The algorithm that allows particle physicists to count higher than 2


Thomas Herman remembers the flood of mathematical expressions that cascaded down his computer screen one day 20 years ago.

He was trying to calculate the chances of three jets of elementary particles erupting from two particles shattering together. This was the type of calculations for bread and butter that physicists often make to test whether their theories match the results of experiments. However, more accurate forecasts require longer calculations, and Herman was big.

Using the standard method developed more than 70 years ago by Richard Feynman, he sketched diagrams of hundreds of possible ways in which colliding particles can transform and interact before firing three jets. Summing up the individual probabilities for these events would give the total chance of a three-jet result.

But Herman needed software only to calculate 35,000 members in his probability formula. As for its calculation? Then “you raise the flag of capitulation and talk to your colleagues,” he said.

Fortunately for him, one of these colleagues happened to know about an as yet unpublished technique for dramatically shortening just this kind of formula. With the new method, Hermann saw the terms merge together and merge by the thousands. In the 19 computable expressions that remained, he saw the future of particle physics.

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

While the algorithm has spread around the world, its inventor Stefano Laporta remains unclear. He rarely attends conferences and does not command a legion of researchers. “A lot of people just thought he was dead,” von Hippel said. On the contrary, Laporta lived in Bologna, Italy, removing the calculations he was most interested in, which gave rise to his pioneering method: an increasingly accurate assessment of how an electron moves through a magnetic field.

One, two, many

The challenge in making predictions about the subatomic world is that an infinite number of things can happen. Even an electron that simply looks at its work can spontaneously emit and then recover a photon. And this photon can cause additional fleeting particles in the meantime. All these busy people slightly interfere with the electrons.

In Feynman’s calculation scheme, particles that exist before and after an interaction are transformed into lines leading in and out of a cartoon sketch, while those that appear briefly and then disappear form cycles in the middle. Feynman developed how to translate these diagrams into mathematical expressions, where cycles become summation functions known as Feynman integrals. More likely events are those with fewer cycles. But physicists need to consider rarer, more closed possibilities when making species accurate predictions that can be tested experimentally; only then can they notice subtle signs of new elementary particles that may be missing in their calculations. And with more cycles come exponentially more integrals.

Illustration: Quanta magazine



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