Extra Dimensions at the LHC: Status Update

The Planck scale is the scale at which quantum gravitational effects are expected to become important. An extrapolation of the strength of gravity gives a value of 10¹⁶TeV, which is far out of reach for collider experiments. In the late 90s however, it was pointed out by Arkani-Hamed, Dimopoulous and Dvali, that this extrapolation does not hold if our spacetime has additional spacelike dimensions with certain properties. If that was the case, the true Planck scale could actually be at a TeV, an idea that is appealing because it does away with the question why the Planck scale is so large, respectively why gravity is so weak, to begin with. The answer would be, well, it isn't, it is only apparently so: Our naive extrapolation doesn't hold because space-time isn't four-dimensional. (For more details, read my earlier post.)

This (and other) extra dimensional models with a lowered Planck scale have been very popular at the beginning of the last decade and caused an extraordinarily high paper production which reflects not only the number of theoretical particle physicists, but also their desperation to put their skills to work. The most thoroughly analysed consequence of such models are the modification of standard model cross-sections through virtual graviton exchange and the production of black holes at the LHC. The latter possibility in particular received a lot of attention in the media due to some folks who accused physicists of planning the end of the world just to increase their citation count. (For more details, read these earlier posts.)

In any case, the LHC is running now, data is coming in and models are being sorted out, so what's the status?

In arXiv:1101.4919, Franceschini et al have summarized constraints from the LHC's CMS and ATLAS experiments on virtual graviton production. For the calculation of the contributions from virtual gravitons one needs to introduce a cut-off Λ of dimension energy that, next to the lowered Planck scale, becomes another parameter of the result. The constraints are then shown as contour plots in a two parameter space, the one parameter being the 'true' fundamental Planck scale, here denoted M_D, and the other one being mentioned cut-off, or its ratio to M_D respectively. One would expect the cut-off to be in the range of the lowered Planck-scale, though it might be off by a factor 2π or so, so the ratio should be of the order one. The figure below (Fig. 6 from arXiv:1101.4919) shows the bounds for the case of 4 additional spacelike dimensions:

The continuous line is the constraint from CMS data (after 36/pb integrated luminosity. Don't know what that means? Read this), and the dashed line is the constraint from ATLAS. The shaded area shows the excluded area. As you can see, a big part of the parameter space for values in the popular TeV range is meanwhile excluded.

Now what about the black holes? A black hole with a mass a few times the lowered Planck mass would already be well described by Hawking's calculation for particle emission, usually called Hawking-radiation. It would have a temperature (or average energy of primary emitted particles) of some hundred GeV. Just statistically, a big fraction of the emitted particles carry color charges and are not directly detected, but they form color strings that subsequently decay into a shower of hadrons, ie color neutral particles (pions, protons, etc). This process is called hadronization, and the event is called a jet. Depending on how many jets you get, it's a di-jet, tri-jet or multi-jet. The black hole's Hawking radiation would typically make a lot of particles and thus contribute to the multi-jets. One expects some multi-jets already from usual standard-model processes ("the background"), but the production of black holes should significantly increase the number. The figure below (from this paper by the CMS collaboration) shows an actual multi-jet event at the LHC:


In the paper arXiv:1012.3375 [hep-ex], the CMS collaboration summarized constraints on the lower mass of black holes in models with extra dimensions. For this, they analyzed the amount of multi-jet events in their data. The figure below (Fig 2 from arXiv:1012.3375) contrasts the predictions from the Standard Model with those of models with black hole production, for events with multiplicity N larger than 3 (that includes jets, but also photons, electrons and muons that don't hadronize).

On the vertical axis is the number of multi-jet events per bin of 100 GeV, on the horizontal axis the total transverse energy of the event (if you don't know what that means think of it as just the total energy). The solid blue line is the Standard Model prediction, the shaded area depicts the uncertainty. The various dotted and dashed lines are the predictions for the number of such events for different values of the minimal black hole mass, usually assumed to be in the range of the lowered Planck scale. These lines are created by use of event generators, ie numerical simulations. From this and similar data, the CMS collaboration is able to conclude that they haven't seen any black holes for minimum masses up to 4.5 TeV. CMS has an update on these constraints here, where they've pushed the limits up to 5 TeV, if not with amazingly high confidence level.

Some comments are in order though for the latter analysis. It argues with the production of multi-jets by black holes. This is a reliable prediction only for black holes produced with masses at least a few times above the lowered Planck scale. The reason is that a black hole of Planck mass is a quantum gravitational object and it is not correctly described by Hawking's semi-classical calculation. How to correctly describe it, nobody really knows. It is for the sake of numerics typically assumed that a black hole of Planck mass makes a final decay into a few particles. But that's got nothing to do with theory, it is literally just a subroutine in a code that randomly chooses some particles and their momenta such that all conservation laws are fulfilled. (The codes are shareware, look it up if you don't believe it.)

That procedure wouldn't be a problem if that was just some pragmatic measure to deal with the situation that has no impact on the prediction. Unfortunately it is the case that almost all black holes that would be produced at the LHC would be produced in the quantum gravitational regime. The reason is simply that the LHC is a hadron collider, and all the energy from the protons is redistributed on its constituents (called partons). As a result of this, the vast majority of the black holes produced have masses as low as possible, ie close by the new Planck scale.

What that means is that it is actually far from clear what the CMS constraints on excess of multi-jets mean for the production of black holes. A similar argument was recently made by Seong Chan Park in Critical comment on the recent microscopic black hole search at the LHC, arXiv:1104.5129.

Summary: It clearly doesn't look good for models with a lowered Planck scale. While it is in many cases not possible to falsify a model, but just to implausify it, large extra dimensions are becoming less plausible by the day. Nevertheless, one should exert scientific caution and not jump to conclusions. The relevance of CMS constraints on multi-jets depends partly on assumptions about the black holes' final decay that are not theoretically justified.

Question for the experts: Why do the curves in Fig 2 of the CMS paper seem to have a bump around the mininum black hole mass even though N > N^min?