Collider data show evidence for a meson made of four quarks

In the six decades since the discovery of the pion, more than a hundred other meson species have been found. Most decay by the strong nuclear interactions and therefore live less than 10⁻²² s. So one sees them only as resonant peaks in scattering cross sections or energy distributions. But until now they all had one thing in common: Every known meson was characterized by a combination of quantum numbers—charge, spin, parity, strangeness, charm, and the like—that could be accounted for simply by a quark–antiquark (q $\overline{q}$ ) pair.

Now the Belle collaboration at the KEKB electron–positron collider in Tsukuba, Japan, has reported impressive evidence for the first manifestly exotic meson—a meson that clearly requires more quarks than just a q $\overline{q}$ pair. ¹ Dubbed Z^± (4430), the new charged meson has a mass of 4.43 GeV, about four and a half times that of the proton. Particle physicists welcome such exceptions as clues to elusive ramifications of quantum chromodynamics, the accepted theory of the strong interactions of quarks and the hadrons (baryons and mesons) they make up.

The giveaway was the new meson’s observed decay mode. From among the debris of a billion e⁺e⁻ collisions recorded by Belle since 1999, group members Soo-Kyung Choi and Stephen Olsen have unearthed a resonant peak of some 170 events indicating the strong-interaction decay of a 4.43-GeV meson to a π^± and a Ψ’ (see the figure on page 19). With a mass of 3.69 GeV, the electrically neutral Ψ’ is a well-established “charmonium” meson. That is, it’s a bound state of the heavy charmed quark (c) and its antiquark ( $\overline{c}$ ). Almost twice as heavy as the proton, the c quark was discovered in the mid-1970s.

Because quarks cannot change character (called flavor) in strong-interaction decays, it’s clear that the parent Z^± already contained a c $\overline{c}$ pair. But c and $\overline{c}$ have equal and opposite charges (± 2e/3). So they alone can’t account for the charge of the Z^± manifested by its charged-pion decay product. Therefore, in addition to the c $\overline{c}$ pair, the new meson must also harbor two of the light quarks that make up more familiar particles like protons and pions. For the Z⁺, it’s an up quark (u) with charge +2e/3 and an antidown quark ( $\overline{d}$ ) with charge +e/3.

The figure shows a distribution of invariant mass—the total energy of the two putative decay products in the reference frame of their center of mass. In the absence of lifetime broadening and experimental error, the histogram would exhibit a zero-width spike at the mass of the parent particle. Taking account of measurement uncertainties, the fit to the invariant-mass peak yields an intrinsic width of about 45 MeV. That’s unusually narrow for so heavy a meson in the absence of a selection rule that inhibits strong-interaction decay. The narrowness, by itself, is suggestive of an exotic state.

KEKB, like the similar PEPII collider that recently ceased operation at SLAC, is called a B factory. That’s because when its beams are tuned to a particular resonant collision energy, a large fraction of all e⁺ e⁻ collisions produce a pair of the very heavy B mesons. The Belle analysis has thus far found the Z^± peak only in collisions in which a charged or neutral B decays to a K meson plus the Ψ’ and the charged pion. So the experimenters had to consider and rule out the possibility that the Ψ’ π invariant-mass peak might be a kinematic artifact reflecting resonant interaction between the K and π.

The Belle group determined that its Z^±(4430) signal, found in its search through 700 million B decays, has a statistical significance of 6.5 standard deviations. Theoretical issues aside, the experimental case for the Z^± is widely regarded as more convincing than was the ephemeral evidence in 2003 for the now largely discredited Θ⁺(1530), which was for a time hailed as the first exotic baryon—a so-called pentaquark requiring five quarks instead of the canonical three (see Physics Today, September 2003, page 19 ). Three quarks couldn’t account for the simultaneous positive charge and positive strangeness of the supposed θ⁺(1530).

Quantum chromodynamics

Hitherto, the absence of exotic mesons whose quantum numbers require qq $\overline{q}$ $\overline{q}$ or exotic baryons requiring qqqq $\overline{q}$ seemed plausible within quantum chromodynamics. But unambiguous predictions are notoriously difficult to calculate from QCD. The theory asserts that quarks of any flavor come in three precisely equivalent sorts, called colors. Quark color is the strong-interaction analogue of electric charge. (See the article by Frank Wilczek in Physics Today, August 2000, page 22 .) QCD does identify q $\overline{q}$ and qqq as the lowest-energy color-singlet configurations—that is, states with the requisite color symmetry for forming free particles. But the theory, as currently understood, cannot rule out mesons and baryons made, respectively, of four- and five-quark color singlets.

The case for four-quark mesons is much the stronger of the two. In recent years the Belle collaboration and BaBar, its equivalent at SLAC’s PEPII, have discovered half a dozen charmonium mesons that don’t fit expectations for straightforward c $\overline{c}$ bound states. ² Because the c quark is so massive, QCD theorists have availed themselves of nonrelativistic approximations to predict the masses and other properties of excited c $\overline{c}$ states with impressive reliability. But the half-dozen new ones don’t fit the picture. The Z^±(4430) is the first that’s manifestly exotic. The others, though putatively exotic, lack the telltale electric charge.

With regard to the Z^±(4430) and the other wayward charmonium states, two different four-quark hypotheses have gotten attention. At least some of the states might be “mesonic molecules,” loosely bound pairs of ordinary q $\overline{q}$ mesons barely held together by the QCD analogue of van der Waals forces. More exciting is the notion for which the term tetraquark is reserved. That hypothesis takes the exotic states to be color singlets formed by the binding of a strongly coupled qq diquark with a $\overline{q}$ $\overline{q}$ antidiquark. Not being color singlets, the individual diquarks that make up the tetraquark could not exist as free particles. But there’s abundant empirical evidence from the spectrum of hadron masses and from scattering phenomena that certain kinds of diquarks are strongly coupled. These favored diquarks are the ones that are antisymmetric under exchange of any of the three quark labels: color, flavor, or spin orientation.

The mesonic-molecule hypothesis is particularly plausible when the mass of the meson in question is very close to the kinematic threshold for decay to a pair of daughters that might be its molecular constituents. And indeed, theorist Jonathan Rosner at the University of Chicago has pointed out that the Z^± mass is close to the sum of the masses of a particular pair of D mesons that might be forming a mesonic molecule. ³ Every D meson carries a single c (or $\overline{c}$ ) quark.

University of Rome theorist Luciano Maiani favors the idea that Z^±(4430) and the other problematic charmonium states are tetraquarks. On that basis, he and coworkers have assigned to each of them a specific diquark–antidiquark bound state and predicted the existence of additional charmonium tetraquarks yet unseen. ⁴ In particular, they predict that experimenters will find two different neutral siblings of the Z^± with masses within a few MeV of 4430. That prediction follows from the strict adherence to isotopic-spin symmetry expected of tetraquarks. Mesonic molecules, by contrast, could exhibit significant violation of that approximate symmetry, which is an elaboration of the charge independence of the strong interactions. Maiani and company also predict more distant tetraquark relatives of the Z^±(4430), with masses up to 4.6 GeV. Some of those, they argue, should have an unusual affinity for decaying into baryon–antibaryon pairs.

Fooled again?

The tetraquark quantum states adduced to account for the observed and predicted charmonium exotics all have the diquark and antidiquark in an s-wave state of zero relative orbital angular momentum. Higher orbital states would weaken the already precarious binding. When evidence of the Θ⁺(1530) pentaquark baryon was reported in 2003, Wilczek and MIT colleague Robert Jaffe considered that it might be a bound state of two diquarks plus a lone strange antiquark. ⁵ In that case, however, Bose statistics forbids an s-wave between the two diquarks. “But because the experimental evidence for the pentaquark at first seemed so compelling,” recalls Jaffe, “we speculated that maybe forming the favored antisymmetric diquark pays so well that a pair of them can bear the insult of being in a p-wave.”

The supposed pentaquark was first sighted in collisions between photons and nuclei at a synchrotron light source and at a nuclear-physics accelerator. When follow-up searches were carried out with higher statistics at particle-physics accelerators, the pentaquark signal was gone. Old particle-physics hands had wondered why, if the Θ⁺(1530) really did exist, they had not found it decades ago when they were searching in the same energy regime for positively charged baryons with positive strangeness. ⁶

The B factories, by contrast, allow experimenters to find hadronic states they probably couldn’t have unearthed earlier. The 5.3-GeV B mesons created there in great profusion are just about as heavy as mesons ever get. They decay (by flavor-changing weak interactions) preferentially into mesons that carry charmed quarks. It’s among such decays that theorists expect exotic mesons to be found—if they exist.

PEPII and KEKB were built primarily to study the tiny asymmetry between particles and antiparticles (see Physics Today, May 2001, page 17 ). As a byproduct of that effort, Belle and BaBar have accumulated enormous reserves of B-decay data that could reveal many more new states. “That’s a fantastic resource we’re just beginning to explore,” says Jaffe. “QCD is a beautiful and complete theory, but nobody has been able to solve it for hadronic states. We need all the help we can get to understand the confinement of quarks inside hadrons.”