This spring, at a meeting of Syracuse University’s quark physics group, Ivan Polyakov announced that he had uncovered the fingerprints of a semi-mythical particle.

“We said, ‘This is impossible. What mistake are you making?’” recalled Sheldon Stone, the group’s leader.

Polyakov went away and double-checked his analysis of data from the Large Hadron Collider beauty (LHCb) experiment, which the Syracuse group is part of. The evidence held. It showed that a particular set of four fundamental particles called quarks can form a tight clique, contrary to the belief of most theorists. The LHCb collaboration reported the discovery of the composite particle, dubbed the double-charm tetraquark, at a conference in July and in two papers posted earlier this month that are now undergoing peer review.

The unexpected discovery of the double-charm tetraquark highlights an uncomfortable truth. While physicists know the exact equation that defines the strong force — the fundamental force that binds quarks together to make the protons and neutrons in the hearts of atoms, as well as other composite particles like tetraquarks — they can rarely solve this strange, endlessly iterative equation, so they struggle to predict the strong force’s effects.

The tetraquark now presents theorists with a solid target against which to test their mathematical machinery for approximating the strong force. Honing their approximations represents physicists’ main hope for understanding how quarks behave inside and outside atoms — and for teasing apart the effects of quarks from subtle signs of new fundamental particles that physicists are pursuing.

Quark Cartoon

The bizarre thing about quarks is that physicists can approach them at two levels of complexity. In the 1960s, grappling with a zoo of newly discovered composite particles, they developed the cartoonish “quark model,” which simply says that quarks glom together in complementary sets of three to make the proton, the neutron and other so-called baryons, while pairs of quarks make up various types of “meson” particles.

Gradually, though, a deeper theory known as quantum chromodynamics (QCD) emerged. It painted the proton as a seething mass of quarks roped together by tangled strings of “gluon” particles, the carriers of the strong force. Experiments have confirmed many aspects of QCD, but no known mathematical techniques can systematically unravel the theory’s central equation.

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Somehow, the quark model can stand in for the far more complicated truth, at least when it comes to the menagerie of baryons and mesons discovered in the 20th century. But the model failed to anticipate the fleeting tetraquarks and five-quark “pentaquarks” that started showing up in the 2000s. These exotic particles surely stem from QCD, but for nearly 20 years, theorists have been stumped as to how.

“We just don’t know the pattern yet, which is embarrassing,” said Eric Braaten, a particle theorist at Ohio State University.

The newest tetraquark sharpens the mystery.

It showed up in the debris of roughly 200 collisions at the LHCb experiment, where protons smash into each other 40 million times each second, giving quarks uncountable opportunities to cavort in all the ways nature permits. Quarks come in six “flavors” of different masses, with heavier quarks appearing more rarely. Each of those 200-odd collisions generated enough energy to make two charm-flavored quarks, which weigh more than the lightweight quarks that comprise protons, but less than the gigantic “beauty” quarks that are LHCb’s main quarry. The middleweight charm quarks also got close enough to attract each other and rope in two lightweight antiquarks. Polyakov’s analysis suggested that the four quarks banded together for a glorious 12 sextillionths of a second before an energy fluctuation conjured up two extra quarks and the group disintegrated into three mesons.

For a tetraquark, that’s an eternity. Previous tetraquarks have contained quarks paired with their equally massive opposing antiquarks, and they tended to puff into nothingness thousands of times faster. The new tetraquark’s formation and subsequent stability surprised Stone’s group, who expected charm quarks to attract each other even more weakly than the quark-antiquark pairs that bind more ephemeral tetraquarks. It’s a fresh clue to the strong force enigma.

Quark Rules of Thumb

One of the few theorists to foresee why two charm quarks might mingle was Jean-Marc Richard, now at the Institute of Physics of the 2 Infinities in Lyon, France. In 1982, he and two colleagues studied a simple quark model and initially found that four quarks would rather form two pairs — mesons. A quark pair can tango much as a proton and electron can. But add two more, and the newcomers tend to get in the way, weakening the attraction and dooming the collective particle.

But the theorists also noticed a loophole: Lopsided quartets can stick together, if the larger pair is heavy enough to not take much notice of the lighter pair. The question was, how skewed would the masses have to be?

Further analysis by Richard and a colleague predicted that it’s not necessary to go all the way to the most gargantuan quarks; a pair of middleweight charm quarks could anchor a tetraquark. But alternative extensions of the quark model predicted different tipping points, and the existence of the double-charm tetraquark remained doubtful. “There were more guesses that it would not exist than there were that it would exist,” Braaten said.

The same was true of “lattice QCD” computer simulations, a powerful approach to approximating QCD. These simulations capture the richness of the theory by analyzing quarks and gluons interacting at points on a fine grid instead of throughout a smooth space. All lattice QCD simulations agreed that the heaviest quarks could make tetraquarks. But when researchers swapped in charm quarks, most simulations found that double-charm tetraquarks couldn’t form.

Now the LHCb experiment has made a definitive ruling: Charm quarks can bind a tetraquark together. (Only barely, though — the physicists calculate that if the composite particle had just one-hundredth of a percent more mass, two mesons would win out instead.) Now theorists have a new benchmark for their models.

For lattice QCD practitioners, the new tetraquark highlights the problem that key details about the midsize quarks may be getting lost between their lattice points. Lightweight quarks can zip around enough to allow their movement to be captured even against a coarse grid. And researchers can deal with heavy, more stationary quarks by pinning them to one spot. But charm quarks inhabit an awkward middle ground, and researchers think they’ll need to zoom in to better discern their behavior. “We need, most likely, a finer lattice,” said Pedro Bicudo, a lattice QCD specialist at the University of Lisbon in Portugal.

More capable lattice QCD simulations will have far-reaching benefits. Particle physicists’ main goal in experiments like LHCb is to find signs of new fundamental particles, such as those that might make up the universe’s dark matter. To do so, they must be able to distinguish the dance of charm quarks and their kin from other, more novel influences.

“Anywhere the charm quark is important, this [discovery] will spread there,” Bicudo said.