Experiments that measure the lifetime of neutrons reveal a perplexing and unresolved discrepancy. While this lifetime has been measured to a precision within 1 percent using different techniques, apparent conflicts in the measurements offer the exciting possibility of learning about as-yet undiscovered physics.

Now, a team of scientists including Dr Chris Bouchard in the School of Physics & Astronomy has enlisted powerful supercomputers to calculate a quantity known as the “nucleon axial coupling,” or gA – which is central to our understanding of a neutron’s lifetime – with unprecedented precision. The method offers a clear path to further improvements that may help to resolve the experimental discrepancy.

To achieve their results, the researchers created a microscopic slice of spacetime, embedded with the laws from the Standard Model of particle physics, to provide a window into the subatomic world. Their study was published online 7 June in the journal Nature.

The nucleon axial coupling is defined as the strength at which one component (known as the axial component) of the “weak current” of the Standard Model of particle physics couples to the neutron. The weak current is given by one of the four known fundamental forces of the universe and is responsible for radioactive beta decay – the process by which a neutron decays to a proton, an electron, and a neutrino.

In addition to measurements of the neutron lifetime, precise measurements of neutron beta decay are also used to probe new physics from beyond the Standard Model. Physicists seek to resolve the lifetime discrepancy by augmenting experimental results with more precise determination of gA .

The researchers focused on quantum chromodynamics (QCD), the part of the Standard Model responsible for quark and gluon interactions. Quarks and gluons are the fundamental building blocks for composite particles including neutrons and protons. The dynamics of these interactions determine the mass of the neutron and proton, and also the value of gA.

But sorting through QCD’s inherent complexity to produce these quantities requires the aid of massive supercomputers. In the latest study, researchers applied a numeric simulation known as lattice QCD, which represents QCD in a discrete spacetime.

The team’s new theoretical determination of gA is based on a simulation of a tiny piece of the universe – the size of a few neutrons in each direction. They simulated a neutron transitioning to a proton inside this simulated universe, in order to predict what happens in nature.

The model universe contains one neutron amid a sea of gluons and quark-antiquark pairs that are bustling under the surface of the apparent emptiness of free space.

“Calculating gA was supposed to be one of the simple benchmark calculations that could be used to demonstrate that lattice QCD can be utilized for basic nuclear physics research, and for precision tests that look for new physics in nuclear physics backgrounds,” said André Walker-Loud, a staff scientist in Berkeley Lab’s Nuclear Science Division who led the new study. “It turned out to be an exceptionally difficult quantity to determine.”

This is because lattice QCD calculations are complicated by exceptionally noisy statistical results that had thwarted major progress in reducing uncertainties in previous gA calculations. Some researchers had previously estimated that it would require the next generation of the nation’s most advanced supercomputers to achieve a 2 percent precision for gA by around 2020.

The team participating in the latest study developed a way to improve their calculation of gA using an unconventional approach and supercomputers at Oak Ridge National Laboratory (Oak Ridge Lab) and Lawrence Livermore National Laboratory (Livermore Lab) in the US. The study involved scientists from more than a dozen institutions, including the University of Glasgow.

Chia Cheng “Jason” Chang, the lead author of the publication and a postdoctoral researcher in Berkeley Lab’s Nuclear Science Division, said, “Past calculations were all performed amidst this more noisy environment,” which clouded the results they were seeking.

Walker-Loud added, “We found a way to extract gA earlier in time, before the noise ‘explodes’ in your face,” Walker-Loud said.

“We now know the value of gA, as predicted by the Standard Model, to a precision of 1%. Not only is this value consistent with experimental measurement, but the precision was not supposed to be possible for years... and not possible at all with the current generation of supercomputers. Human ingenuity, a smarter way to calculate, was the key,” Bouchard said.

“This was an intense 2 1/2-year project that only came together because of the great team of people working on it,” Walker-Loud said.

This latest calculation also places tighter constraints on a branch of physics theories that stretch beyond the Standard Model – constraints that exceed those set by powerful particle collider experiments at CERN’s Large Hadron Collider. But the calculations aren’t yet precise enough to determine if new physics have been hiding in the gA and neutron lifetime measurements.

The main limitation to improving upon the precision of the calculation is in supplying more computing power. “We don’t have to change the technique we’re using to get the precision necessary,” Walker-Loud said.

The latest work builds upon decades of research and computational resources by the lattice QCD community. In particular, the team relied upon QCD data generated by the MILC Collaboration; an open source software library for lattice QCD called Chroma, developed by the USQCD collaboration; and QUDA, a highly optimized open source software library for lattice QCD calculations.

The team drew heavily upon the power of Titan, a supercomputer at Oak Ridge Lab equipped with graphics processing units, or GPUs, in addition to more conventional central processing units, or CPUs. GPUs have evolved from their early use in accelerating video game graphics to current applications in evaluating large arrays for tackling complicated algorithms pertinent to many fields of science. The axial coupling calculations used about 184 million “Titan hours” of computing power – it would take a single CPU about 75,000 years to work through the same set of calculations.

As the researchers worked through their analysis of this massive set of numerical data, they realized that more refinements were needed to reduce the uncertainty in their calculations.

The team was assisted by the Oak Ridge Leadership Computing Facility staff to efficiently utilize their 64 million Titan-hour allocation, and they also turned to the Multiprogrammatic and Institutional Computing program at Livermore Lab, which gave them more computing time to resolve their calculations and reduce their uncertainty margin to just under 1 percent.

“Establishing a new way to calculate gA has been a huge rollercoaster,” Walker-Loud said.

With more statistics from more powerful supercomputers, the research team hopes to drive the uncertainty margin down to about 0.3 percent. “That’s where we can actually begin to discriminate between the results from the two different experimental methods of measuring the neutron lifetime,” Chang said. “That’s always the most exciting part: When the theory has something to say about the experiment.”

He added, “With improvements, we hope that we can calculate things that are difficult or even impossible to measure in experiments.”

Already, the team has applied for time on a next-generation supercomputer at Oak Ridge Lab called Summit, which would greatly speed up the calculations.

In addition to the University of Glasgow, the team included researchers at Berkeley Lab and UC Berkeley, the University of North Carolina, RIKEN BNL Research Center at Brookhaven National Laboratory, Lawrence Livermore National Laboratory, the Jülich Research Center in Germany, the University of Liverpool, the College of William & Mary, Rutgers University, the University of Washington, NVIDIA Corp., and Thomas Jefferson National Accelerator Facility.

First published: 5 June 2018

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