## Is the Higgs boson already discovered?

Alberto Palma's recent paper Arxiv:1202.0217 says in its conclusions part: "The ATLAS collaboration presents first results of the direct search for the SM Higgs boson decaying to $b\bar b$. No evidence of the Higgs boson was found in a $pp$ collision data sample of $\mathcal L=1.04\ \mathrm f\mathrm b^{-1}$ at $\sqrt{s}=7\ \mathrm T\mathrm e\mathrm V$. Instead, upper limits on the Higgs boson production cross section of between 10 and 20 times the SM value were determined, in a mass range $110<m_H<130\ \mathrm G\mathrm e\mathrm V$".

Does it mean that the Higgs boson is already discovered or not yet? What is the exact meaning of these words? What are the most recent news in this area?

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 Recognitions: Gold Member My understanding is that the folks at CERN think they have probably discovered the Higgs but the results are not yet conclusive and any announcement would be premature at this point. What they definitely HAVE done is refine the range of possible values for the mass for the Higgs if it does exist.
 Recognitions: Science Advisor The current trend is we think the Higgs is living somewhere at ~126 GeV, see: http://arxiv.org/abs/1202.1408 But the statistical significance of this is low enough that we shouldn't (and cannot) declare it to be a true detection. The paper you cite is looking at an (I believe) more difficult decay channel, and is using less data. Plus, it looks like they've only set a bound at ~2sigma.

## Is the Higgs boson already discovered?

 Quote by Ruslan_Sharipov Does it mean that the Higgs boson is already discovered or not yet? What is the exact meaning of these words? What are the most recent news in this area?
The important sentence in your quote is "No evidence of the Higgs boson was found." They looked, but they didn't see it. However they weren't able to rule out its existence if it has a mass between 110 and 130 GeV. If the Higgs boson does exist and has a mass in this range, they expected not to see it. Note that this is only reporting the result of one particular method of searching for the Higgs. Other searches, which look at other possible decay products, have produced hints (not proof) that the Higgs exists and has a mass around 125 GeV.

 Hi, without invoking higgs, the electroweak is said to be non-renormalizable because one has to introduce mass directly to it. Can anyone please explain briefly why introducing mass directly to the equation would make it non-renormalizable? Thanks.
 Concerning renormalizability, I have heard the following proposition: "A field-theoretic model is renormalizable if and only if its Lagrangian is of the degree not higher than 4 with respect to the fields involved". I don't know its proof and I would like to ask someone more competent than me here: is this proposition true or not?
 The main point is that in order to have a consistent theory with gauge bosons (or generally, vector bosons) , you need to have a symmetry which is called gauge invariance. This symmetry doen't exist if you introduce masses to the gauge bosons. Why do you need this symmetry? An inspection leads to that a massless vector boson (spin 1 particle) has two degrees of freedom (for exmaple ,a photon has two polarizations) and a massive has three degrees of freedom. However, to introduce a vector boson to your theory in a lorentz invariant way, you have to use an object which is a lorentz vector A_{μ}, which has 4 degrees of freedom. Therefore, some of them are not physical and the gauge invariance makes sure they don't contribute to physical observables. If you would introduce masses directly to the vector bosons , these degrees of freedom would behave badly at high energies, producing results which make no sense( probabilities not summing into one...) New degrees of freedom are required to cancel this bad behaviour( in the SM case, its the higgs), which are exaclty the degrees of freedom which restore the gauge invariance. In that sense, introducing a mass directly results in a thoery which makes sense only up to an energy scale which these new degrees of freedom are required. similar to a standard non renormalizable theory which is a valid only up to a certain cut off scale. For the standard model without the higgs, this cut off scale is about 800GeV, meaning some new degrees of freedom have to exist up to that scale( the higgs or something else) Hope that helps
 The original papers which discovered that massive gauge bosons lead to nonrenormalizable theories are listed in reference 13 of http://arxiv.org/abs/hep-ph/0401010. Studying their arguments might be a good way to learn about renormalization technicalities, because there are many subtle details. For example, you can have a massive abelian gauge boson; it's massive nonabelian gauge bosons which lead to a nonrenormalizable theory, because they contain some extra interactions (and thus extra divergences) not present in the abelian case. Also, as often happens in QFT, it seems there is no absolute proof of nonrenormalizability - as late as Veltman's paper in 1968, he's emphasizing that renormalizing the theory will be difficult but maybe not impossible - it seems that everyone gave up only after Boulware 1970. And 't Hooft's construction of renormalizable theories where the gauge bosons get a mass through the Higgs mechanism came just a year or two later. Also let's remember that nonrenormalizable theories are not useless or evil, it's just that renormalizability is good because it means the theory can be extrapolated to high energies. As Weinberg mentions, Fermi's original theory of the weak interaction was nonrenormalizable. But it still works within its range of validity.
 Recognitions: Gold Member Science Advisor Recent reports [http://arxiv.org/abs/1202.1408] suggest an overabundance of events around 126 Gev with 3.5 sigma [roughly 99.9%] probability. The probability of this being due to random background noise over a range of energies is estimated at 1.4% [2.2 sigma]. The next LHC run may tell the tale. Particle physicists prefer a 5 sigma confidence level before detection is deemed confirmed.
 You mean that if I take an abelian gauge theory ( for example,QED ) and add an explicit mass term which breaks gauge invariance, the theory will have no problems with unitarity? At these , up to the scale where you hit a landau pole?
 Wow. The higgs is almost found. Since the LHC hasn't found any Superpartners and no hidden dimensions nor blackholes. I guess the only thing the LHC will ever find is the Higgs before it shuts down in a few years.
 Mentor What a load of ill-informed nonsense! First, there is no such thing as "almost found". Either its found or it's not The experiments have presented their data. Either you are convinced that they have found it, or you are not. The experiments themselves are not convinced. Second, the idea that because no new physics has been seen with 1% of the total data at half the design energy that no new physics will ever be see is utterly ridiculous. Finally, "a few years" is more like 20.

 Quote by Vanadium 50 What a load of ill-informed nonsense! First, there is no such thing as "almost found". Either its found or it's not The experiments have presented their data. Either you are convinced that they have found it, or you are not. The experiments themselves are not convinced. Second, the idea that because no new physics has been seen with 1% of the total data at half the design energy that no new physics will ever be see is utterly ridiculous. Finally, "a few years" is more like 20.
Oh, so there is still chance the supersymmetric partners that will solve the Hierarchy Problem will be found. Good. I thought they were given up already as not one of them was seen. Thanks for the heads up.

 Quote by ofirg You mean that if I take an abelian gauge theory ( for example,QED ) and add an explicit mass term which breaks gauge invariance, the theory will have no problems with unitarity? At these , up to the scale where you hit a landau pole?
Yes, it's true - just look up unitarity and renormalizability of Proca theory.

 Thanks. If I understand correctly, massive QED (proca theory) is just a particular gauge of a gauge invariant theory (the stukerberg model), where the scalar field can be removed from the theory. basically, in order to render massive qed gauge invariant, one only needs to add non physical (gauge redundant) degrees of freedom, in contrary to the non abelian case, where at least one physical degree of freedom is needed (higgs particle). I this also true for an abelian gauge field which couples chirally to fermions, like hypercharge?

 Quote by mitchell porter .....For example, you can have a massive abelian gauge boson; it's massive nonabelian gauge bosons which lead to a nonrenormalizable theory, because they contain some extra interactions (and thus extra divergences) not present in the abelian case.....
Massive QED is renormalizable? Can you give some reference for that?

 Quote by mitchell porter Yes, it's true - just look up unitarity and renormalizability of Proca theory.
I looked it up and it is indeed true. The troublesome kk term droups out in any Feynman diagram due to U(1) gauge invariance.