June 18, 2004  




Old Equations Tell New Stories

By Davide Castelvecchi

Future experiments at the Large Hadron Collider (LHC), at the Tevatron and at the Linear Collider will hunt for the elusive particles that could exist beyond the Standard Model. Finding new particles amidst the barrage of old ones produced by any collision may require calculating Standard Model predictions with unprecedented precision. A recent paper by Charalampos ‘Babis’ Anastasiou and Lance Dixon (both of THP) and their colleagues introduces a method to make such predictions with a previously inaccessible level of accuracy.

Production of Z bosons at the LHC, at three different orders of approximation. The bands represent the chance that a particle shoots out at a given angle. (Graphic by Lance Dixon)

In the paper, soon to appear in Physical Review D, the researchers also applied their method to a special case, the copious W and Z particles that will come out of strong-force interactions at the LHC, plotting curves that predict how such particles will disperse inside the detector.

“You can’t make experiments that only produce new physics,” Dixon points out.

“The data you are looking for,” he says, “could be masked or mimicked by Standard Model particles. In many cases, to pin down the new physics you have to figure out what the Standard Model background is going to be.” That’s not easy.

If nature were a chess game, Richard Feynman used to say, the fundamental laws of physics would be the rules for how pieces are allowed to move.

And just as knowing the rules doesn’t make you a grandmaster chess player, knowing the basic equations of physics—as encoded in the Standard Model—is not enough by itself to know what those equations actually predict.

Making predictions on the strongforce is notoriously hard, and gets increasingly harder if one tries to improve the level of accuracy. Known as order of approximation, these predictions quickly lead to impossibly complex calculations. Until now, the complete curves for any particles produced by hadron colliders were known only ‘in first approximation,’ known as leading order, and at the ‘first step up’, or next-to-leading order. Dixon’s team carried out the first calculation at the next level, known as next-to-next-to-leading order, or NNLO.

The NNLO involves enormous numbers of challenging mathematical formulas, which correspond to the many possible strong-force interactions, or Feynman diagrams. Brute-force calculations would be too complex even for advanced computing farms such as SLAC’s, so physicists have had come up with clever shortcuts.

The method employed in the new paper was first introduced by Laporta in 2000, building on earlier work by Chetyrkin and Tkachov and others. Laporta’s technique uses algebra to reduce the calculation to a manageable number of formulas.

Calculating the NNLO still required solving between 10,000 and a million interdependent equations. Dixon’s team devised several methods to reduce the amount of calculations by a factor of 1,000. The results were better than expected.

To estimate the reliability of their curves, the physicists repeated the calculation wiggling certain parameters, and they plotted bands that represented how the curves changed in the process. The bands came out surprisingly thin, meaning that the results were quite reliable, with less than one percent error. “We were pretty shocked when the bands came out so thin,” Dixon says.

“Calculations at the NNLO level are truly daunting,” comments Michael Peskin (THP). “This is a major piece of work.”

Dixon and his team are making their software publicly available, and hope that other researchers will find it a valuable tool. Dixon himself plans to use it in future projects. “The need to do this basic, not very flashy theoretical work is not always recognized. But there are many more types of NNLO calculations that can be done over the next few years,” he says.

NNLO predictions are precise enough for practical purposes – but how about going to the NNNLO? “That would be almost total insanity,” Dixon says. “But maybe it can be done.”


The Stanford Linear Accelerator Center is managed by Stanford University for the US Department of Energy

Last update Tuesday June 15, 2004 by Emily Ball