CLICK

These days CERN hosts the CLIC workshop. CLIC is the famous italian porno comic book, and also the name of a future linear collider that is developed here at CERN. Somewhat disappointedly, the workshop is more focused on the latter. Most of the talks report on very hard-core R&D, but there is something for a wider audience too. A nice wrap-up of physics prospects was delivered yesterday by John Ellis.

If the technology turns out feasible (which should be concluded by the end of the decade), the machine is planned for the year two thousand twenty something. It will collide electrons with positrons at 3-5 TeV center-of-mass energies. This is not a big energy gain as compared to the LHC, but the much cleaner environment of a lepton collider will open up many new opportunities.

A light Standard Model-like higgs boson will be pinned down at the LHC, but a precise study of its properties must wait for a new linear collider. CLIC seems perfectly suited for this. The dominant production mode at a lepton collider is the W fusion whose cross section strongly increases with energy (see the plot). Various rare Higgs decays may be observed and the higgs coupling can be determined quite accurately. For example, the coupling to muons will be determined at the 2% level, while that to bottom quarks at 4% level. This will be a good test of the Standard Model predictions. Also, the higgs self-coupling can be measured, for example, the triple coupling can be determined with a 10% precision.

If the higgs is not found at the LHC, CLIC remains useful. It will be able to measure WW scattering precisely (something that is very tough at the LHC) and determine once and for all if the electroweak breaking is weakly or strongly coupled. Unfortunately, John did not talk about it and only a slight mention is made in the yellow report.

Obviously, if there is some new physics at the TeV scale, CLIC will be able to explore it. Whether we encounter extra dimensions, the little higgs or John's favourite supersymmetry, CLIC will measure the masses and couplings of the new particles. Have a look at the slides for a comparison of the CLIC and ILC performances in several supersymmetric models. CLIC is indispensable if the new particles have TeV or higher masses.

Just like LEP, CLIC will be able to indirectly probe physics up to scales much higher than its center of mass energy. This can be done by searching for effects of four-fermion interactions in the process of e+e- annihilating into muons. Such four-fermion interactions would appear as an effect of heavy virtual particles and they are suppressed by the mass scale of these heavy particles. CLIC will be able to probe these operators up to the scale of a few hundred TeV. In the nightmare scenario - only the Standard Model + the higgs boson found at the LHC - CLIC may tell us if there is some new physics within the reach of the next, more powerful machine. In that case, however , the CLIC performance is not terribly better than that if the ILC, as shown on the plot. CLIC people should better pray for new physics at the LHC.

Slides are available via the workshop page. There you also find video recordings of several other talks at the workshop. For those well-motivated, here is the yellow report.

Football @ CERN

In autumn otherwise important issues like PiMs or inner threesome magnets cease to attract any attention here at CERN. The focus is all on football. More precisely, the CERN indoor football tournament. This year is very special because one of the participating teams consists almost entirely of CERN theorists (since technical problems may sometimes arise, e.g. tying shoelaces, the team includes one experimentalist). The team plays under the name ThC which apparently stands for Theory Club. You probably imagine particle theorists as an awkward lot of short-sighted geeks that trip over their own legs. While this naive picture is correct in 95.4% of cases, the CERN theory group is large enough to have some reasonable players in the Gaussian tail. ThC played their first match last week and did not lose, which is already a better result than any theory team have achieved in CERN's history. The rumour is that if ThC continues to impress, they might choose a theorist for a new DG.

Buffalo Conspiracy

By pure chance i have made an amazing discovery. During my Sunday walk near the LHC point 7 i spotted THIS

Yes, these are buffalos quietly grazing on a pasture above the LHC ring. You would think that buffalos in the Geneva area should be a rare sight. I thought so too at first, but then i realized that they can also be found in Fermilab. And in an instant flash it all became clear.

The only logical explanation is that both the LHC and the Tevatron have been designed by buffalos who are in reality the second most intelligent species on Earth (after dolphins). The hadron collider installations must serve some important purpose that is conspicuous only to higher beings. To keep us humans motivated, the buffalos made up the hierarchy problem, supersymmetry, extra dimensions and string theory. The mystery to solve is what is THE question the LHC is supposed to answer. Once i find out, i'll let you know.

Degravitation

Last time I scolded the speaker for giving an utterly unattractive seminar title. Degravitation - which is the title of Gia Dvali's talk two weeks ago - is on the other hand very catchy and will certainly attract many Roswell aficionados to my blog. But this post, I'm afraid, is not about classified experiments with gravity performed here at CERN but about a new interesting approach to solving the cosmological constant problem. Gia is going to be around for some time, so you may expect more posts with weird titles in future.

The cosmological constant problem is usually phrased as the question why the vacuum energy is so small. Formulated that way, it is very hard to solve, given large existing contributions (zero-point oscillations, vacuum condensates) and vicious no-go theorems set up by Weinberg. The problem has ruined many lives and transformed some weaker spirits into anthropic believers. Gia does not give up and attempts to tackle the problem from a different angle. He tries to construct a theory where the vacuum energy may be large but it does not induce large effects on the gravitational field. This is of course impossible in Einstein gravity where all forms of energy gravitate. The idea can be realized, however, in certain modified gravity theories.

Gia pursues theories where gravity is strongly modified at large distances, above some distance scale L usually assumed to be of similar size as the observable universe. The idea is to modify the equations of gravity so as to filter out sources whose characteristic length is larger than L. The gravitational field would then ignore the existence of a cosmological constant, which uniformly fills the entire universe.

On a slightly more formal level, Gia advocates a quite general approach where the equations for the gravitational fields can be written as
$ ( 1 - \frac{m^2(p^2)}{p^2} ) G_{\mu \nu} = \frac{1} {2} T_{\mu \nu}$
where, as usual, $G$ is the Einstein tensor and $T$ is the energy-momentum tensor. Deviations from the Einstein theory are parameterized by $m^2(p^2)$ which is a function of momentum (or a funtion of derivatives in the position-space picture). For $m^2=0$, the familiar Einstein equations are recovered. The effects of $m^2$ set in at large distance scales.
At low momenta/large distances one assumes $m^2 \sim L^{-2} (p^2 L^2)^\alpha$ with $0 <= \alpha < 1$. The case $\alpha = 0$ corresponds to adding the graviton mass, the case $\alpha = 1/2$ corresponds to a certain 5D framework called the DGP model (where Gia is the D). In fact, the latter case is the only one for which the full, non-linear, generally covariant completion is known. Other values of $\alpha$ may or may not correspond to a sensible non-linear theory.

Gia argues that any consistent theory effectively described by this kind of filter equations has to be a theory of a massive or resonance graviton. This means that the graviton propagates 5 degrees of freedom and not 2 as in the Einstein theory. In addition to 2 tensor polarizations, there are 2 vector and 1 scalar polarization. The additional polarizations also couple to massive sources and their exchange contributes to the gravitational potential.

Everybody who ever played with modified gravity knows well that Einstein gravity reacts histerically to all manipulations and often breaks down. In the present case what happens is that, once the theory is extended beyond the linear approximation, the scalar polarization gets strongly coupled far below the Planck scale. But Gia argues that one can live with it and, in fact, the strong coupling saves the theory. It is well known since ages that the massive gravity suffers from the so-called van Dam--Veltman discontinuity: the potential between two sources is different than in Einstein gravity, even in the zero-mass limit. The responsible for that is precisely the scalar polarization. The predictions from massive gravity are at odds with precise tests of gravity, for example with observations of the light-bending by the Sun. These predictions, however, are derived using the linear approximation which breaks down near massive sources. Gia argues that the effect of the strong coupling is to suppress the scalar polarization exchange near massive sources and there is no contradiction with experiment.

So the picture of the gravitational field around a massive source in massive or resonance gravity is more complex, as shown to the right. Apart from the Schwarzschild radius, there are two other scales. One is the scale L above which gravity shuts off. The other is the r* scale where the scalar polarization gets strongly coupled. At scales larger than r* we have a sort of scalar-tensor gravity that differs ifrom Einstein gravity. At scales shorter than r* Einstein gravity is approximately recovered up to small corrections. Gia estimates that these latter corrections can be measured in future by the lunar laser ranging experiment if $\alpha$ is of order 1/2.

Coming back to the cosmological constant problem, the analysis is complicated and depends on the non-linear completion of the theory. Gia's analysis shows that this class of theories can indeed degravitate the cosmological constant when $\alpha < 1/2$. I'm not sure if this conclusion is bulletproof since it is derived in a special limit where the equations for the tensor and scalar polarizations decouple. What is certain is that the complete non-linear DGP model (corresponding to $\alpha = 1/2$) does not enjoy the mechanism of degravitation. The hope is that theories with $\alpha < 1/2$ do exist and that a full non-linear analysis will demonstrate one day that the cosmological constant problem is solved.

Slides available here. The paper has been out for 6 months now. It is worth looking at the previous paper of Gia, where the strong coupling phenomenon is discussed at more length. Try also to google degravitation to see how amazing paths the human mind may wander.

About LHC Progress

There are rumours appearing here and there about further imminent delays of the LHC start-up. As for the facts, two weeks ago Lyn Evans, who is the LHC project leader, gave a colloquium about the current status of the LHC. He did not mention any delays, but he described in great detail the efforts they are currently undertaking and the problems that have emerged. The video recording of this talk is available here. In particular, at 52:35 Lyn devotes some time to the plug-in modules between magnet interconnects, whose faults spawned the recent rumours. While I personally don't understand why can't they tie up the magnets with strings (or superstrings in the case of superconducting magnets), i guess those more experimentally oriented may get some insight. Anyway, experts advise not to get excited with this particular problem; there will be many others. As Lyn himself put it, at this point we are far less deterministic.

Deep Throats and Phase Transitions

Both of my readers have expressed their concern about my lack of activity in the last weeks. OK, let's say i wasn't in mood and go back to business.

Last week John March-Russell gave a seminar entitled Throats with Faster Holographic Phase Transitions. This sounds very encouraging to stay for another coffee in the cafeteria. This time, however, the first intuition would be wrong, as behind this awkward title hides an interesting and less studied piece of physics.

The story is about the Randall-Sundrum model (RS1, to be precise): five-dimensional theory in approximately AdS5 space cut off by the Planck and the TeV branes. The question is what happens with this set-up at high temperatures. There is a point of view from which the high-temperature phase can be simply understood. Here at CERN the local folks believe that the Randall-Sundrum set-up is a dual description of a normal (though strongly coupled) gauge theory in four dimensions. Therefore at high temperatures such phenomena as deconfinement or the emergence of a gluon plasma should be expected. How this phase transition manifests itself in the 5D description?

This last question was studied several years ago in a paper by Creminelli et al based on earlier results by Witten. It turns out that one can write down another solution of the Einstein equations that describes a black hole in the Ads5 space. The black hole solution is a dual description of the high-temperature deconfined phase: the TeV brane (whose presence implies the existence of a mass gap in the low-temperature phase) is hidden behind the black hole horizon.

Which of the two solutions dominates, that is to say, which one gives the dominant contribution to the path integral depends on the free energy F = E- T S. One can calculate that at zero temperature the RS1 solution has lower free energy. But the black hole solution has entropy associated with the black hole horizon and its free energy ends up being lower at high enough temperature. This black hole solution effectively describes a high-temperature expanding universe filled with a hot gluon plasma. As the temperature goes down to the critical value, the RS1 solution with a TeV brane becomes energetically more favorable and a first order phase transition occurs.

Creminelli et al computed the critical temperature at which free energies of the two phases are equal. They also estimated the rate of phase transition between the black hole and the RS1 phases. It turns out that, with the assumption they made about the mechanism stabilizing the fifth dimension, the rate is too low so that the phase transition could never be completed. The universe expands too fast and, although bubbles of the RS1 phase do form, they do not collide. One ends up with an empty ever-inflating universe. From this analysis it seems that, if RS1 is to describe the real world, the temperature of the universe should never exceed the critical one. Although this assumption does not contradict any observations, it makes life more problematic (how to incorporate inflation, bariogenesis...)

According to John, the problem with too slow phase transitions is not general but specific to the stabilization mechanism assumed by Creminelli et al. In his recent paper, John studied a modified version of RS1 - a string-inspired set-up called the Klebanov-Tseytlin throat. From the picture it is obvious that the Klebanov-Tseytlin throat is dual to a punctured condom. John found that in this modifed set-up the phase transition is fast enough to complete. The key to the success seems to be the fact that the different stabilization mechanism results
in a strong breaking of conformal symmetry in IR.

So much for now, more details in the paper. I think this subject is worth knowing about. It connects various areas of physics and cosmology and does not seem to be fully explored yet. First order phase transitions, like the one in RS1, may also leave observable imprints in the gravity waves spectrum, as discussed here.

Slides available.

Drowning the Hierarchy Problem

For a change, the third week of the New Physics workshop turned out to be very interesting. In this post I tell you about Gia Dvali and his brand new idea of solving the hierarchy problem. Several other talks last week deserves attention and I hope to find more time to write about it.

Gia first argued for the following result. Suppose there exists N particle species whose mass is of order M. Further suppose that these species transform under exact gauged discrete symmetries. Then there is a lower bound on the Planck scale:

$M_p > N^{1/2} M$

The proof goes via black holes. As argued in the old paper by Krauss and Wilczek, gauged discrete symmetries should be respected by quantum gravity. Therefore, if we make a black hole out of particles charged under a gauged discrete symmetry, the total charge will be conserved. For example, take a very large number N of particles, each carrying a separate Z2 charge. Form a black hole using an odd number of particles from each species, so that the black hole carries a Z2^N charge. Then wait and see what happens. According to Hawking, the black hole should evaporate. But it cannot emit the charged particles and reduce its charge before its temperature becomes of order M. The relation between the black hole temperature and mass goes like $T \sim M_p^2/M_{BH}$. Thus, by the time the charge starts to be emitted, the black hole mass is reduced to $M_{BH} = M_p^2/M$. To get rid of all its charge the black hole must emit at least N particles of mass M, so its mass at this point must satisfy $M_{BH} > N M$. From this you easily obtain Gia's bound.

The bound has several interesting consequences. One is that it can be used to drown the hierarchy problem in the multitude of new particles. Just assume there exists something like 10^32 new charged particle species at the TeV scale. If that is the case, the Planck scale cannot help being 16 orders of magnitude higher than the TeV scale. For consistency, gravity must somehow become strongly interacting at the TeV scale, much as in the ADD or RS model, so that the perturbative contributions to the Higgs mass are cut off at the TeV scale. Thus, in Gia's scenario the LHC should also observe the signatures of strongly interacting gravity.

You might say this sounds crazy...and certainly it does. But, in fact, the idea is not more crazy than the large extra dimensions of the ADD model. The latter is also an example of many-species solution to the hierarchy problem. In that case there are also 10^32 degrees of freedom - the Kaluza-Klein modes of the graviton, which make gravity strongly interacting at TeV. The difference is that most of the new particles is much lighter than TeV, which creates all sorts of cosmological and astrophysical problems. In the present case these problems can be more readily circumvented.

Transparencies available on the workshop page.