A hidden link has been found between two seemingly unrelated particle collision outcomes. It’s the latest example of a mysterious web of mathematical connections between disparate theories of physics.

The new “antipodal duality” inverts the terms used to calculate one particle scattering process to get the terms for another, in a way that’s similar to inverting the coordinates of points on a sphere.

Last year, the particle physicist Lance Dixon was preparing a lecture when he noticed a striking similarity between two formulas that he planned to include in his slides.

The formulas, called scattering amplitudes, give the probabilities of possible outcomes of particle collisions. One of the scattering amplitudes represented the probability of two gluon particles colliding and producing four gluons; the other gave the probability of two gluons colliding to produce a gluon and a Higgs particle.

“I was getting a little confused because they looked kind of similar,” said Dixon, who is a professor at Stanford University, “and then I realized that the numbers were basically the same — it’s just that the [order] had gotten reversed.”

He shared his observation with his collaborators over Zoom. Knowing of no reason the two scattering amplitudes should correspond, the group thought perhaps it was a coincidence. They started calculating the two amplitudes at progressively higher levels of precision (the greater the precision, the more terms they had to compare). By the end of the call, having calculated thousands of terms that kept agreeing, the physicists were pretty certain they were dealing with a new duality — a hidden connection between two different phenomena that couldn’t be explained by our current understanding of physics.

Now, the antipodal duality, as the researchers are calling it, has been confirmed for high-precision calculations involving 93 million terms. While this duality arises in a simplified theory of gluons and other particles that does not quite describe our universe, there are clues that a similar duality might hold in the real world. Researchers hope that investigating the strange finding could help them make new connections between seemingly unrelated aspects of particle physics.

“This is a magnificent discovery because it is totally unexpected,” said Anastasia Volovich, a particle physicist at Brown University, “and there is still no explanation of why it should be true.”

The DNA of Particle Scattering

Dixon and his team discovered the antipodal duality by using a special “code” to compute scattering amplitudes more efficiently than they could with traditional methods. Typically, to figure out the probability of two high-energy gluons scattering to produce four lower-energy gluons, for example, you must consider all the possible pathways that might yield this outcome. You know the beginning and the end of the story (two gluons become four), but you also need to know the middle — including all the particles that can temporarily pop in and out of existence, thanks to quantum uncertainty. Traditionally, you must add up the probability of each possible middle event, taking them one at a time.

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