*The Rumors Predict The Obvious.*

While the rumors are reportedly based on inside information, their substance is really pretty obvious the same as what one would predict without insider information.

This is not really surprising. The Large Hadron Collider continues to produce more data and all other things being equal the new data from the same experiment to look a lot like the old data from that experiment. If the Higgs boson is there, mathematical projected based upon the rate of LHC data generation that we're experiencing makes it highly likely that a five sigma result will be announced sometime this year. The ICHEP conference next month is one of half a dozen or events left this year where this result would be likely to be announced (big results are usually announced at academic conferences). And, even if there isn't a five sigma announcement at ICHEP, there could easily be a higher sigma Higgs boson data announcement that is short of five sigma, but more significant than the result from last winter (which, given the trend line, would reassure everyone who was worried that last winter's accouncement was just a cruel statistical fluke).

Indeed, if there was announcement that the statistical significant of the apparent Higgs boson find had not increased, that would call the previous result into doubt. For this to happen, the Higgs boson signals seen at the LHC in the last few months would have to be quite a bit weaker than the Higgs boson signals seen in LHC's first few months, indicating that the early result might have been a statistically fluke.

*If a Higgs boson is there, it will be a Standard Model Higgs boson.*

For reasons that I've discussed previously at this blog, the nature of the search methods used to identify a potential Higgs boson (such as the quantum mechanical limits on the kinds of interactions that can produce diphoton events) tends to strongly imply that any particle discovered i this search has all of the properties of a Standard Model Higgs boson (i.e. an intrinsic spin of zero, zero electromagnetic charge, the predicted quantum number that describes the strength of its weak force interactions, no weak force decay modes into non-Standard Model particles, and no color charge in the sense meant by the quantum chromodynamics theory that describes the nuclear strong force).

Bayseans out there would also give weight to the fact that the Standard Model has been incredibly accurate to date, so the discovery of something that looks a lot like a Standard Model Higgs boson, which is the last undiscovered particle in that model, right where it belongs more or less based on predictions from several decades ago, also gives us confidence that if we have discovered something that it is the Standard Model Higgs boson because it fits appropriately developed prior expectations.

So, don't take the hype about the need for months of additional research to determine if the particle we've found is really a Standard Model Higgs boson very seriously.

*The announcement will have few new implications for BSM theories.*

Now, it turns out that plenty of beyond the standard model theories, including all variations of SUSY, have more than one Higgs boson, one of which, typically the lightest, looks more or less exactly like the Standard Model Higgs boson. So this discovery doesn't itself exclude them. But, theories that don't have at least one Standard Model Higgs boson that could have a mass in the 124 GeV-126 GeV range (such as most versions of "Technicolor" and "non-linear sigma" models, which were invented in substantial part to hedge against the possibility that no Standard Model Higgs boson would be discovered), of course, are toast.

*What helpful new information remains to be discovered?*

Since a huge number of physicists already assume that we've discovered the Higgs boson somewhere in a roughly 2 GeV mass range, the speculative implications of new data really boil down to a few points that are still uncertain.

First, the details of the

**Higgs boson mass**still matter. A mass discrepency as subtle as the difference between 124 GeV and 126 GeV turns out to have lots of importance in many beyond the Standard Model theories, for example, having considerable power in determining SUSY parameter space. One extreme is a much more natural number for SUSY, in what is already a liminal mass range for it, than the other (honestly, I don't even recall which is which without looking it up, since I am bearish on SUSY theories for other reasons).

The exact mass number is also relevant in determining if the Higgs boson mass is realy a fundamental constant or can be derived from some formula of other known Standard Model constants. The Standard Model doesn't have such a formula in it, but doesn't preclude the possibility that there are deeper relationships between the constansts that it does have which are being determined with ever greater certainty that makes formulas relating them less and less likely to be numerological coincidences.

Second,

**are we really seeing just one Higgs boson, or is there more than one kind of Higgs boson each of which has all of the same non-mass properties and each of which has a similar, but not identical mass**? Some BSM theories have two nearly indistinguishable Higgs bosons of very similar mass and more data could rule out the possibility that there is both a 124 GeV and a 126 GeV neutral Higgs boson, for example.

Third,

**what is the "width" of the Higgs boson resonnance (which is a function of its half-life)?**There should be a measureable width because Higgs bosons are not stable particles either in theory or as observed in practice, since decays are observed and stable Higgs bosons are not), but the constant is not strongly determined theoretically. Increasingly accurate data about the Higgs boson rest mass should also provide increasingly accurate data about the Higgs boson resonnance width, since generally you use the same data (a measurement of the overall resonnance of the Higgs boson, i.e. hill in the chart), to determine both at the same time.

Resonnance widths have been estimated for all of the quarks, for the charged leptons, and for composite particles made of quarks (although not for neutrinos to any great level of precision so far as I know, as their masses are also not known with much accuracy), but the only bosons for which resonnance widths are known are the W and Z boson widths, which are themselves not independent of each other. The Higgs boson resonnance width is the only boson resonnance width in the Standard Model which is independent of the W and Z boson value, so it might help us to find a pattern more generally.

Knowing this number is also helpful in refining the accuracy of the calculated "Standard Model backgrounds" in high energy physics interactions which physicists aided by computers calculate as a reference point against which the experimental data can be compared to see if there are any statistically significant evidence of beyond the standard model physics in the experimental results. The more accurately the constants of the Standard Model background are known, the more statistical power a set of experiments has to detect deviations from that background expectation (even, in principle, out of data from experiments already concluded and reanalyzed based on new estimates for Standard Model constants to use in calculating background expecations).

*Other Unfinished Business: Revisiting High Energy SM Predictions*

Scores, if not hundreds or thousands, of physics papers have been written discussing the predictions of the Standard Model at high energies given the then known constants and accepted equations of the Standard Model. But, almost all of those papers were hampered by the need to hedge the question of the mass of the Higgs boson and either made only broad generalizations based upon a wide range of favored masses and made a guess regarding Higgs boson mass which was in most cases wrong.

We also know a whole host of other Standard Model constants more precisely as a result of the work that has been done at the LHC, and the dramatic surge in computing power over the last decade or so has also steadily increased the number of terms that can be calculated from the infinite series approximations used to do calculations within the Standard Model thereby reducing "theoretical" error in these predictions, particularly at higher energies where the higher order terms in the equations used to calculate the approximate numerical results are more important.

The time has come to do another really serious and complete high energy extrapolation of Standard Model predictions, now that much more accurate estimates can be made of all of its parameters, now that more terms can be included in the calculations, and now that we can say with increasing confidence, for example, that there is not a fourth generation of the four kinds of Standard Model fermions out there.

One of the driving forces behind research into beyond the Standard Model physics has been an awareness that at high enough energies, the unmodified Standard Model blows up as its equations start to give unphysical answers (e.g., the sum of the probabilities of all possible events stops adding up to 100% called a violation of unitarity, and vacuum instability). The existence of a Standard Model Higgs boson at 124 GeV +/- has kicked this threshold up significantly from many previous estimates. But, I haven't seen any real definitive efforts to quantify this impact directly integrating all of the new data that LHC has provided.

These problems aren't overwhelming anymore, however.

A Higgs boson mass of 125 GeV implies a "metastable" vaccum (per the link in the paragraph above) at least up to something close to the GUT scale (10^10 GeV at the least optimistic estimate with the lighest experimentally supported Higgs boson mass to 10^18 GeV+ with a Higgs boson mass at the high end of the current range). The GUT scale is often described as 10^16 GeV, and the Planck scale is about 10^19 GeV.

There is also a near complete absence of unitarity problems at the currently favored Higgs boson mass:

[F]or . . . [a] Higgs mass around 125 GeV, which is currently phenomenologically favorable, the quartic coupling remains perturbative at all scales and preserves unitarity at all scales, both at tree level and when electroweak logarithms are included, which suppress amplitude and cross section of longitudinal gauge boson scattering significantly at high energies.

Knowing when this starts to happen and what is driving this mathematically, within the theory, can point us towards the weak spots in the theory that need to be investigated in further experiements (beyond mere brute force higher and higher energy colliders that try to determine what happens directly). If the Standard Model is flawed in some way, it is probably in what ever parts of the model are most strongly driving the unphysical results that are predicted, or because "new physics" is lurking at the relevant energy scale, waiting to be discovered.

Of course, if these problems virtually vanish with the currently favored Higgs boson mass, they perhaps they aren't problems any more and the beyond the standard model theories motivated by a desire to solve these no longer existing problems are no longer well motivated. Indeed, a Higgs boson mass of roughly the measured amount virtually insures that the Standard Model does not break down in theory, at least, at any energy that can be produced in an Earth bound laboratory (where energies are ca. 10^4 GeV with current techologies).

There is also an absence of observable weirdness of the type predicted at high energies if there is a Standard Model breakdown, such as vacuum instability, at the places that are home to the highest energy interactions that can be observed via astronomy, suggesting that to the extent that the Standard Model does break down at extreme high energies this could be due to our own errors in estimating the Higgs boson mass, or flaws in how we extrapolate the Standard Model to very high energies, or to special structural features of those kinds of extremely high energy interactions that make what is theoretically possible unphysical in practice.

Moreover, the current Higgs boson mass estimates suggests that if there does need to be a fix to the Standard Model at very high energies to prevent it from breaking down, that this fix can afford to be very, very subtle with a tweak that is equivalent in impact to the effect of having a Higgs boson mass that is just 1-2% heavier than the current estimate at the highest of available energy scales.

*Where Could The Standard Model Be Flawed At High Energies?*

What parts of the Standard Model might perform almost perfectly at moderately high energies, but fail catastrophically at higher energies that are not yet succeptible to being produced in experiments or post-Big Bang astronomical events?

I've previously suggested that the unphysical results at high energies might be driven by flaws in describing the "beta functions" that are used to describe the "running of the coupling constants" of the three Standard Model forces (strong, weak and electromagnetic) at different energy levels. Minor flaws in either the form or the constants used in these equations would be almost invisible at low energies but could give rise to dramatic problems at higher energies.

Another plausible place to look for flaws would be in areas where effects from general relativity or quantum gravity might be ignored. The Standard Model is built to accomodate special relativity, but not the additional implications of general relativity, which are usual expected at an order of magnitude level in the systems we study in high energy physics experiements to have a negligible impact even though we can't precisely computer them in a theoretically rigorous way. But, simply ignoring these effects at high energies may be inappropriate.

*Asymptotic safety*

One of the papers that accurately predicted the Higgs boson mass before it was determined last fall, at least provisionally, assumed a quantum gravitational concept called asymptotic safety (see, e.g., Percacci (2007)) to achieve that result, which suggests that this avenue of inquiry might be fruitful. The notion that the beta function of the gravitational force might have special characteristics that make it renormalizable (despite the fact that gravity is not renormalizable in naiive efforts to express it through quantum mechanical equations) has been kicking around since Weinberg proposed it this as a possibility in 1979, but the relevant mathematical breakthroughs to show that it might be possible to devise a mathematically coherent theory that could act in this manner have surfaced only recently.

Another paper, Peracci (2010) spells out asymptotic safety in the context of Standard Model interactions a bit more specifically:

The strong interactions are already described by an asymptotically safe theory, and there are reasons to believe that this result is not ruined by the coupling to gravity. The electroweak and Higgs sectors of the standard model are perturbatively renormalizable, but some of their beta functions are positive. This means that either new weakly coupled degrees of freedom manifest themselves at some scale, before the couplings blow up, or else the theory is consistent, but in a nonperturbative sense. The simplest realization of the latter behavior is AS [asymptotic safety]. If the world is described by an AS theory, there are two main possibilities: one is that AS is an inherently gravitational phenomenon, in which case AS would manifest itself at the Planck scale; the other is that each interaction reaches the FP [fixed point] at its characteristic energy scale.

For example, the Higgs vacuum expectation value (vev) might run with the energy scale of a system.

For criticism of the asymptotic safety program in quantum gravity, see for example, this July 11, 2009 post by Lubos Motl.

**UPDATE June 20, 2012**

There is considerable additional discussion in the comments (mostly from me, much of it quoting Matt Strassler's blog), about what kind of experimental outcomes could contradict a conclusion that what has been found so far is a Standard Model Higgs boson, and you can read the comments to follow that analysis.

What is less obvious is that if the particle detected truly is the Standard Model Higgs boson, this is inconsistent with SUSY theories that generically require that the Higgs sector consist of multiple Higgs bosons that collectively give rise to the effects attributed to the Higgs boson.

Moreover, string theory, generically, implies SUSY, although the reverse is not true.

Hence, the LHC, should it establish conclusively that the particle it has found really is the Standard Model Higgs boson has falsified essentially all versions of both SUSY and Sting Theory.

Now, in reality, the LHC is not capable of directly testing every single property of the Higgs boson and comparing it to the Standard Model. Some of the possible decays from a Higgs boson are so rare and subtle that you'd need a collider so powerful it might be impossible to make to test them. But, LHC probably can test enough Higgs boson properties to generically rule out any kind of SUSY theory that a theoretical physicist could ever love. And, as I've noted before another kind of LHC result (the exclusion of like SUSY particle candidates) combined with results from non-LHC experiments related to neutrinoless double beta decay, both of which are unrelated to exploration of the properties of the Higgs boson, are already on the verge of falisfying a huge swath of SUSY theories in a completely independent way. A failure to observe neutrinoless double beta decay in non-LHC experiments that are growing increasingly precise also essentially implies that neutrinos have only Dirac mass.

If the LHC and neutrinoless double beta decay experiments do this, and it will come very close in just a year or two, SUSY and String Theory are dead. If so, there are really no mainstream Beyond the Standard Model Particle Physics theories left to test (the linear sigma and technicolor models, for example, already having been pretty much killed by the discovery of the Higgs boson as well), although there is still room to infer more fundamental theories that reduce to precisely the Standard Model from fewer parameters.

Killing off all of these theories affects more than just the high energy physics community. It also removes almost all of the plausible dark matter candidates from the discussion.

Of course, LHC or neutrinoless double beta decay experiments could find that we haven't found the Standard Model Higgs boson, or that there is a considerable amount of neutrinoless double beta decay. But, the far more likely possibility is that they won't.

## 6 comments:

I skipped through that post, so maybe you I missed it... but I would add that we should also want to measure the couplings of the Higgs to the individual fermions. We don't know if it couples directly to all of them, or just to a few of them (with the other fermions obtaining mass indirectly), or what.

Fair enough, and yes, I did miss that point. While there is a very strong theoretical expectation regarding the strength of this coupling, the particle observed could certainly act differently in practice in a way that isn't necessarily automatically fixed by the quantum numbers we can infer at this point.

Lubos piles on the Higgs rumor band wagon.

Matt Strassler despises rumors about big science results but is talking about them anyway because everyone else is doing it.

But, he does have some interesting discussion in related posts about how a Standard Model 125 GeV Higgs boson is supposed to behave. For example he notes that the data seem to include about 100,000 Higgs boson decays so far and that it should decay as follows:

■60% of such particles would decay to bottom (b) quark/antiquark pairs

■21% would decay to W particles (though see below!)

■9% would decay to two gluons (g)

■5% would decay to tau (τ) lepton/antilepton pairs

■2.5% would decay to charm (c) quark/antiquark pairs

■2.5% would decay to Z particles (though see below!)

■0.2% would decay to two photons (γ)

■0.15% would decay to a photon and a Z particle . . .

There are three classes of decays in this plot:

First, there are decays through direct interactions to a particle and its antiparticle; see Figure 2. From largest to smallest probability, these are

■decay to a bottom quark/antiquark pair (the bottom quark has a mass of 4.5 GeV)

■decay to a tau lepton/antilepton pair (the tau lepton has a mass of 1.8 GeV)

■decay to a charm quark/antiquark pair (the charm quark has a mass of 1.3 GeV)

There are also other decays, to other quarks and leptons, that are not shown. Why not? You already know why the decay to an electron isn’t shown; why bother? it is far too small to measure. The same is true for muons and for strange, down and up quarks. They are all very lightweight, and their interaction with the Higgs field is therefore very weak, implying that the probability that the Higgs particle decays to them is very small. And why isn’t there a decay to a top quark and antiquark shown? The top quark has a mass of 173 GeV or so, so a Higgs of 140 GeV and below cannot decay to a top quark and a top antiquark. . . .

Second, there are decays through indirect interactions to gluons and to photons. These occur through an effect of “virtual `particles’ ” (which are not really particles at all, but disturbances in the corresponding fields.) In particular, because

■gluons interact directly with top quarks

■photons interact directly with top quarks and W particles

■Higgs particles interact directly and rather strongly with W particles and top quarks

the Higgs gets to decay to gluons through the indirect effect of virtual top quark/antiquark pairs (i.e. through a generalized disturbance in the top quark field), and it gets to decay to photons through the indirect effect of virtual top quark/antiquark particles and virtual W particles. These indirect interactions are quite a bit smaller than the direct ones, which is why these decays are rather rare, especially the decay to photons, which happens only for about 1 in 1000 Higgs particles. . . .

Third — and most important, as we’ll see — there are decays which, on the graph, are marked WW and ZZ. That looks as though these refer to two W particles and two Z particles. But wait! That can’t be right! The Z particle has a mass-energy of 91 GeV. If the Higgs particle has a mass-energy of 140 GeV, how can it decay to two Z particles, which collectively have a mass-energy of 182 GeV to start with (and possibly additional motion-energy, which is always greater than zero)? It’s clear how a 200 GeV Higgs particle could decay to two Z particles, but why is it still true for a 140 GeV Higgs particle?

[Answer: Virtual particles again.]

Another good post from Strassler on the precise experimental outcomes that are involved in deciding if a detected particle is really a Higgs boson is here. Some highlights:

"The thing that makes a particle a Higgs particle, by definition, is that the field in which it is a ripple participates in giving mass to the W and Z particles. . . . the Higgs “sector” might consist of several closely related particles, all of which are typically called Higgs particles, and at least one of which must have the property I just described. . .. If a field gives the W and Z particles all or part of their masses, then the field’s particle will have a strong direct interaction with two W particles and with two Z particles. And this in turn automatically leads to three large effects:

■the decays H –> WW and H –> ZZ,

■the production process quark + antiquark –> W H and quark + antiquark –> Z H, and

■the production process quark + quark –> quark + quark + H.

if we can observe . . . any of these processes for a new particle . . . the new particle is a Higgs particle. . .

We want to know whether the Higgs behaves exactly like the Standard Model Higgs as far as the W and Z particles [top quarks, bottom quarks and tau leptons] are concerned . . .

These boil down to the questions of whether gW, gZ, gt, gb, gτ [Higgs boson coupling constants] are the numbers predicted in the Standard Model, which in each case are the particle’s mass divided by v (up to a square root of 2.) . . . lighter particles . . . are probably out of reach at the LHC.

Also, . . . are the interaction strengths gg and gγ (γ standing for photon) what the Standard Model would predict? . . . it’s not so easy to answer these questions right away . . . when we measure the rate for g g –> H –> γγ, we are measuring something proportional to (gg gγ)2. Similarly the rate for g g –> H –> WW is proportional to (gg gW)2. There’s no way to easily measure the individual interaction strengths separately.

But . . .

if the rates for gg –> H –> γγ, g g –> H –> W W and gg –> H –> Z Z come out as predicted in the Standard Model . . . then that will give us some confidence that none of the couplings gW, gZ, gγ, gg can be very different from what it is expected for the Standard Model Higgs particle — which in turn will give confidence that gt, which contributes to gγ and gg, is also what it is predicted. . .To convince ourselves that gb and gτ are as predicted in the Standard Model will take longer [from observation of other more subtle decays]. . .

If instead it turns out that some of these measurements differ from the predictions of the Standard Model . . . we’re dealing with a Higgs more complicated than the Standard Model Higgs. . .

For instance, if the rates for g g –> H –> γγ, g g –> H –> W W and g g –> H –> Z Z are all in the predicted proportion, but are uniformly smaller from what is predicted in the Standard Model, that could suggest that there are two or more Higgs particles . . . [each] giving the known particles only a part of their masses.

If . . . the ratio of two-photon events to WW and ZZ events differs from the expectation in the Standard Model, then . . . unknown particles [are] contributing to the indirect interaction between photons and the Higgs particle.

If the ratio of gb and gτ is not as predicted . .. either . . . there is one Higgs field giving mass to the quarks and a different Higgs field giving mass to the leptons, or . . . there are new particles which are indirectly affecting the interaction of Higgs particles with bottom quarks and/or tau leptons."

The discussion above points out something I hadn't really understood until now. You can get a pretty good fix on Higgs boson mass from diphoton channels (which are the cleanest) pretty fast. This, in turn, precisely bounds the relative proportions of diphoton, WW and ZZ decays.

If the experiments match these "loud" decay channel proportions, BSM theory space starts to get incredibly claustraphobic, and ill motivated. And, the process of searching for the existence of the Higgs in these three channels in the first place has already highly constrained deviations from the predicted values.

If, eventually, you can show that no only are the diphoton, WW and ZZ decays in the right proportions, but that they are also present in the correct amount in absolute terms, you have established that there is a simple, single Higgs boson Higgs sector, and that result falsifies SUSY theories generally, and a fortiori, string theory.

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