‘Inside the box' look at excited hadrons could help solve mystery of particle X(3872)

NEWPORT NEWS, VA – An elusive particle that first formed in the hot, dense maelstrom of the early universe has puzzled physicists for decades. Following its surprise discovery in 2003, scientists began observing a slew of other strange objects tied to the millionths of a second after the Big Bang. 

Appearing as “bumps” in the data from high-energy experiments, these signals came to be known as short-lived “XYZ states,” for lack of a better label. They defy the standard picture of particle behavior and are a leading problem in contemporary physics, sparking several attempts to understand their mysterious nature. 

But theorists at the U.S. Department of Energy’s Thomas Jefferson National Accelerator Facility suggest the experimental data could be explained with fewer XYZ states, also called resonances, than currently claimed.

Representing Jefferson Lab’s Center for Theoretical and Computational Physics and the U.K.’s Cambridge University, the researchers used a branch of quantum physics to compute the energy levels, aka mass, of particles containing a certain “flavor” of the subatomic building blocks known as quarks. 

The team found that multiple particle states sharing the same degree of spin – aka angular momentum – are coupled, meaning only a single resonance exists at each spin channel. This fresh interpretation is contrary to several other theoretical and experimental studies.

“We would advocate that we’re more likely to get to an understanding of the experimental spectrum if the data are combined into a coupled-channel analysis,” said Jozef Dudek, a Jefferson Lab staff scientist and professor at William & Mary. “Our hypothesis is that the approach might end up reducing the number of resonances needed to explain all the data.”

Dudek and his Theory Center colleagues presented their results in a pair of companion papers published for the international Hadron Spectrum Collaboration (HadSpec) in Physical Review Letters and Physical Review D. The exciting work could also soon provide clues about a perplexing particle with an enigmatic name: X(3872).

The Charm of X(3872)

The charm quark, one of six quark “flavors,” was first observed experimentally in 1974. It was discovered alongside its antimatter counterpart, the anticharm, and particles paired this way are part of an energy region called “charmonium.”

Fast forward to 2003, and the Belle experiment at the High Energy Accelerator Research Organization (KEK) in Japan discovered a new charmonium candidate dubbed X(3872). Its cryptic name conjures images of interstellar objects such as  exoplanets, but X(3872) is a short-lived particle state that appears to defy the present quark model. 

Some scientists claim X(3872) could be a tetraquark, which is a composite particle (hadron) made up of two quarks and two antiquarks. For comparison, protons and neutrons are hadrons with three quarks. Other possible explanations for X(3872) include a molecule-like bound system of two mesons, each containing two quarks, or some sort of quark-gluon hybrid.

“X(3872) is now more than 20 years old, and we still haven’t obtained a clear, simple explanation that everyone can get behind,” said David Wilson, a Jefferson Lab scientific user from the U.K.’s University of Cambridge and the lead author on the HadSpec study.

Other exotic candidate states have been observed, such as Y(4260) and Zc(3900). Hence the label, “XYZ.” In fact, so many were being discovered that in 2017, the Particle Data Group revamped its naming scheme.

This hodgepodge of excited states is the result of an explosion in the amount of data captured by modern particle accelerators.

“High-energy experiments began measuring processes that are hundreds of times fainter,” Dudek said. “They started seeing bumps, interpreted as new particles, almost everywhere they looked. And very few of these states agreed with the model that came before.”

The “XYZ” alphabet soup motivated the HadSpec group to begin sorting the spectra of states using quantum field theory. 

From the Lattice

Quantum chromodynamics (QCD) describes quarks’ interactions with gluons, the photon-like carriers of the strong force. Supercomputers, with their ability to crunch huge numbers of numbers, can be applied to QCD by placing the theory on a ‘lattice.’

Think of the lattice as a small, tightly packed grid of points representing space and time. Theorists can use the possible configurations of quarks and gluons inside this “box” to predict properties of hadrons such as their masses and lifetimes.

The lattice box is tiny, with dimensions of 2 to 3 femtometers – nearly a million times smaller than a single atom. But even such a tiny volume requires an enormously powerful computer to sample the possible behaviors of quarks and gluons. That’s why the HadSpec group used several high-performance computing clusters, including those at Jefferson Lab, to perform the mind-boggling math.

“If you hated calculus in school, just imagine the worst calculus problem ever,” Dudek said. 

The HadSpec group computed the masses and lifetimes of mesons in the charmonium region, where XYZ states have been claimed in experiments. These mesons decay rapidly into “D mesons” and their antimatter counterparts.

D mesons consist of a charm quark, which is heavy, and a lighter antiquark of the flavors “up,” “down” or “strange.” Anti-D mesons are the exact opposite: They contain an anticharm quark and an ordinary quark of one of those lighter flavors. 

If you’re wondering where the extra quarks are coming from, QCD predicts vacuum fluctuations in which quark-antiquark pairs are constantly created and annihilated. These phenomena are a long-theorized quantum quirk of empty space.

“Somewhere along the line, at least one pair of light quarks must have come into existence,” Dudek said. “They weren't there when you had a charm-anticharm just buzzing around, but they are there in this well-separated, D-meson pair.” 

The authors used the lattice results to infer all the possible ways in which the charmonium mesons could decay. To do this, they had to relate the results from a tiny box to what would happen in a virtually infinite volume – that is, the size of the universe.

“In our calculations, unlike experiment, you can't just fire in two particles and measure two particles coming out,” Wilson said. “You have to simultaneously calculate all possible final states, because quantum mechanics will find those for you.”

The results can be understood in terms of just a single short-lived particle (a resonance) whose appearance could differ depending upon which possible decay state it is observed in.

“We're trying to simplify the picture as much as possible, using fundamental theory with the best methods available,” Wilson said. “Our goal is to disentangle what has been seen in experiments.”

Now that the HadSpec team has proved this type of calculation is feasible, they are ready to apply it to the mysterious particle X(3872). 

“X(3872) is quite interesting,” Wilson said. “Its origin is an open question. It appears very close to a threshold, which could be accidental or a key part of the story. This is one thing we will look at very soon." 

HadSpec Collaboration

Wilson said the study was a massively complex undertaking. His contribution was made possible in part by an eight-year fellowship with the Royal Society, the U.K.’s most prestigious independent science academy. 

But he noted that support from mentors and colleagues in the Theory Center, where Dudek helped him get his start as a postdoctoral fellow in 2012, helped lay the foundation for the research. 

“Many of the ingredients for this project, including the code, go back to my early days at Jefferson Lab,” said Wilson, who led the data analysis. “Knowing I had so much time and support, I made it happen. I was quite lucky in that regard.”

Adding expertise in analysis and code-writing were Robert Edwards, the deputy director of Jefferson Lab’s Theory Center, and Christopher Thomas, a Cambridge professor who like Wilson was once a Jefferson Lab postdoctoral fellow.

“Everyone on the paper went through Jefferson Lab’s Theory Center at some point,” Wilson said. “We’ve worked together on various things for some time now.” 

Dudek added that “the Jefferson Lab Theory Center has been an internationally visible focal point for hadron spectroscopy for a couple decades, attracting many talented early-career people.”

The HadSpec group also received support from the U.K. Science and Technology Facilities Council, both in Cambridge and through the DiRAC computing facility; DOE contracts at William & Mary and Jefferson Lab; the Exascale Computing Project involving the DOE and National Nuclear Security Administration; and the DOE Office of Advanced Scientific Computing Research (ASCR) and Office of Nuclear Physics, Scientific Discovery through Advanced Computing (SciDAC) program. The Oak Ridge Leadership Computing Facility (OLCF) at Oak Ridge National Laboratory and the National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory provided supercomputing resources.

“In some ways, what high-performance computing provides is the easy part for us, because impressive work has already been done by others to make the calculations run quickly,” Dudek said. “But then we have the intellectual challenge of turning it into physics results, and that's best done by bouncing around ideas with people who between them understand all facets of the physics. The Jefferson Lab Theory Center has made that possible.”

Further Reading
Scalar and Tensor Charmonium Resonances in Coupled-Channel Scattering from Lattice QCD
Charmonium 𝜒C0 and 𝜒C2 resonances in coupled-channel scattering from lattice QCD
Charmonium Spectrum and Quark Confinement
Measurement of the J/psi photoproduction cross section over the full near-threshold kinematic region

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