I am spending a few pleasant days in Split for the conference "LHC Days". I will be representing the D0 and CDF collaborations here in a talk on top physics at the Tevatron; in the meantime, I am pleased to witness that talks are of high quality. This morning the most interesting to listen to (at least to me) was the one by Guido Altarelli, a distinguished theorist from the University of Roma III. Altarelli has given crucial contributions to the advancement of our understanding of Quantum Chromo-Dynamics in the seventies, and it is always a pleasure to listen to him (a previous report of a talk he gave in Perugia two years ago is here).

I have tried to follow Guido's talk while I typed his exact words. I missed a few, so the prose that follows may be in some parts broken -the responsibility for that is of course mine. If you wish to know what he discussed, besides finding his slides at the conference site, perhaps you will be interested in reading the transcript below. Enjoy!

Guido Altarelli, LHC Physics in the Standard Model and Beyond

Guido started by announcing that finally, the LHC era has started. The top priority is to clarify the EW symmetry breaking sector, and possibly identify the dark matter particle if there is one, plus of course to search for new physics. But also there are other important experiments, LHCb and ALICE, which will extract important information. At this point in particle physics a fresh input from experiment is badly needed!

In a slide he showed how the machine's performance is improving, explaining that physics is back at CERN in its greatest form.

He then asked the question: What is the status of particle physics today ? Everybody is convinced that the Standard Model (SM) is a low-energy effective theory. It is a renormalizable theory, calculable with precision, well-supported by the data. However we expect corrections to it from higher energy processes. But it is true that the SM is not satisfactory even as a low-energy effective theory. The SM is composed of two parts. The QCD and gauge theory part of EW theory are fine, but the Higgs sector is only a conjecture. It is a sector very uncertain and problematic.

All problems of SM show up in the Higgs sector: the potential has a vacuum energy problem, it is at the origin of quadratic divergences, it yields possible instabilities depending on the Higgs mass, and then there is the flavour sector: large unexplained ratios of Yukawa couplings. These shortcomings were discussed also by Antonio Masiero in a previously reported talk.

While the symmetric part of the Lagrangian is very well tested, for the Higgs sector almost nothing is known. All we know is the direct bound of LEP II and Tevatron; radiative corrections constrain the mass to be below 186 GeV; and we also know that wherever the Higgs is it must be a doublet of weak isospin.

That the same sort of spontaneous symmetry breaking mechanism is at work has been already established (couplings are symmetric, the spectrum is totally non symmetric). But the question is the nature of the Higgs mechanism and the nature of the corresponding particle(s). Is it only one or more doublets, SM or SUSY, fundamental or composite, a pseudo-Goldstone boson of an enlarged symmetry, a manifestation of extra dimensions like a fifth component of a gauge boson, an effect of orbifolding, or some combination ?

Altarelli tried to answer this very hot question: Can we do without the Higgs ? Suppose we take the gauge part of the SM and put masses by hand. One loses understanding of the observed accurate validity of gauge predictions, however those predictions could be reobtained by fine tuning the parameters. So what is the fatal problem at the LHC scale ? The most immediate is that there is unitarity violation.

As is well known, the Higgs is essential in ensuring that the scattering amplitudes with longitudinal weak bosons satisfy tree-level unitarity constraints. If there is no Higgs, something must happen. Either there are Higgses, or new states (for example new vector bosons). So something must happen at the TeV scale.

A connected question is therefore, what saves unitarity ? This is a crucial question at the LHC. Is it the Higgs or some new W', Z' boson ? Maybe some KK recurrence, or resonances from the strong sector.

On the SM Higgs mass, there are theoretical limits expressed on lambdam the scale of energy at which the SM breaks down for the turning on of new interactions or effects. Perturbation theory brings a upper limit which goes down if you want the SM to be valid to high scales. Also there is a lower limit from the stability of the vacuum in the SM, wich makes the Higgs safe at all energy scales only if it is heavier than 128 GeV. 180 GeV is the upper limit for lambda up to 10^18 GeV.

There are beautiful successes of SM in precision tests: radiative correction fits give the mass of the Higgs as Log(Mh)=1.94+-0.15. The central value is 87 GeV, with +35-26 GeV error bars. There is some tension with experimental bounds.

Another question that Guido posed to himself was the following: is it possible that the Higgs is not found at the LHC (by which we mean the solution of the EW breaking mechanism) ? This seems unlikely, since the discovery range is large at LHC. A heavy Higgs boson would make perturbation theory to collapse. This is very hard to reconcile with EW precision tests plus the theory "simulating" a light Higgs. It would be sort of a conspiracy that the heaviness of a higgs is canceled to our eyes in SM fits.

He then offered the following gedankenexperiment. Suppose you find the Higgs, so then the SM is complete. Why should we continue particle physics ? His answer is simple: because of the conceptual problems of the SM and of the experimental clues that there must be something beyond which is at arm's reach. On the theory side, the conceptual problems include the inclusion and formulation of quantum gravity, the hierarchy problem, and the flavour puzzle. On the experimental side, the clues are dark matter, baryogenesis, new effects like neutrino masses.

Even more important is that some of these problems point at new physics already at the weak scale. Dark matter (DM) is a very impressive phenomenon: most of matter is dark, and most of the energy content in the universe is not even matter but a different form of vacuum energy. We also know that most DM is cold, non relativistic at freeze-out). Many extensions of the SM have good candidates for DM, like a SUSY neutralino, but there are other possibilities. Axions are one of the most conservative, introduced to solve the strong CP violation problem.

The LHC has a great chance because the case for WIMPS (weakly interacting massive particles) is very different. These are supposed to have electroweak-intensity couplings. These wimps are exceptional in two respects: they give the correct relic density for dark matter, contrarily to axions (which you have to tune to get the right amount). The second great aspect of WIMPS is that they can be seen at the LHC. The LHC can say yes or no to WIMPS, this is really the main question to answer.

Altarelli then moved on to discuss a few more specific aspects of the current theory and the proposed solutions. The hierarchy problem, in particular the little hierarchy one, is that renormalization nowadays is seen as not as a fundamental concept, but a trick to extract information from a theory which we modified at higher energy. The cutoff to new effects to quench singularities has a physics significance, so in this resopect the renormalized quantities must make sense physically. The radiatiove corrections to H and W which would be normally quadratic must not exceed the mass itself, so you expect something to happen around 1 TeV. Then some nervousness kicks in, because if new physics (NP) is so close, why did not we see it already ? We had recently two powerful probes, LEP on one hand, and more recently we had an additional powerful exploration, flavour physics from B factories. Yet no deviations were found from SM predictions. How is it possible that NP is so close and it does not show up ? This needs a very special type of physics.

This brought in another crucial question that Guido posed to the audience and to himself: what dampens the top loop effects ? Since the H is most coupled to the top, there is no surprise that the top loop is the more sensitive. What dampens the lambda squared dipendence ? Possibilities are a scalar top quark (SUSY) or some new fermion (t' -little Higgs) , or KK recurrences of the top as in extra dimensions. There are many solutions that have been suggested. The most complete is SUSY, where the cutoff in the formula is replaced by a gap between masses of SUSY and ordinary particles. Or some kind of strong binding foce, technicolor. Models of extra symmetry allow the mass of the Higgs only at two loops and the non perturbative regime starts at 10 TeV. Or extra spacetime dimensions.

But there might be also a rather cynical solution: invoke the anthropic principle and ignore the problem. The discovery of a number for the cosmological constant (CC) is the hint. We measured it as rho_lambda=(2E-3 eV)^4 = (0.1 mm)^-4 . The empirical value of the CC is not understood. What is impressive is that before the discovery of this number, Weinberg had presented an upper bound of the CC in order to allow galaxy formation, and the value observed later is close to the Weinberg one. Does this suggest that our Universe is one bubble among infinitely many, where we are in a dynamically stationary state? The idea is that our universe is not stationary, but there is a multitude of Universes and different physics is realized in each of them. The frustration of string theory is that the compactification of Calabi-Yau manifolds leads to a multitude of possible solutions, and you could imagine all these realizations to be different. 10^500 of them, a huge number. So the idea is that perhaps we live in a very unlikely Universe, but the one that allows our existence.

Guido's point about this anthropic explanation invoked to mend the SM problems is that all this is very nice, but applying it to the SM hierarchy problem is not appropriate. There are plenty of models that reduce the fine tuning from 10^14 to 10^2: so why make our Universe so terribly unlikely ? It does not make much sense, even in the language of the anthropic principle. There would be many bubbles with SUSY, which would solve the problem otherwise.

So all points to the notion that we expect we will find NP. Which one ? SUSY remains the main model, because it is the most complete, consistent, computable. In agreement with coupling unification (GUTs). This is unique among NP models. It also has a good DM candidate. It remains the main route. All other models of physics beyond the SM become strongy interacting at some intermediate scale, and do not allow extrapolations.

If you add SUSY you get a resolution of the tension between electroweak observables and the Higgs mass. Actually people have added to the classic precision tests also the data from B_s decays to dimuons and the anomalous moment of the muon. The fit results in less tension among theory and experiment, and with a good solution of DM neutralino. All that with values of the parameters which are light enough for discovery at LHC.

At this point Altarelli mentioned that the 3-sigma deviation between experimental determination of the muon anomaly and theoretical predictions might well be a real signal of NP. In fact it is a plausible location for the NP signal, since that is such a precise measurement. A light SUSY mass with reasonable tan(beta) fits in well.

Altarelli then discussed briefly a few other models. The little Higgs model is a virtuoso game in group theory. One enlarges the symmetry in order to make the generation of the Higgs mass corerctions only at two loops. Beyond that the theory is not computable, it loses transparency. However you have plenty of particles at the LHC range, so this theory gives a target for LHC to shoot at. Technically possible.

Extra dimensions (ED) are more revolutionary. They come from string theory. The idea is that some of the EDs survive at low energy. A large domain of contemporary beyond-the-SM constructs come from that. The old approach was of large compactified EDs, which now has been replaced by a more modern approach, with warped extra dimensions a' la Randall-Sundrum. This emerges as the most promising formulation. In this scheme we live, or at least the Higgs boson lives in the infrared brane, and the physics at the Planck scale is red-shifted. The metric is warped. This can be appleid to gauge symmetry breaking even without the Higgs. H is a sort of boundary condition effect, and of course you may ask how comes that unitarity is restored: this is due to KK recurrences, so the real problem of this theory is the tension with precision tests. Otherwise they could work if KK recurrences are very near, so visible at the LHC.

The most popular realistic models are composite Higgses. For example in 5-dimension holographic theory. Here all SM fields are in the bulk except the Higgs, which is a pseudo-Goldstone of an enlarged symmetry, and electroweak symmety breaking is triggered by bulk effects. The Higgs here is rather light. It is interesting that in warped geometries the fermion mass hierarchy the masses are explainable by a warp factor which is exponential. One could test this scheme.

A more model-independent approach by Georgi and Kaplan is that the light higgs is a bound state of a strongly interacting sector. A pseudo-Goldstone boson of an enlarged symmetry, for instance deriving from SO(5)/SO(4). There is a phenomenology wich has been studied and is testable at the LHC.

To conclude, from model building we get some lesson. There almost everywhere is a Higgs which is light, and there is always some percent-level fine-tuning at least. It is in the data, in some way. It is, so to speak, imposed by the data. Everybody asks the following question: is it possible that the LHC does not find a Higgs ? Yes, but in that case something else must be found because of the unitarity problem.

A more critical scenario is described by the following question: Is it possible that LHC finds the Higgs but no other new physics (pure and simple SM) ? Yes, it is possible but not natural, it entails that we live with an enormous fine tuning.

Finally, is it possible that the LHC finds neither the Higgs nor NP ? Altarelli claims that this is impossible, except for the fact that the energy and luminosity need to be sufficient to fully explore the electroweak scale. Is it sufficient ? Normally it should. But we cannot exclude that the solution is right beyond. That is why it is "approximately impossible".