Lance Dixon was preparing a lecture last year when he spotted two similar formulas.

Scattering amplitude formulas give particle collision probabilities. One scattering amplitude reflected the likelihood of two gluons colliding and producing four gluons; the other represented the possibility of two gluons colliding and producing a gluon and Higgs particle.

Dixon, a Stanford University professor, was confused because the numbers seemed identical, but the arrangement was wrong.

He told his team via Zoom. The group assumed it was a coincidence that the two scattering amplitudes matched. They calculated the amplitudes with increasing precision (the greater the precision, the more terms they had to compare). After calculating hundreds of terms that continued agreeing, the physicists were quite sure they were dealing with a new duality — a hidden relationship between two different phenomena that can’t be described by conventional physics.

Antipodal duality has been confirmed for 93 million-term high-precision calculations. While this duality develops in a simplified theory of gluons and other particles, there are signs that it may hold in the real world. The odd discovery may help researchers make new connections in particle physics.

Anastasia Volovich, a particle physicist at Brown University, called the discovery “magnificent”

Scattering’s DNA

Dixon and his team discovered antipodal duality by employing a customised “code” to compute scattering amplitudes more quickly. To calculate the chance of two high-energy gluons scattering to produce four lower-energy gluons, consider all conceivable paths. Two gluons form four, but you also need to know the middle — all the particles that can temporarily pop in and out of existence due to quantum uncertainty. Traditionally, you add the likelihood of each middle event individually.

Four researchers, including Volovich, developed a shortcut in 2010. Reorganizing everything into a new structure reduced numerous difficult amplitude expressions. “Letters” denote combinations of each particle’s energy and momentum. Six letters form words, which form scattering amplitude phrases.

Dixon compares this new approach to the genetic code, where four chemical building components generate DNA genes. “DNA of particle scattering,” as he describes it, includes laws governing word combinations. Some regulations obey scientific or mathematical concepts, whereas others seem arbitrary. Look for hidden patterns in long calculations to find some rules.

These perplexing criteria have allowed particle physicists compute scattering amplitudes more precisely than before. Restructuring also helped Dixon and his colleagues find a hidden relationship between two scattering amplitudes.

Antipodemap

“Antipode map” symbolises dualism. An antipode map inverts a point’s coordinates on a sphere, bringing you through the centre to the opposite side. It’s like excavating from Chile to China.

Dixon’s antipode map is abstract in scattering amplitudes. It inverts the amplitude letters. After a simple change of variables, this antipode map reveals the scattering amplitude for two gluons becoming one gluon plus a Higgs.

In Dixon’s DNA example, duality is like reading a genetic sequence backward and discovering it encodes a new protein.

“We all thought the antipode map was useless. Matt von Hippel, an amplitude specialist at the Niels Bohr Institute in Copenhagen, wasn’t engaged in the research. “Now it has this unexplainable duality, which is weird.”