resonance in the diphoton channel - where the detection remains most significant - is only a circumstantial evidence for the Higgs nature of the particle. Indeed, any fool can couple to 2 photons or 2 gluons even if it has nothing to do with electroweak symmetry breaking. So let's define here, once and for all, what is a Higgs boson. Sometimes the Higgs is described as the one that

*gives mass*to other particles, or the one that has a

*vacuum expectation value,*but that cannot be unambiguously defined (one can always rewrite the theory such that the scalar has no vev at all, at the cost of the symmetries being non-linearly realized). Instead, the best definition is based on the couplings of the particle: a Higgs boson is a scalar that

*couples to mass*. To be more specific, for the couplings to W and Z bosons in the lowest order of the effective theory expansion we can write the following interactions:

which couple the

*h*scalar to the W and Z mass terms. These couplings are present for the standard model Higgs with cV=1. At the next order of the effective theory expansion many more interactions are possible:

which are not couplings to mass terms. These are higher dimensional couplings than those in L1, so generically they should be less important. Nevertheless, some symmetry reasons or selection rules may forbid the couplings in L1, in which case the

*h*scalar would be an impostor and not the Higgs boson. Any of the couplings in L1 or in L2 could mediate Higgs decays to W bosons and Z bosons (as observed at the LHC), or mediate Higgs production in association with W/Z and in the vector-boson-fusion process (also kind of observed). However, the difference between the couplings in L1 and L2 is that the latter play no role in electroweak symmetry breaking. In the technical jargon, they don't affect the amplitude of the longitudinal gauge boson scattering at high energies, therefore they are irrelevant for restoring unitarity of the theory with massive gauge bosons.

So we the following definition.

**A Higgs boson**is a scalar particle that couples to W and Z bosons as in L1, with cV > 0. Along the same vein, one can define

**the Higgs boson**as a unique Higgs boson with the cV coupling close to one.

Thus, to prove we are dealing with a Higgs and not an impostor it is enough to prove the coupling cV is non-zero. Actually, we already know that based on the current data. The shabby figure on the right shows the fit of the cV parameter to the LHC Higgs data (blue) and to LEP electroweak precision data (red), after marginalizing over the remaining parameters of the effective theory. Both of these data sets independently exclude cV=0 at a high confidence level, and even more so when they are combined (black). So, with very few assumptions, and independently on what the values of the other couplings are, one can argue

*the particle discovered at the LHC is a Higgs boson*. At 95% confidence level cV is within 15% of the standard model value cV=1, so it clearly

*smells like the Higgs boson*. But of course that last statement is less robust as there's still a lot of room for other Higgs bosons being present in nature.

In summary, for theorists the answer to the question in the title is "since several months". For the LHC experimenters the coming Moriond conference would be a good opportunity to make that bold step forward, were it not for the fact that the H-word is banned in there ;-)

## 27 comments:

"Experimental data also disfavors a a sub-150 GeV spin-0 particle of any kind" (obviously, other than at 125 GeV +/- 1 GeV).

Poor Nima, he is also going to kill himself if the Higgs is a dilaton...

Excellent!

If I remember correctly "dilaton" = "quit physics"

When it is spin-zero this “-like” can be removed.

Furthermore, there are many physicists who feel the Higgs Nobel cannot (and will not) be awarded for this until that spin-zero is verified.

The press, bloggers, and “Close-like” (pun intended) physicists who write books don’t want to hear this but that is how many practicing physicists feel.

As I said: strictly speaking you will never prove spin zero; practically speaking you already did with high confidence.

Anonymous: Flattered that "Close-like" is now a subset of physicists who "dont want to hear this", but as I suspect that spin 0 proof is a necessary condition, and dont have any problem with hearing this, I seem not to belong to the subset named after me.

More precisely, Nima said he will quit physics if it is a techni-dilaton ;-)

I would by no means be to blame for it :-D

"Nima said he will quit physics if it is a techni-dilaton."

That settles it. It's definitely a techni-dilaton with spin 2.

" most of us don't wish Nima dead."

Prove it.

I completely agree. People who are using "Higgs-like" expletives have almost the same reason to talk about top-like quarks, W-like gauge bosons, Sun-like star behind Venus, carbon-like nucleus with six protons and six neutrons in it, and so on, and I mean those particles, elements, and stars we know.

This is the most unfathomable gibberish I've encountered since the miner keeping a lookout for the new sheriff of Rock Ridge in Blazing Saddles. Well done!

"For spin 2, the new particle would couple to all matter via higher-dimensional non-renormalizable operator, and then simple estimates suggest that the ratio of branching fractions in different channels, e.g. in ZZ vs gamma-gamma, should be completely different than what is observed unless the couplings take highly unnatural values."

"press, bloggers" - who are we talking about here? I don't know anyone outside CERN who still says "Higgs-like" without a clear sense of irony

The Moriond-like meeting (in La Thuile) will certainly settle the issue about naming the Brout-Englert-Higgs-like Higgs.

So it seems now that we have found the first not composite (fundamental?) not pseudo (even parity) not spin half or one or two (scalar) boson of the standard model.

From a phenomenological point of view, low scale supersymmetry seems in danger. Ok, let's wait and listen to the Mother Nature Oracle in the near future (Susy in the sky with AMS-02 ?)

Now a posteriori (from an "epistemological" point of view) could a "connoisseur" draw us a sane conclusion (not predicting the Apocalypse) about the fact that the vacuum stability constraint seemed to be the most efficient way to postdict the Higgs mass (as far as I understand it) ?

I am somewhat mind boggled by all this. Does ATLAS resolved the twin peaks puzzle? And what about CMS gamma-gamma decay? Maybe this is the time for definitely calling it Higgs but I see some odd points yet.

Yes, the twin peaks are coming closer. And, yes, CMS observes the Higgs-to-gamma-gamma rate in perfect agreement with the SM.

Oh good. I've been informally trying to convince people at workshops that the particle having spin 2 is a completely unreasonable thing to consider, but I'm glad to see it stated with the true voice of authority. Now that it's in blog form no one will question it anymore :)

This paper may interest you all

http://arxiv.org/abs/1303.0208

Moriond should give direct spin measurements of the Higgs boson, and hopefully end that -like-stuff. Just a few more days...

@Luboš Motl: Exactly. Let's call the top-quark "top-like quark" :D.

You mentioned "a scalar boson (as opposed to scalar fermions)". I may have missed something, but "scalar fermions" seems a non-sense. If scalar means a spin 0 particle it cannot be a fermion.

Anonymous 7 March,

You must be new around here.

It was deliberate non-sense

It was facetious ... but actually, one couldn't just say "a scalar" because it is too general: a scalar what? Perhaps "scalar particle" ... but that is not a very suggestive title. One must specify that it is a boson. And then "scalar" is an adjective for that boson, as in "not a > 0 spin boson". So scalar boson is not redundant, as the "scalar fermion" remark suggests.

I have always thought that "scalar fermion" was the usual way to name the scalar partner of a SM fermion in the context of SUSY. The "stop" is not the super-top, but rather the "scalar top".

even we prove that its a spin zero particle, but we have to work very hardly to prove that is a SM-like Higgs Boson.

The quantum of a ghost field is a scalar fermion

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