The problem arises from the disparity between gravity and the weak nuclear force, which is about 100 million trillion trillion (10^32) times stronger and acts at much smaller scales to mediate interactions inside atomic nuclei. The particles that carry the weak force, called W and Z bosons, derive their masses from the Higgs field, a field of energy saturating all space. But it is unclear why the energy of the Higgs field, and therefore the masses of the W and Z bosons, isn’t far greater. Because other particles are intertwined with the Higgs field, their energies should spill into it during events known as quantum fluctuations. This should quickly drive up the energy of the Higgs field, making the W and Z bosons much more massive and rendering the weak nuclear force about as weak as gravity.
Supersymmetry solves the hierarchy problem by theorizing the existence of a “superpartner” twin for every elementary particle. According to the theory, fermions, which constitute matter, have superpartners that are bosons, which convey forces, and existing bosons have fermion superpartners. Because particles and their superpartners are of opposite types, their energy contributions to the Higgs field have opposite signs: One dials its energy up, the other dials it down. The pair’s contributions cancel out, resulting in no catastrophic effect on the Higgs field. As a bonus, one of the undiscovered superpartners could make up dark matter.
“Supersymmetry is such a beautiful structure, and in physics, we allow that kind of beauty and aesthetic quality to guide where we think the truth may be,” said Brian Greene, a theoretical physicist at Columbia University.
Over time, as the superpartners failed to materialize, supersymmetry has grown less beautiful. According to mainstream models, to evade detection, superpartner particles would have to be much heavier than their twins, replacing an exact symmetry with something like a carnival mirror. Physicists have put forward a vast range of ideas for how the symmetry might have broken, spawning myriad versions of supersymmetry.
But the breaking of supersymmetry can pose a new problem. “The heavier you have to make some of the superpartners compared to the existing particles, the more that cancellation of their effects doesn’t quite work,” Martin explained.
Most particle physicists in the 1980s thought they would detect superpartners that are only slightly heavier than the known particles. But the Tevatron, the now-retired particle accelerator at Fermilab in Batavia, Ill., found no such evidence. As the Large Hadron Collider probes increasingly higher energies without any sign of supersymmetry particles, some physicists are saying the theory is dead. “I think the LHC was a last gasp,” Woit said.
Today, most of the remaining viable versions of supersymmetry predict superpartners so heavy that they would overpower the effects of their much lighter twins if not for fine-tuned cancellations between the various superpartners. But introducing fine-tuning in order to scale back the damage and solve the hierarchy problem makes some physicists uncomfortable. “This, perhaps, shows that we should take a step back and start thinking anew on the problems for which SUSY-based phenomenology was introduced,” Shifman said.
But some theorists are forging ahead, arguing that, in contrast to the beauty of the original theory, nature could just be an ugly combination of superpartner particles with a soupçon of fine-tuning. “I think it is a mistake to focus on popular versions of supersymmetry,” said Matt Strassler, a particle physicist at Rutgers University. “Popularity contests are not reliable measures of truth.”
In some of the less popular supersymmetry models, the lightest superpartners are not the ones the Large Hadron Collider experiments have looked for. In others, the superpartners are not heavier than existing particles but merely less stable, making them more difficult to detect. These theories will continue to be tested at the Large Hadron Collider after it is upgraded to full operational power in about two years.