[/caption]It’s a Higgs boson. No. We’re not talking about some swarthy seaman standing at the helm of a boat and keeping watch. We’re talking about a hypothetical massive elementary particle predicted to exist by the Standard Model of particle physics. Its presence is supposed to help explain our lack of consistences when it comes to theoretical physics – and observing it has been one of the prime functions of the Large Hadron Collider. But the LHC hasn’t found it yet. As a matter of fact, we might wonder just what else it hasn’t found…

Right now, scientists have answered – or at least postulated the answer to – some very ponderous questions that lay just beyond the scope of the standard model. One of the foremost is the existence of dark matter. To find the solution, they’re using a model called supersymmetry. It’s an easy enough concept, one that states for every particle a stronger one echoes it at higher energy levels. The only trouble with this theory is that there isn’t any proof of these “super-particles” to be found yet. “Squarks” and “gluinos”, the antithesis of quarks and gluons, have been canceled out at energies up to 1 teraelectronvolts (TeV) of the standard model, according to an analysis of the LHC’s first year of collisions.

It should be easy, shouldn’t it? Given the broad spectrum, there should be simple members found within the supersymmetric models – even leaving the more complex and energetic to be explored at another time. But “the air is getting thin for supersymmetry”, says Guido Tonelli of the LHC’s CMS collaboration. At the same time, there is no sign yet of gravitons – particles that transmit gravity and are essential for a quantum theory of the force – below an energy of 2 TeV.

This lack of findings is causing some folks to wonder if we’re expecting answers to the wrong questions, but Rolf-Dieter Heuer, CERN’s director general is more optimistic. He knows the LHC has only produced about 1/1000th of its eventual data. “Something will come,” he says. “We just have to be patient.” But what of the Higgs boson? So far it has only been a blip on the LHC screen. “We will have answered the Higgs’s Shakespeare question – to be or not to be – by the end of next year,” Heuer predicts.

*Original News Source: NewScientist News and Wikipedia.*

Sometimes you feel supersymmetric… and sometimes you don’t. This article lacks certain symmetry, as if we are going to list all ongoing particle search we should add neutrino experiments and DM search.

More important still if we are discussing progress, since neutrino physics now lies outside the Standard Model. In the model neutrinos lack mass, but discovered neutrino oscillations predicts they have masses. Likewise, their recently discovered oscillations between all types means that they can be investigated for CP breaking. Perhaps they explain the matter-antimatter asymmetry of our matter universe.

While we are on the topic of general search, it bear to point out that LHC is not the place where people look for gravitons. That is done at dedicated observatories, since the only feasible production source is astronomical events.

On to the specific topic of supersymmetry. Supersymmetry is not the existence of heavier particles, which in terms of accelerator physics takes more energy to produce. Hence special relativity come into gear, and its mass-energy relation E = mc^2 is used to describe particle mass in energy terms.

And heavier particles are not stronger, in whatever interaction they may mediate or be mediated by. Quite the opposite. One simple example is in solid state physics. There wlectrons in crystals acquire effective masses if they can travel in the crystal, say as metal conduction electrons.

Effective masses can be lighter or heavier than the free space mass, but the heavy electrons travels slower and lower mobility (higher resistance) translates to lower current at the same voltage differential. Heavier particles makes for less interaction.

As the link tells us, supersymmetry is a symmetry where every particle has a spin twin superpartner. The spin difference is the smallest possible of 1/2, which makes bosons (even number of 1/2 units of spin) have fermion (odd number of 1/2 spin) superpartners and vice versa. And the idea what makes them important for particle physics is that they can change identity once in a while, and affect “the other half” of the particle world.

Supersymmetry was not as easy to detect as hoped for, and the lightest particles may be heavy indeed at more than ~ 1 TeV. This take the boll back to Higgs searches*:

“Ultimately it will be the Higgs searches that have the final say. SUSY predicts a light Higgs with higher mass partners. If the Higgs is found to be something different SUSY will be much harder to motivate. Until the Higgs sector is resolved, SUSY lives on.”

And if there is no supersymmetric Higgs, supersymmetry may be unhelpful right now but hide up among the high energies of Planck energy physics.)

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* As for Higgs searches, several experiments at several accelerators sees an excess right where the Higgs/light Higgs are expected to be. Which is more encouraging than one could have hoped for, I guess.

Supersymmetry comes about because it is the one way in which the internal symmetries of gauge fields and the external symmetries of spacetime. Supersymmetry should exist in some way. The one trend has been that the mass gap for broken supersymmetry has consistently shifted upwards with the energy of accelerators. Back in the 1970s and early 80s the idea was the superpartners of particles has 10-50GeV masses, and now it is in the 100s. I outline the Coleman-Mandula theorem which laid down the case for supersymmetry.

The S-matrix acts on shift the state or momentum state of a particle. A state with two particle states |p, p’> is acted upon by the S matrix through the T matrix

S = 1 – i(2?)^4 ?^4(p – p’)T

So that T|p, p’> != 0. For zero mass plane waves scatter at almost all energy. The Hilbert space is then an infinite product of n-particle subspaces H = (x)_nH^n (here (x) = “otimes” or Cartesian product). As with all Hilbert spaces there exists a unitary operator U, often U = exp(iHt), which transforms the states S acts upon. U transforms n-particle states into n-particle states as tensor products. The unitary operator commutes with the S matrix

SUS^{-1} = [1 – i(2?)^4 ?^4(p – p’)T]U[1 + i(2?)^4 ?^4(p – p’)T^†]

= U + i(2?)^4 ?^4(p – p’)[TU – UT^†] + [(2?)^4 ?^4(p – p’)]^2(TUT^†).

By Hermitian properties and unitarity it is not difficult to show the last two terms are zero and that the S-matrix commutes with the unitary matrix. The Lorentz group then defines operator p_? and L_{??} for momentum boosts and rotations. The S-matrix defines changes in momentum eigenstates, while the unitary operator is generated by a internal symmetries A_a, where the index a is within some internal space (the circle in the complex plane for example, and we then have with some

[A_a, p_?] = [A_a, L_{??}] = 0.

This is a sketch of the infamous “no-go” theorem of Coleman and Mundula. This is what prevents one from being able to place internal and external generators or symmetries on the same footing.

The way around this problem is supesymmetry. The generators of the supergroup, or a graded Lie algebra, have 1/2 commutator group elements [A_a, A_b] = C_{ab}^cA_c (C_{ab}^c = structure constant of some Lie algebra), plus another set of graded operators which obey

{Q_a, Q_b} = ?^?_{ab}p_?,

which {Q_a, Q_b} = Q_aQ_b + Q_bQ_a. If one develops the SUSY algebra you find this is a loophole which allows for the intertwining of internal symmetries and spacetime generators. One might think of the above anti-commutator as saying the momentum operator, as a boundary operator p_? = -i??_? which has a cohomology, where it results from the application of a Fermi-Dirac operator Q_a. Fermi-Dirac states are such that only one particle can occupy a state, which has the topological content of d^2 = 0. This cohomology is the basis for BRST quantization.

This is why most physicists who work on this stuff take supersymmetry seriously. It is also one reason why many schemes which purport to derive gravitation or unify gravitation with EM in some elementary was can be subject to strong questions. Of course supersymmetry remains a hypothetical, though some signatures of it have been detected. We will have to wait for the LHC to yield more results before anything is conclusive.

LC

Thanks! I learn a lot and it makes me think.

So, since I do not have the tools of bra-ket and QFT (but at least a superficial idea of what the former representation says in terms of basic QM), I will just list my layman reflections on what I believe I see here:

– The S-matrix seems to be the particle state evolution operator in relativistic space. So I think you lost “position” in “acts on [particles to] shift the [position] state or momentum state of a particle.”

I can see that we want to have a simple formulation for the theorem. I think I can see how the shift comes in (especially if <a href="the S-matrix spans the whole t axis), and the necessity of how it is asymptotic behavior and needs time ordering et cetera.

– The Coleman-Mandula theorem tells us how generic cases of local space-time and particle symmetry groups behaves in combination.

If the theory describing the particles has a mass gap the particles behave like the particles we know and love (relativistic particles). We can assume that here.

– Without loopholes external symmetries trivially does not couple to internal symmetries: roughly, “G is locally isomorphic to the direct product of the Poincaré group and an internal symmetry group (“internal” means symmetries that commute with the Poincaré group).”

– The reason we would want to have loopholes is because:

a) such a coupling helps constrain internal symmetries (with external): “This means that the properties and structure of the Poincaré group are of no help in choosing the set of other symmetries.”

b) such a coupling makes (symmetries of) field theories constrain potentially all particle properties (with tensors and spinors): “But the most important implication is that symmetries cannot relate particles with different mass and spin and thus the hope to describe the full variety of particle types through symmetry considerations was destroyed.”

I am not so sure I got the b) part correct, because I haven’t read the paper yet!

– Some loopholes are (according to my 2nd link at least): broken symmetries; supersymmetries; quantum group symmetries.

Of those broken symmetries are known to exist (say CP in SM).

– Now I start to worry about the project of supersymmetry. While loopholes to CM exist, they are still loopholes. The known loopholes tend to be broken symmetries, which we see regularly and expect as we cool the universe down.

And the reason for wanting it isn’t because it looks like a natural (trivial) representation, but because it is the old physics dream of locking down all parameters in “an ultimate theory (of everything)”.

We need to test it, obviously, but I don’t see how it would fare any better than other TOE ideas. They have not shown themselves to be a solid support to stand on. 😀

Also, it strikes me that maybe my naive idea of supersymmetry adding symmetry is totally backwards. But that is again a naive interpretation:

From the description of CM, SUSY pins internal symmetries by constraining them, not creating them. It may even work out so that the full theory is less symmetrical than the maximum amount of symmetries the direct product could make!?

Great, maybe I have to read that paper, and more, to get this. First, tensor theory… [grumble, grumble.]

No collision ‘on earth’ can bring out Higgs. I literally mean ‘on earth’, because these are not the condition which can take us back to the so-called big bang. Further, Higgs is theory. In practice gravity is due to particles whose spin is of course 0, but the rest is not so definitive as being thought in the SM. My site gives a chronology of the developments in my research efforts; don’t be too much disappointed by the absence of details (it’s a blog really), the details shall be published with the publication of my US patent application.

The point with LHC is that, while the SM doesn’t predict the free parameter of Higgs mass, other SM particles aren’t on the inflation reheating scale. And other theories that _do_ predict Higgs concur AFAIU. So it will likely be found.

Anyway, in ~ 1/2 year we will know, at the current data collection rate. The links Lord Haw-Haw and I gave all says this (because that was what the scientists at the Europhysics meet said).

As for theory, it is awkward to discuss in term of “[something] is theory”. It is a fuzzy idea that connects facts with theory in an erroneous way.

If we begin by looking at a tested theory for what it is, it is “a super-fact”. A theory predicts several facts, or it wouldn’t be a theory.

So if theories under test get some facts correct, chances are the rest are good too. (If the theory meets some minimum requirements of being consistent, relatively parsimonious, connected to the area, not ad hoc, etcetera.)*

The problem here is that SM is known to be an effective theory. Or in other words we know that either some actual facts will be different and/or there will be more facts related to the area. That doesn’t tell us if Higgs is real or not, just that the chances for its existence are really good.

A nitpick: gravitons are not part of SM, so I don’t know why you make such a connection. That is (one) reason why “the only feasible production source is astronomical events” as I noted before. Their existence is as of yet unconnected to SM (aside from the fact that they are both quantized theories).

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* Of course the science of science is arguable, as we don’t know much more than that we need (some) testability, and that parsimony works (in most cases). And both have theories predicting those facts.

But that is about as far as that takes us. Add some measurement theory, and we can realize that the area is still wide open for more work!

Last Friday at the International Europhysics Conference in Grenoble, France, researchers from both CMS and Atlas revealed that they had independently found unusual bumps in their data.

The Higgs Boson is believed to have a mass of between 120-185 GeV. Please see:

http://www.exploratorium.edu/origins/cern/ideas/higgs.html

The CMS group found two bumps, and the Atlas group found a bump between 120-140GeV. Theoretical physicist Professor Matt Strassler on his blog urges caution until more data becomes available in the future:

http://profmattstrassler.com/2011/07/22/atlas-and-cms-summarize-their-higgs-searches/

Only time will tell if Professor Stephen Hawking will lose his $100 scientific wager that the Higgs will not be found under laboratory conditions….. meantime we can only monitor any future leaked memos circulating within CERN.

Interesting.

I’m sure you know this, but the Tevatron sees this too as well as a rough-and-dirty data combination (which have more errors, like fluke signals, however this shouldn’t be the problem here), see my last link in my previous comment.

As your last link tells it, the Atlas and CMS didn’t “know” about the mutual statistics, and can’t just throw everything together. (IIRC they used the same simulation data for background, which is a no-no for a combo.) But that means there will be “more” data soon.

I didn’t know about Hawking’s wager. The contra-wager will be that he is wrong as he has been wrong before (on black holes unitarity vs eventual extinction by radiation loss). 😀

The two bumps are less than 3-?, which is “suggestive,” but not acceptable enough to draw conclusions. One of the bumps interestingly overlaps a theoretical exclusion zone of m_h ~ 125GeV. This “light Higgs” would result in vacuum stability problems. Of course this is a theory/phenomenology issue, which for all we know might be as worthless as dust. The last couple of months has made me ponder whether the universe might be very different from what we have been thinking. There are aspects of theory which offer structures that I think are reasonable, but they are threaded together in phenomenology which could be completely wrong.

The AdS ~ CFT duality of Maldecena, and prior holographic work of Susskind and ‘t Hooft, seems to be one of those “reasonable structures.” The boundary of an AdS_n, n dimensions, is a conformally flat spacetime which contains a conformal field CFT_{n-1}. The AdS_n boundary is a conformally flat spacetime, which can be a de Sitter spacetime. The CFT_{n-1} lives on this boundary space, which has “no gravity,” or should we say the spacetime has curvature which may be conformally mapped to flatness. However, the CFT has modes which run from the UV to the IR, and at the IR this is a massive conformal theory. Mass though breaks conformal symmetry of the spacetime — one gets local curvatures, or the mass can cause the tangent plane on the AdS_n boundary to penetrate the AdS interior where the graviton exists. Yet the holographic content of this theory tells us that the UV domain is equivalent to the IR domain. This means that a gluon chain in our spacetime, the conformally flat region bounding the AdS is equivalent to a graviton in the interior.

As a result of this at energy in the renormalization group flow domain, or conformal domain, a gluon chain might then have a small quantum probability for being a black hole. If the energy could be ramped up to near the string limit (Hagedorn temperature) that amplitude for a black hole increases to near unity or one. The quantum black hole has a quantum uncertainty with respect to its event horizon. In other words the horizon permits the interior and exterior states to be indistinguishable from each other. As a result exterior and interior states of the black hole exist in quantum superpositions. This has the effect of creating an ambiguity on the time ordering of states, or quantum bits, so information can appear outside of the black hole along a path that is not causal or what might be called “faster than light.” This is different from saying that spacetime has quantum fluctuations and has some graininess. Thus gravity appears completely classical, and its underlying quantum physics is not directly accessible. If I introduce a perturbing potential on the AdS_n there is a breaking of chiral symmetry, and gravity emerges on the AdS boundary in a way similar to the onset of superconductivity.

This might mean that supersymmetry, the Higgs field and so forth are not directly accessed in our spacetime. Of course this is spectulative, but it could be that much of the phenomenology built up over decades is just not correct. Thinking along different lines may be required.

LC

“One of the bumps interestingly overlaps a theoretical exclusion zone of m_h ~ 125GeV.”

Ah! I was afraid there was a slight risk for that, since someone made a graph (somewhere I can’t find right now) with these added exclusion zones. The ~ 120 GeV was just under it (low resolution graph).

“Thus gravity appears completely classical, and its underlying quantum physics is not directly accessible.”

So we can quantize the effective theory (as have already been done), but it wouldn’t be the renormalizable quantized theory we would like? That could work.

“This might mean that supersymmetry, the Higgs field and so forth are not directly accessed in our spacetime.”

Sounds comfortable, but as I just realized in another comment here, now we are discussing loopholes (supersymmetry vs CM theorem). This is a loophole for (among other things) a loophole. 😀

Interesting idea though.

What might be happening is what happens with a political party after a losing election, where they clear the decks and start over. A whole lot of phenomenology is going to be sent to the rubbish bin. Supersymmetry has always been “right around the corner” ever since the Fermilab accelerator was build. The light mass supersymmetric pairs failed to appear. The same was voiced with the start of the Tevatron, and again no dice. The Tevatron was supposed to be the original Higgs machine as well. Then in the 1990s and 2000s these claims were made with the LHC, and now we are faced with a relative paucity of confirming data. In many ways I greet this as a great clearing away of clutter.

The anti-de Sitter spacetime is a sort of renormalization group flow. The hyperbolic dynamics are such that particle follow large arcs which reach the boundary at IR energy, very low energy. The spacetime has negative Gaussian curvature which means particles tend to flow with near zero energy from the boundary, reach the interior at high energy and then flow back to the boundary at near zero energy along hyperbolic arcs. A look at Escher’s Limit Circle drawings gives a sense of this dynamics on a Poincare disk. If such a particle emits quanta of radiation on its path to the boundary an observer in the AdS interior would seen this radiation more blue shifted as the particle approaches the boundary. In the parlance of spacetime holography this is an equivalency between the ultraviolet and infrared spectrum of particle fields. We live on the boundary of this AdS, and so the physics we observe is low energy, ie it is 1-10 TeV or less and attempts to push this to higher energy means we only reproduce more physics on that energy scale. Direct observations of much higher energy physics is sealed off from us. We live in this low energy domain where the conformal symmetry in the AdS_n is broken. The black hole holographic stretched horizon should then have this same property.

This might sound a bit gloomy, but not all is lost. The appearance of mass on the boundary is a breaking of conformal symmetry. It also means there is the appearance of mass, which induces gravity on the surface of what in an unbroken phase would be a gravity-less world. As such gravity introduces dips into the AdS. So a tangent plane on the AdS boundary penetrates the AdS interior. This means that some signatures of physics in the AdS interior should be present. I might attempt to propose something of this nature, where as a toy model consider a five dimensional “spacetime plus R” space. This fifth dimension is a space with a gauge connection or potential A = ? which defines a force F = -d?/dx_5, for x_5 a parameter on this fifth dimension. To make this even simpler the potential might just be ? = -gx_5, similar to simple gravity near Earth and the force. For the fifth dimension a simple interval [0, L] the black hole case is x = L and the quasi-black hole or QCD plasma is at x = 0. So the black hole at the top for particle masses m ~ 0 has this continual flow to heavy masses at the bottom. This might connect with Zamolodchickov’s s = -1/2 massive conformal theory. The duality between spacetime isometries on these boundaries and conformal symmetries, such as the massive conformal symmetry might exist on x = 0. So there should be subtle amplitudes associated with this physics that “probes” into the AdS interior.

Curiously this might explain why we do not see proton decay. The amplitude for proton decay should be A^2 ~ g^2/4? log(?/M_x), for ? the energy cut off and M_x the mass of the GUT bosons which cause proton decay. The time interval for this decay is ?t ~ 1/E >> 1/M_x, and such scales are not directly observable in our world.

Anyway, don’t take any of this as somehow that real, but we are at a time where people do need to think in ways which have departures from standard ideas.

LC

Phenomenology – How do you know you or anything else exists?

Evolution would like to have a word with you.

A classic film, and they love to blow up planets that are unstable! I have been a long time since I have seen this.

LC

I concur, Dark Star is a classic film; I’m glad that you like it – and it is available on DVD at Amazon.

“Only time will tell if Professor Stephen Hawking will lose his $100 scientific wager that the Higgs will not be found under laboratory conditions.”

——

Which would make him 0-for-3 in scientific wagers, wouldn’t it? He lost his bet with Kip Thorne over Cygnus X-1, lost the bet with John Preskill over information loss in a black hole, and probably this one as well.

For his sake, I hope Professor Hawking never gets into horse racing.

[]

In discussions with some other physics folks on the lack of signatures for the Higgs that symmetry breaking physics might be Technicolor. This is an interesting alternative to the Higgs boson in some ways. It models the symmetry breaking particle which plays the role of the Higgs boson as a quark condensate, in fact usually the T T-bar (top quark & anti-quark) condensate. This is a transformation of the quark system into a single particle, similar to Sugawara’s transformation of the u and d quark systems into mesons. This is sort of a way of rewriting the Higgs boson, and the standard signature for the Higgs field sited on is the H — > T + T-bar, which decays into other secondary channels. The prospect then is that if I am right about this “momentum horizon” that the Higgs particle is really a gluons chain which can emerge from a quark-anti-quark condensate. Gluon chanins have dualities to gravitons, and so the Higgs particle might be a sort of manifestation of this duality.

LC