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What’s next for physics’ standard model? Muon results throw theories into confusion

A silhouetted figure in a hard hat stands in the LHCb Magnet.

The Large Hadron’s Collider LHCb detector, pictured, reported anomalies in the behaviour of muons, two weeks before the Muon g – 2 experiment announced a puzzling finding about muon magnetism.Credit: Peter Ginter/CERN

Physicists should be ecstatic right now. Taken at face value, the surprisingly strong magnetism of the elementary particles called muons, revealed by an experiment this month, suggests that the established theory of fundamental particles is incomplete. If the discrepancy pans out, it would be the first time that the theory has failed to account for observations since its inception five decades ago — and there is nothing physicists love more than proving a theory wrong.

But rather than pointing to a new and revolutionary theory, the result — announced on 7 April1 by the Muon g – 2 experiment near Chicago, Illinois — poses a riddle. It seems maddeningly hard to explain it in a way that is compatible with everything else physicists know about elementary particles. And additional anomalies in the muon’s behaviour, reported in March2 by a collider experiment, only make that task harder. The result is that researchers have to perform the theoretical-physics equivalent of a triple somersault to make an explanation work.

Zombie models

Take supersymmetry, or SUSY, a theory that many physicists once thought was the most promising for extending the current paradigm, the standard model of particle physics. Supersymmetry comes in many variants, but in general, it posits that every particle in the standard model has a yet-to-be-discovered heavier counterpart, called a superpartner. Superpartners could be among the ‘virtual particles’ that constantly pop in and out of the empty space surrounding the muon, a quantum effect that would help to explain why this particle’s magnetic field is stronger than expected.

If so, these particles could solve two mysteries at once: muon magnetism and dark matter, the unseen stuff that, through its gravitational pull, seems to keep galaxies from flying apart.

Until ten years ago, various lines of evidence had suggested that a superpartner weighing as much as a few hundred protons could constitute dark matter. Many expected that the collisions at the Large Hadron Collider (LHC) outside Geneva, Switzerland, would produce a plethora of these new particles, but so far none has materialized. The data that the LHC has produced so far suggest that typical superpartners, if they exist, cannot weigh less than 1,000 protons (the bounds can be higher depending on the type of superparticle and the flavour of supersymmetry theory).

“Many people would say supersymmetry is almost dead,” says Dominik Stöckinger, a theoretical physicist at the Dresden University of Technology in Germany, who is a member of the Muon g – 2 collaboration. But he still sees it as a plausible way to explain his experiment’s findings. “If you look at it in comparison to any other ideas, it’s not worse than the others,” he says.

There is one way in which Muon g – 2 could resurrect supersymmetry and also provide evidence for dark matter, Stöckinger says. There could be not one superpartner, but two appearing in LHC collisions, both of roughly similar masses — say, around 550 and 500 protons. Collisions would create the more massive one, which would then rapidly decay into two particles: the lighter superpartner plus a run-of-the-mill, standard-model particle carrying away the 50 protons’ worth of mass difference.

The LHC detectors are well-equipped to reveal this kind of decay as long as the ordinary particle — the one that carries away the mass difference between the two superpartners — is large enough. But a very light particle could escape unobserved. “This is well-known to be a blind spot for LHC,” says Michael Peskin, a theoretician at the SLAC National Accelerator Laboratory in Menlo Park, California.

The trouble is that models that include two superpartners with similar masses also tend to predict that the Universe should contain a much larger amount of dark matter than astronomers observe. So an additional mechanism would be needed — one that can reduce the amount of predicted dark matter, Peskin explains. This adds complexity to the theory. For it to fit the observations, all its parts would have to work “just so”.

Meanwhile, physicists have uncovered more hints that muons behave oddly. An experiment at the LHC, called LHCb, has found tentative evidence that muons occur significantly less often than electrons as the breakdown products of certain heavier particles called B mesons2. According to the standard model, muons are supposed to be identical to electrons in every way except for their mass, which is 207 times larger. As a consequence, B mesons should produce electrons and muons at rates that are nearly equal.

The LHCb muon anomalies suffer from the same problem as the new muon-magnetism finding: various possible explanations exist, but they are all “ad hoc”, says physicist Adam Falkowski, at the University of Paris-Saclay. “I’m quite appalled by this procession of zombie SUSY models dragged out of their graves,” says Falkowski.

Other options

The task of explaining Muon g – 2’s results becomes even harder when researchers try concoct a theory that fits both those findings and the LHCb results, physicists say. “Extremely few models could explain both simultaneously,” says Stöckinger. In particular, the supersymmetry model that explains Muon g – 2 and dark matter would do nothing for LHCb.

Some solutions nevertheless exist that could miraculously fit both. One is the leptoquark — a hypothetical particle that could have the ability to transform a quark into either a muon or an electron (which are both examples of a lepton). Leptoquarks could resurrect an attempt made by physicists in the 1970s to achieve a ‘grand unification’ of particle physics, showing that its three fundamental forces — strong, weak and electromagnetic — are all aspects of the same force.

Most of the grand-unification schemes of that era failed experimental tests, and the surviving leptoquark models have become more complicated — but they still have their fans. “Leptoquarks could solve another big mystery: why different families of particles have such different masses,” says Gino Isidori, a theoretician at the University of Zurich in Switzerland. One family is made of the lighter quarks — the constituents of protons and neutrons — and the electron. Another has heavier quarks and the muon, and a third family has even heavier counterparts.

Apart from the leptoquark, there is one other major contender that might reconcile both the LHCb and Muon g – 2 discrepancies. It is a particle called the Z′ boson because of its similarity with the Z boson, which carries the ‘weak force’ responsible for nuclear decay. It, too, could help to solve the mystery of the three families, says Ben Allanach, a theorist at the University of Cambridge, UK. “We’re building models where some features come out very naturally, you can understand these hierarchies,” he says. He adds that both leptoquarks and the Z′ boson have an advantage: they still have not been completely ruled out by the LHC, but the machine should ultimately see them if they exist.

The LHC is currently undergoing an upgrade, and it will start to smash protons together again in April 2022. The coming deluge of data could strengthen the muon anomalies and perhaps provide hints of the long-sought new particles (although a proposed electron–positron collider, primarily designed to study the Higgs boson, might be needed to address some of the LHC’s blind spots, Peskin says). Meanwhile, beginning next year, Muon g – 2 will release further measurements. Once it’s known more precisely, the size of the discrepancy between muon magnetism and theory could itself rule out some explanations and point to others.

Unless, that is, the discrepancies disappear and the standard model wins again. A new calculation, reported this month, of the standard model’s prediction for muon magnetism3 gave a value much closer to the experimental result. So far, those who have bet against the standard model have always lost, which makes physicists cautious. “We are — maybe — at the beginning of a new era,” Stöckinger says.

Nature 593, 18-19 (2021)

References

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