After the Big Bang, the universe swelled with energy, but there was no mass. Everything moved at the speed of light. But as the universe expanded, it also began to cool. This chilling awoke a sleeping giant—the Higgs field. Particles suddenly took on unique personalities as they absorbed parts of the Higgs field, giving them their masses.
Scientists at the Large Hadron Collider want to understand what happened during the advent of mass in the early universe. Because they cannot directly measure the early universe, they study heavy particles produced inside the LHC to look for clues about their ancestry. Physicist Aram Apyan, an assistant professor at Brandeis University, and his colleagues on the ATLAS experiment at CERN are looking for particles that contain a vestige from this period of transformation: longitudinal polarization, which is related to particle spin.
“Spin is a quantum mechanical and intrinsic property of elementary particles,” Apyan says. “Polarization is how a particle spins relative to its motion.”
Though to be clear, “The particles are not actually rotating,” says Daniel Camarero Muñoz, a postdoc at Brandeis University. “There's no classical equivalence.”
Some particles have only two polarization states: their rotations can be clockwise or counterclockwise relative to the direction of motion (like a curveball thrown by a right-handed or left-handed pitcher).
Apyan and his colleagues are interested in heavy particles that can have a third type of polarization: longitudinal. Longitudinal polarization is when the spin of the particle is perpendicular to its direction of motion (the classic fastball).
At low energies, particles called W bosons—along with other particles called Z bosons—exist in a mixture of the three polarization states, all happening at once, thanks to quantum mechanics. But as their energies creep up, the bosons start to favor one polarization state over the others. The bosons that choose longitudinal polarization have a profound connection to the Higgs field and can help scientists study the Higgs mechanism and how it gives particles their mass.
“Basically, parts of the Higgs field were absorbed into the fields of the W and Z bosons, and the result is that these bosons can have longitudinal polarization,” says Max Stange, who worked on the ATLAS analysis of W boson polarization as a graduate student. “Finding W bosons with longitudinal polarization is like finding people with a high percentage of Neanderthal DNA; they carry inside them information about an ancient ancestor, which in our case is the Higgs field as it existed in the early universe.”
Studying pairs of W bosons with longitudinal polarization gives scientists a small window into the Higgs field that came alive 10-12 seconds after the Big Bang.
“We want to study longitudinally polarized W boson pairs because they can interact with each other through an intermediary Higgs boson,” Apyan says. “It’s a really sensitive test of the Higgs mechanism.”
But there’s a problem: Finding pairs of longitudinally polarized W bosons to study is incredibly difficult.
Scientists cannot measure the polarization of W bosons directly; to determine the polarization of a W boson, scientists must look at variables such as the momentum, energy and the angles between the particles into which the W bosons decay.
“It’s kind of like detective work,” Camarero says.
The challenge is that this study looked at W boson decays in which one of the products is a neutrino, a ghostly particle that rarely interacts and will fly through detectors without a trace.
“If there is just one neutrino, we can infer its momentum based on the symmetry of the collision,” Camarero says. “But we are looking at collisions that produce pairs of W bosons, which give us two neutrinos. We cannot just simply say, ‘Which direction did they go?’ There is ambiguity.”
To deal with this complex analysis, the team started experimenting with machine-learning techniques, such as boosted decision trees and deep neural networks.
“Neural networks work like neurons in your brain,” Stange says. “The layers of nodes are interconnected with each other, and as the algorithm learns important connections, it creates stronger links between those nodes."
Stange quickly discovered the power of machine-learning algorithms, but also their pitfalls. "We needed training data to train our networks, but this meant that we could be biased by our own expectations," he says.
Stange and his colleagues developed a multi-step machine-learning training and validation system to eliminate as much bias from the analysis as possible. “In the end, we had several groups of neural networks, which allowed us to evaluate and compare their performances and suppress any training biases,” Stange says.
When they applied the algorithms to real data, they found evidence for pairs of W bosons in which at least one had longitudinal polarization. “We see very good agreement with the theory, which is just beautiful," Camarero says.
The next step is to refine the analysis techniques and expand the data set, with the goal of pushing the experimental statistical significance above the threshold that generally constitutes a discovery in particle physics. Eventually, the team hopes to isolate pairs of W bosons that are both longitudinally polarized.
“This is one of the main processes that will eventually give us a complete understanding of the Higgs mechanism,” Apyan says. “These novel techniques got us much closer than originally foreseen, but we need a lot more data if we want to make the first experimental observation of W boson pairs in which both are longitudinally polarized. There is a lot more work to do."
