Holographic Baryons

Last week Deog Ki Hong was explaining how baryons can be realized in holographic QCD. Holographic QCD is a new sport discipline that consists in modelling the symmetries and dynamics of strongly coupled QCD using weakly coupled theories in more-than-four dimensions. This approach is inspired by the AdS/CFT conjecture that links N=4 superconformal gauge theories with large number of colours and large t'Hooft coupling to higher dimensional supergravity. QCD, however, is neither supersymmetric nor conformal and it is unclear whether a holographic dual exists. In fact, one can argue that it does not. Nevertheless, some bottom-up, phenomenological constructions turned out to be quite successful, against all odds.

There are two roads that lead to holographic QCD. That of Sakai and Sugimoto, rooted in string theory, uses the language of D8-branes embedded in a D4-brane background. A more pedestrian approach takes its origin from the paper of Erlich et al. , who skip the stringy preamble and exploit 5D gauge theories in curved backgrounds. The global chiral symmetry of QCD - $U(2)_L x U(2)_R$ (or U(3)xU(3) if we wish to accommodate strangeness) - is promoted to a local symmetry group in 5D. Besides, the 5D set-up includes a bifundamental scalar field with a vacuum expectation value. The Higgs mechanism breaks the local symmetry group to the diagonal $U(2)_V$, which mimics chiral symmetry breaking by quark condensates in QCD.

So far, most of the studies were focused on the meson sector. Spin 1 mesons (like the rho meson) are identified with Kaluza-Klein modes of the 5D gauge fields. The spin 0 pions are provided by the fifth components of the 5D gauge fields (mixed with pseudoscalars from the Higgs field). Employing usual methods of higher dimensional theories, one can integrate out all heavy Kaluza-Klein modes to obtain a low-energy effective theory for pions. The result can be compared with the so-called chiral lagrangian - the effective theory of low-energy QCD that is used to describe pions and their interactions. Coefficients of the lowest-order operators in the chiral lagrangian have been measured in experiment. Holographic QCD predicts values of (some combinations of) these coefficients, and the results agree with observations. Furthermore, holographic QCD predicts various form factors of the vector mesons that also have been measured in experiment. Again, there is a reasonable agreement with observations. The accuracy is comparable to that achieved in certain 4D approximate models based on large N QCD. All in all, a rather simplistic model provides quite an accurate description of low-lying mesons in low energy QCD.

Baryons are more tricky. In the string picture, they are represented by D5 branes wrapping S5, which sounds scaring. In the 5D field theory picture, they are identified with instanton solitons - still somewhat frightening. But it turns out that these instantons can be effectively described by a pair of 5D spinor fields. Now, study of fermions in a 5D curved background is a piece of cake and has been done ever so often in different contexts. The original instanton picture together with the AdS/CFT dictionary puts some constraints on the fermionic lagrangian (the 5D spinor mass and the Pauli term).

With this simple model at hand, one can repeat the same game that was played with mesons: look at the low-energy effective theory, compare it with the chiral lagrangian predictions and cry out of joy. There are two points from Deog Ki's talk that seem particularly interesting. One is the anomalous magnetic moment of baryons. Holographic QCD predicts that those of proton and neutron should sum up to zero. In reality, $\mu_p = 1.79 \mu_N$, $\mu_n = - 1.91 \mu_N$ where $\mu_N = e/2 m_N$ is the nuclear magneton. The other interesting point concerns electric dipole moments. In the holographic model the electric dipole moment of the neutron can be simply connected to the CP-violating theta angle in QCD (something that seems messy and unintuitive in other approaches) . There is another sum rule that the electric dipole moments of protons and neutrons should sum up to zero.

In summary, simple 5D models yield surprisingly realistic results. Of course, more conventional approaches to QCD may achieve a similar or better level of precision. The drawback is also that the holographic approach has no rigorous connection to QCD, so that it's not clear what is the applicability range and when should we expect the model to fail. Nevertheless, the 5D approach provides a simple and intuitive picture of low-energy QCD phenomena. The experience that is gained could also be useful in case we stumble upon some new strong interactions in the LHC.


Although technological consciousness at CERN TH is clearly improving, some convenors have not yet discovered the blessings of modern means of communication. Translating to English: slides from this talk are not available. Here you can find partly overlapping slides from some conference talk. If you long for more details, check out these papers.

Higgs and Beyond

Every year in autumn, physicists follow atavistic instincts and spam the arXive with conference proceedings. While book proceedings may be of some use as a paper weight, the ones posted on the arXive are typically cut&paste from existing papers awkwardly clipped to fit the page limit. From time to time, however, one may stumble upon a nice, concise review. I recommend the recent short article by Gian Giudice about theories of electroweak symmetry breaking. The article gives a pretty accurate picture of the current state-of-art in the field; it covers everything that deserves being mentioned plus a few things that does not.

As an appetizer, I review here one interesting and not so well known point raised by Gian. Everybody knows that the LEP and SLD precision measurements hint towards a light higgs boson and constrain the standard model higgs boson mass to a quite narrow range. The best fit value, $76_{-24}^{+33}$ GeV, is a little disturbing, given the direct search limit 115 GeV, but still it lies comfortably within the 2-sigma limits. The situation is however more involved, as explained below.

The plot shows the higgs boson mass as inferred from individual measurements . The two most sensitive probes: the leptonic left-right asymmetry and the bottom forward-backward asymmetry do not really agree. The former points to a very light higgs boson, $31_{-19}^{+33}$ GeV, already excluded by LEP, while the latter suggests a heavy higgs $420_{-190}^{+420}$ GeV. Only when we combine these two, partially incompatible measurements in an overall fit of the standard model parameters, we get an estimate that is roughly compatible with the direct search limit. The bottom asymmetry is often considered a mote in the eye, as this is the only LEP measurement that is more than 3-sigma away from the standard model predictions. However, if we decided that this measurement suffers from some systematic errors and removed it from the fit, we would conclude that the standard model is almost excluded by direct higgs searches. That's irony.

This tension raises some hopes that the standard model higss boson is not the whole story and some new physics will emerge at the LHC. For a critical review of the alternatives, read the article.

Habemus DG

Here at CERN, Director General is as an important figure as the Pope for catholics or Papa Smurf for small forest creatures. He rules the greatest laboratory on Earth with an iron hand, while diplomatic immunity allows him to avoid parking tickets in Geneva. The current DG, Robert Aymar, is supposed to step down at the end of 2008. Last week, the CERN conclave rolled dice to decide who will take over the post for the following 5 years. The lot fell on Rolf-Dieter Heuer, currently one of the DESY directors. By the end of this year, he should officialy become DG elect.

Good news is that the nominee is a physicist, which might prove useful in the LHC days... It's also good news for ILC supporters, probaly less good for those who bet on CLIC. It's not a good news for me, as my April Fools prank will remain an April Fools prank :-( . By 7:10.

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.