Physicists Sifted Three Years of LHC Collisions for the Spherical Spray a Microscopic Black Hole Would Leave When It Evaporates. They Found None Up to 12 TeV, Which Means Any Extra Dimensions Are Smaller Than Hoped and String Theory's Ten Dimensions Can Shrink to No More Than Two That Matter Here.

Two decades after the Large Hadron Collider briefly frightened the public with talk of black holes, physicists have carried out the most sensitive search yet for the microscopic version the machine might actually produce, and have come up empty. The result, published in Progress in High Energy Physics by a team at the University of California, Santa Barbara, rules out quantum black holes up to a mass of about 12 teraelectronvolts and tightens the limits on the extra spatial dimensions that would be needed to make them.

The idea behind the search is one of the more elegant proposals for fixing a deep problem in physics. Gravity is absurdly weaker than the other three fundamental forces, and the energy scale at which it should become quantum, the Planck scale, sits some 17 orders of magnitude above anything a collider can reach. One explanation, proposed in the late 1990s, is that gravity is not actually weak but is leaking into extra dimensions too small to see. If so, gravity would grow stronger much faster at short distances, the true Planck scale could be within reach, and a head-on proton collision at the LHC could, very rarely, pack enough energy into a small enough volume to fold spacetime into a black hole.

"So what do you need to make a black hole? Well, you have to compress some energy into a really small volume," said Steven Giddings, the UCSB theorist who was among the first to propose the scenario. Such an object would evaporate almost the instant it formed. "They wouldn't stick around very long. If you made one, it would disintegrate immediately," Giddings said. That instant evaporation is what turned the 2008 safety scare into a non-event, and it is also what makes the objects detectable: they should decay into a spray of many high-energy particles flying out in every direction at once.

That signature is what Tamas Vami, a postdoctoral researcher on the Compact Muon Solenoid experiment, and graduate student Danyi Zhang went looking for in CMS data recorded between 2016 and 2018. They used two approaches. One measured sphericity, how evenly the debris of a collision is distributed around the collision point. The other simply summed the energy of all the decay products and looked for events where the total was implausibly large. "We know that black holes are very high energy," Zhang said. "If the sum is large enough, we can say that this is the region where we are likely to find the signal."

The team also tried something new. UCSB theorist Nathaniel Craig and collaborators had developed a way to define a "phase-space distance" between two collision events, a single number that captures how different they are once every particle's energy and momentum is accounted for. Feeding those distances into a support vector machine, a supervised machine-learning classifier whose internal math can be inspected, produced a score for each event that separated black-hole-like signals from ordinary Standard Model background. "We compared phase-space distance with the sphericity variable, and our conclusion is that phase-space distance outperforms sphericity," Zhang said. It is the first time the method has been applied to a real particle-physics analysis.

Neither method found anything. The data are consistent with the Standard Model alone, which means that within the models the team considered, quantum black holes lighter than about 12 TeV do not exist, and extra dimensions large enough to produce them are excluded. Vami put the constraint bluntly. String theory assumes a total of ten dimensions, he said, "but these measurements say that, assuming the parameters of the theories we considered, you cannot have more than two" that are large enough to affect LHC collisions.

"Had we found evidence, we could have begun to directly study quantum gravity," Vami said. "It's a step toward unifying all of the known fundamental forces, which has been a goal of physicists for more than a century." Zhang argued the null result is knowledge in its own right. "It's not a dead end," she said. "The result is an exclusion limit, which is a real, publishable statement: If this thing existed with these properties, we'd have seen it. We didn't, so we can rule it out here."

The LHC is probing distances down to about 10 to the minus 20 meters, a scale that is to an atom what an atom is to a person. "As with microscopy, higher energies mean smaller wavelengths, allowing one to probe smaller distances," said Joe Incandela, the UCSB professor who leads the group and a former CMS spokesperson. The collider's ongoing high-luminosity upgrade will deliver far more collisions in the 2030s, and the phase-space tools built for this search are designed to be turned on whatever else might be hiding in them.