Searches at ATLAS and CMS constrain models of extra dimensions.
At 10.00 a.m. on 9 August 2016, physicists gathered at the Sheraton hotel in Chicago for the “Beyond the Standard Model” session at the ICHEP conference. The mood was one of slight disappointment. An excess of “diphoton” events at a mass of 750 GeV reported by the LHC’s ATLAS and CMS experiments in 2015 had not shown up in the 2016 data, ending a burst of activity that saw some 540 phenomenology papers uploaded to the arXiv preprint server in a period of just eight months. Among the proposed explanations for the putative new high-mass resonance were extra space–time dimensions, an idea that has been around since Theodor Kaluza and Oscar Klein attempted to unify the electromagnetic and gravitational forces a century ago.
In the modern language of string theory, extra dimensions are required to ensure the mathematical consistency of the theory. They are typically thought to be very small, close to the Planck length (10–35 m). In the 1990s, however, theorists trying to solve problems with supersymmetry suggested that some of these extra dimensions could be as large as 10–19 m, corresponding to an energy scale in the TeV range. In 1998, as proposed by Arkani-Hamed and co-workers, theories emerged with even larger extra dimensions, which predicted detectable effects in contemporary collider experiments. In such large extra-dimension (LED) scenarios, gravity can become stronger than we perceive in 3D due to the increased space available. In addition to showing us an entirely different view of the universe, extra dimensions offer an elegant solution to the so-called hierarchy problem, which arises because the Planck scale (where gravity becomes as strong as the other three forces) is 17 orders of magnitude larger than the electroweak scale.
Particle physicists normally ignore gravity because it is feeble compared with the other three forces. In theories where gravity gets stronger at small distances due to the opening of extra dimensions, however, it can catch up and lead to phenomena at colliders with high enough rates that they can be measured in experiments. The possibility of having extra space dimensions at the TeV scale was a game changer. Scientists from experiments at the LEP, Tevatron and HERA colliders quickly produced tailored searches for signals for this new beyond-the-Standard Model (SM) physics scenario. No evidence was found in their accumulated data, setting lower limits on the scale of extra dimensions of around 1 TeV.
By the turn of the century, a number of possible new experimental signatures had been identified for extra-dimension searches, many of which were studied in detail while assessing the physics performance of the LHC experiments. For the case of LEDs, where gravity is the only force that can expand in these dimensions, high-energy collider experiments were just one approach. Smaller “tabletop” scale experiments aiming to measure the strength of gravity at sub-millimetre distances were also in pursuit of extra dimensions, but no deviation from the Newtonian law has been observed to date. In addition, there were also significant constraints from astrophysics processes on the possible number and size of these dimensions.
Enter the LHC
Analysis strategies to search for extra dimensions have been deployed from the beginning of high-energy LHC operations in 2010, and the recent increase in the LHC’s collision energy to 13 TeV has extended the search window considerably. Although no positive signal of the presence of extra dimensions has been observed so far, a big leap forward has been taken in excluding large portions of the TeV scale phase-space where extra dimensions could live.
A particular feature of LED-type searches is the production of a single very energetic “mono-object” that does not balance the transverse momentum carried by anything else emerging from the collision (as would be required by momentum and energy conservation). Examples of such objects are particle jets, very energetic photons or heavy W and Z vector bosons. Such collisions only appear to be imbalanced, however, because the emerging jet or boson is balanced by a graviton that escapes detection. Hence SM processes such as the production of a jet plus a Z boson that decays into neutrinos can mimic a graviton production signal. The absence of any excess in the mono-jet or mono-photon event channels at the LHC has put stringent limits on LEDs (figure 1), with 2010 data already bypassing previous collider search limits. LEDs can also manifest themselves as a new contribution to the continuum in the invariant mass spectrum of two energetic photons (figure 2) or fermions (dileptons or dijets). Here too, though, no signals have been observed, and the LHC has now excluded such contributions for extra-dimension scales up to several TeV.
In 1999, another extra-dimension scenario was proposed by Randall and Sundrum (RS), which led to a quite different phenomenology compared with that expected from LEDs. In its simplest form, the RS idea contains two fundamental 3D branes: one on which most if not all SM particles live, and one on which gravity lives. Gravity is assumed to be intrinsically strong, but the warped space between the two branes makes it appear weak on the brane where we live. The experimental signature of such scenarios is the production of so-called Kaluza–Klein (spin-2 graviton) resonances that can be observed in the invariant mass spectra of difermions or dibosons. The most accessible spectra to the LHC experiments include the diphoton and dilepton spectra, in which no new resonance signal has been found, and at present the limits on putative Kaluza–Klein gravitons are about 4 TeV, depending on RS-model parameters. Analyses of dijet final states provide even more stringent limits of up to 7 TeV. Further extensions of the RS model, in particular the production of top quark–antiquark resonances, offer a more sensitive signature, but despite intense searches, no signal has been detected.
Searching in the dark
At the start of 2000, it was realised that large or warped extra dimensions could lead to a new type of signature at the LHC: microscopic black holes. These can form when two colliding partons come close enough to each other, namely to within the Schwarzschild radius or black-hole event horizon, and can be as large as a femtometre in the presence of TeV-scale extra dimensions at the LHC. Such microscopic black holes would evaporate via Hawking radiation on time scales of around 10–27 s, way before they could suck up any matter, and provide an ideal opportunity to study quantum gravity in the laboratory.
Black holes that are produced with a mass significantly above the formation threshold are expected to evaporate in high-energy multi-particle final states leading to plenty of particle jets, leptons, photons and even Higgs particles. Searches for such energetic multi-object final states in excess of the SM expectation have been performed since the first collisions at the LHC at 7 TeV, but none have been found. If black holes are produced closer to the formation threshold, these would be expected to decay in a much smaller final-state topology, for instance into dijets. The CMS and ATLAS experiments have been looking for all of these final states up until the latest 13 TeV data (figure 3), but no signal has been observed so far for black-hole masses up to about 9 TeV.
Several other possible incarnations of extra-dimension theories have been proposed and searched for at the LHC. So-called TeV-type extra dimensions allow for more SM particles, for example partners of the heavy W and Z bosons, to enter in the bulk, and these would show up as high-mass resonances in dilepton and other invariant mass spectra. These new resonances have a spin equal to one, and hence such signatures could be more tedious to detect because they can interfere with the SM Drell–Yan production background. Nevertheless, no such resonances have been discovered so far.
In so-called universal extra-dimension (UED) scenarios, all particles have states that can go into the bulk. If this scenario is correct, a completely new particle spectrum of partners of the SM particles should show up at the LHC at high masses. Although this looks very much like what would be expected from supersymmetry, where all known SM particles have partners, the Kaluza–Klein partners would have exactly the same spin as their SM partners, whereas supersymmetry transforms bosons into fermions and vice versa. Alas, no new particles either for Kaluza–Klein partners or supersymmetry candidates have been observed, pushing the lower mass limits beyond 1 TeV for certain particle types.
Collider data so far have not yet given us any sign of the existence of extra dimensions, or for that matter a sign that gravity is becoming strong at the TeV scale. It is possible that, even if they exist, the extra dimensions could be as small as predicted by string theory, in which case they would not be able to solve the hierarchy problem. The idea is still very much alive, however, and searches will continue as more data are recorded at the LHC.
Even excellent and attractive ideas always need confirmation from data, and inevitably the initial high enthusiasm for extra-dimension theories may have waned somewhat in recent years. Although such confirmation could come from the next generation of colliders, such as possible higher-energy machines, there is unfortunately no guarantee. It could be that we have to turn to even more outlandish ideas to progress further.