## Hooman Davoudisal: Extra dimensions and the LHC May 25, 2008

Posted by dorigo in physics, science.
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Let me continue the long string of posts describing what I heard at the PPC 2008 conference last week with a report on a talk by Hooman Davoudisal, who gave a very clear and entertaining overview of the issue of Large Extra Dimensions, and their testability in the near future.

He started by saying that the topic he was given to report on is narrow, but hundreds of papers have been written on the matter of large extra dimensions (LED) theories. He thus had to pick a few things to discuss about this widely studied topic.

Extra dimensions are not a new idea – they date back on an attempt by G.Nordstrom in 1914, who tried to unify pre-general relativity gravity and electromagnetism in a 5-dimensional world. This was followed by the work of Kaluza in 1921, and Klein in 1926. More recently, string theory has been recognized to require 10 or 11 dimension. The extra ones are compactified at a fundamental scale. This is motivated by the hierarchy problem, that is the fact that there is a very small ratio between electroweak scale and the Planck mass: $M_W/M_P = 10^{-17}$.

Arkadi-Hamed, Dimopoulos, and Dvali in 1998 studied the case of N compact extra dimensions to stabilize the hierarchy: the fundamental scale is now of the universe is of the order of a TeV. Extra dimensions are large in units of the fundamental scale.  Their scales range from a fermi to a millimeter.  The standard model particles are localized on a “3-brane”, which is a four-dimensional sheet in the multi-dimensional space. Gravity propagates in all dimensions, and therefore gets diluted by the extra dimensions. Kaluza-Klein modes are quantized momenta in the extra dimensions. They correspond to our picture of particles in a box: if you took a course in quantum mechanics, you know that particles confined in a box get their energy levels quantized.

Hooman said that the key signal for LED detection is, what do you know, missing energy! [Apparently, if LHC does not find anything in its missing energy spectrum it will put on the road string theorists, SUSY phenomenologists, and LED aficionados all together: quite a democratic turn of events, if you ask me].  Kaluza-Klein (KK) gravitons escape in the “bulk” -the extra dimensions- and they leave behind the energy bill to pay. KK gravitons could be produced by quark-antiquark annihilation. Also, spin-2 “towers” of KK gravitons  can give rise to spin-2 mediated angular distributions of the final state particles. Further, a possibility is black hole production. When you bring the Planck scale down, you can create  black holes in reasonably sized particle accelerators, such as the LHC -it does not fit in your living-room, but it is smaller than the solar system after all.

The signature of black hole production would be potentially spectacular signals, with energetic  multijets, multi-lepton events. However, this picture is under debate. Meade and Randall say  that this turn of events is difficult at LHC.

For large extra dimensions, searches have been done at the Tevatron and LEP. LEP has a better bound for few additional extra dimensions (well above a TeV), while for many extra dimensions -4 and above- the Tevatron wins, and has limits just below one TeV. These are extracted from both the jet plus missing  energy signature and the photon plus missing energy signature.

A more generic framework is that of universal extra dimensions (UED). This scenario entails Lorentz violation along the extra dimensions, and the lightest Kaluza-Klein particle  is stable. The resulting pheonomenology has the potential of mimicking supersymmetry at the LHC. If you are a believer, you may expect a huge debate going off between UED and SUSY aficionados as soon as ATLAS and CMS start observing missing energy signatures.

Hooman pointed out that the latest UED limit was obtained at CDF using Run 1 data! The lower limit is at 280 GeV. I rushed to check and by jove, he is right: what a jolly gathering of lazy bums CDF is! No results from Run II have been produced [and may I say, I see none in preparation either… Maybe D0 does ?]

The Randall-Sundrum model with a 4-dimensional Standard Model (1999) has its pros: a natural Planck-weak hierarchy, and striking signals. However, the fundamental cut-off is of the order of a TeV, and this is dangerous. [There follows a sentence I cannot make much sense of… Explanations by experts is appreciated here:] Standard Model flavor from a warped bulk: it was realized by placing the SM in the 5-dimensional bulk; the bulk has all SM particles in it. One wants to keep the Higgs boson localized  to the 4-D brane. Localizing the zero-mode of fermions, and fermions have fundamental scale which gives  a higher effective scale. This modifies the RS phenomenology quite a bit because now couplings get diluted. To place the collider reaches in perspective, assume bulk profiles for fermions, realistic flavor. KK gluon exchange contribution: one is required $M_{KK}>20 TeV$, 1-2 TeV is not favored by these  bulk models. So if you want to explain flavor and other things in these models you are  pushed to higher scales. [Ok, back to better understood sentences.]

In conclusion, Hooman explained that extra dimensions offer the possibility to solve the hierarchy problem, and shed light on the flavor sector of the SM. New phenomena can be discovered at TeV scale. He asked the audience to acknowledge that a discovery of extra dimensions would be a fundamental revolution in science, and as far as I could detect, nobody objected. He concluded by saying that various scenarios can be tested at the LHC.  The original Randall-Sundrum model had rosier signals, but once one introduces more sophistication, signals may become more elusive. This is true also for LED, where black hole signals could be less obvious or likely.

1. Alejandro Rivero - May 25, 2008

Old-fashioned Kaluza Klein extra dimensions could have a role at the mathematical level: unbroken standard model needs 7 extra dimensions (for an action of SU3xSU2xU1); completely broken standard model needs 5 extra dimensions (for an action of SU3xU1); and the GSW-broken standard model lives somewhere in the middle. Also, stringers like to speak of 6 extra dimensions, and Connes-Chamseddine speaks of dimension 6 mod 8 KO for its version of the standard model.

2. dorigo - May 26, 2008

Ok, but why are these required to be of the KK type ? That is, I do not understand well what makes them different from other kinds (I admit, I did not read the papers)…

Cheers,
T.

3. Alejandro Rivero - May 27, 2008

Indeed, a big issue about string theoretists is that they keep divulgating about Kaluza Klein, while their procedure to obtain gauge groups is not the one of Kaluza Klein theories, as far as I can understand. They get the gauge groups from putative SO(32) or E8xE8 symmetries coming from the quantum strings, more akin to flavour groups, only that in the string these flavour groups are local gauge groups too. The extra dimensions in the string sometimes seem to have a role to break the symmetry, sometimes seem to produce the generations, sometimes they are pretty ignored.

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