A theoretical study has confirmed that a particle observed at CERN’s LHCb experiment in 2022 is indeed a tetraquark – supporting earlier hypotheses that were based on the analysis of its observed decay products. Tetraquarks comprise four quarks and do not fit into the conventional classification of hadrons, which defines only mesons (quark and an antiquark) and baryons (three quarks). Tetraquarks are of great interest to particle physicists because their exotic nature provides opportunities to deepen our understanding of the intricate physics of the strong interactions that bind quarks together in hadrons.
“X(3960) is a new hadron discovered at the Large Hadron Collider (LHC),” Bing-Dong Wan of Liaoning Normal University and Hangzhou Institute for Advanced Study, and the author of the study, tells Physics World. “Since 2003, many new hadrons have been discovered in experiments, and some of them appear to be tetraquarks, while only a few can be confirmed as such.”
Named for its mass of 3.96 GeV – about four times that of a proton – X(3960) stands out, even amongst exotic hadrons. Its decay into D mesons containing heavy charm quarks implies that X(3960) should contain charm quarks. The details of the interaction of charm quarks with other strongly interacting particles is rather poorly understood, making X(3960) interesting to study. Additionally, by the standards of unstable strongly interacting particles, X(3960) has a long lifetime – around 10-23 s – indicating unique underlying quark dynamics.
These intriguing properties of X(3960) led Wan to investigate its structure theoretically to determine if it is a tetraquark or not. In a recent paper in Nuclear Physics B, he describes how he used Shifman-Vainshtein-Zakharov sum rules in this calculations. This approach examines strongly interacting particles by relating their properties to those of their constituent quarks and the gluons that bind them together. The dynamics of these constituents can be accurately described by the fundamental theory of strong interactions known as quantum chromodynamics (QCD).
Wan assumed that the X(3960) is composed of a strange quark, a charm quark and their antiparticles. Using the sum rules, he derived its mass and the lifetime to compare these parameters with the observed values.
Mathematical machinery
Using the mathematical machinery of QCD and extensive numerical simulations, he found that the mass of the tetraquark he formulated is 3.98 ± 0.06 GeV. This is a close match to the measured mass of X(3960) at 3.956±0,005 GeV. This confirms that X(3960) comprises a strange quark, a charm quark and their antiparticles. Furthermore, Wan was able to compute the lifetime of his model particle to be 1.389±0.889×10−23 s, which aligns well with the observed value of (1.53−0.26+0.41)×10−23 s, further validating his identification.
While Wan’s work strongly supports the hypothesis that X(3960) is a charm–strange tetraquark, he acknowledges that it is not conclusive proof. In the subatomic world, particles can transform into others and the match of the quark composition of the tetraquark he studied and the decay products of X(3960) is not enough, Indeed, in principle, X(3960) can be even better described by some other quark composition.
“There are many possible structures for tetraquarks, and my work finds that one possible structure can explain the properties of X(3960),” says Wan. “But some other researchers may be able to explain the properties of X(3960) using different quark structures.”
To further validate his approach, Wan applied the sum rule technique to a particle similar to X(3960), called X(4140), previously discovered at the Tevatron collider. His calculations yielded mass and lifetime values very close to the measured ones, further confirming his method’s accuracy.
However, to definitively determine the structure of X(3960), further theoretical and experimental studies are needed. Analysing a larger number of decay events will help reduce measurement errors. On the theoretical side, using the sum rules or other QCD techniques to more accurately analyse these parameters will help reduce computational uncertainties.
“Studying new hadrons may greatly enrich the hadron family and our knowledge of the nature of strong interactions,” Wan concludes. “It is highly expected that we are now at the dawn of enormous discoveries of novel hadronic structures, implying a renaissance in hadron physics.”
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