The algorithm that allows particle physicists to count more than 2


Thomas Gehrmann remembers the deluge of mathematical expressions cascading across his computer screen one day 20 years ago.

He was trying to calculate the odds of three jets of elementary particles erupting from two particles breaking together. This was the kind of calculation physicists often do to see if their theories match the results of experiments. More accurate predictions require longer calculations, however, and Gehrmann was going big.

Using the standard method devised over 70 years ago by Richard Feynman, he had sketched diagrams of hundreds of possible ways the colliding particles could transform and interact before launching three jets. Adding up the individual probabilities of these events would give the overall odds of the outcome to three rolls.

But Gehrmann needed software just to count the 35,000 terms of his probability formula. As for the calculation? This is when “you raise the flag of surrender and talk to your colleagues,” he said.

Fortunately for him, one of his colleagues knew a still new technique to considerably shorten this kind of formula. With the new method, Gehrmann saw the terms merge and dissolve by the thousands. In the 19 computable expressions that remained, he glimpsed the future of particle physics.

Today, the reduction procedure, known as the Laporta algorithm, has become the main tool for generating accurate predictions of particle behavior. “It’s everywhere,” said Matt von Hippel, a particle physicist at the University of Copenhagen.

While the algorithm has spread across the world, its inventor, Stefano Laporta, remains in the dark. He rarely attends conferences and does not command a legion of researchers. “A lot of people thought he was dead,” said von Hippel. On the contrary, Laporta lives in Bologna, Italy, cutting back on the calculus close to his heart, the one that spawned his pioneering method: an ever more precise assessment of how the electron moves through a magnetic field. .

One, two, many

The challenge of making predictions about the subatomic world is that endless things can happen. Even an electron that is just minding its own business can spontaneously emit and then retrieve a photon. And this photon can conjure up additional ephemeral particles in the meantime. All of this commotion slightly interferes with the affairs of the electron.

In Feynman’s calculus, particles that exist before and after an interaction become lines in and out of a cartoon, while those that appear briefly and then disappear form loops in the middle. Feynman discovered how to translate these diagrams into mathematical expressions, where the loops become summation functions called Feynman integrals. The most likely events are those with fewer loops. But physicists have to consider rarer and more closed-ended possibilities when making the kind of precise predictions that can be tested in experiments; only then can they spot subtle signs of new elementary particles that may be missing from their calculations. And with more loops come exponentially more integrals.

Illustration: Quanta Magazine
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