When particle physicists try to model experiments, they confront an impossible calculation — an infinitely long equation that lies beyond the reach of modern mathematics. 

Fortunately, they can generate largely accurate predictions without seeing this arcane math all the way through. By cutting the calculation short, scientists at CERN’s Large Hadron Collider in Europe make forecasts that match events they actually observe when they send subatomic particles barreling toward each other around a nearly 17-mile track.

Unfortunately, the era of agreement between forecast and observation may be ending. As measurements grow more precise, the approximation schemes theorists use to make predictions may not be able to keep up.

“We’re getting close to exhausting what can be done,” said Claude Duhr, a particle physicist at CERN. 

But three recent papers from a group of physicists led by Pierpaolo Mastrolia of the University of Padua in Italy and Sebastian Mizera of the Institute for Advanced Study in Princeton, New Jersey, have revealed an underlying mathematical structure in the equations. The structure provides a new way of collapsing interminable terms into just dozens of essential components. Their method may help bring about new levels of predictive accuracy, which theorists desperately need if they are to move beyond the leading but incomplete model of particle physics.

“They have delivered lots of proof-of-concept results which show that this is a very promising technique,” Duhr said.

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