Discovery of exotic hadrons stimulates theoretical development

Objects consisting of four quarks display different configurations from those consisting of protons, neutrons and mesons. The possibility of their existence had been predicted by quantum chromodynamics.

By José Tadeu Arantes

Agência FAPESP – The quark model is 50 years old and was proposed independently by US physicists Murray Gell-Mann and George Zweig in 1964. This long-lived model has continued to be developed both theoretically and experimentally.

One such development is the discovery of an object comprising four quarks. Known as Z+(4430), it was first found in 2008 at Japan’s High Energy Accelerator Research Organization (KEK). Its existence was convincingly confirmed in 2014 at the Large Hadron Collider (LHC), operated by CERN on the Franco-Swiss border.

The number 4430 refers to the object’s mass in mega electron volts over the speed of light squared (MeV/c²). For comparison, a proton’s mass is approximately 938.3 MeV/c². By contrast, Z+(4430) survives for only a tiny fraction of a second, whereas a proton’s half-life exceeds 2.1×10²⁹ years (almost 20 times the estimated age of the Universe).

Z+(4430) has aroused considerable interest because there is no explanation for its existence other than that it is an exotic four-quark particle.

The usual particle compositions are three quarks forming a baryon (such as a proton or neutron) or a quark-antiquark pair forming a meson (such as the pion, or pi meson), the latter of which was predicted theoretically by Japanese physicist Hideki Yukawa in 1935 and discovered experimentally by Brazilian physicist César Lattes in 1947.

For a long time, exotic compositions were only a theoretical possibility, but they began to be discovered in particle accelerators over the course of the past decade.

“Z+(4430) may be either a molecule made up of two mesons, each consisting of a quark-antiquark pair, or a tetraquark consisting of four loosely bound quarks held in a confined volume by strong interaction,” said Marina Nielsen, Full Professor and Head of the Department of Experimental Physics at the University of São Paulo’s Physics Institute (IF-USP) in Brazil.

Nielsen is the principal investigator for the Thematic Project “Hadron Physics”, which is supported by FAPESP. “The study of these exotic hadrons is one of the lines of research in our project and the one with which I’m most intensely involved,” Nielsen told Agência FAPESP.

The structure of exotic hadrons discovered previously is still controversial. For example, X(3872), found at KEK in 2003, also appears to consist of four quarks organized either as a two-meson molecule or a tetraquark.

However, the structure cannot be determined with certainty because the object is electrically neutral. Some researchers argue that it is merely a charmonium, i.e., a meson composed of a charm and anti-charm quark pair. The charm quark is the third most massive of all quarks.

“But the case of Z+(4430) leaves no room for doubt,” Nielsen said. “It has electric charge, so in addition to the charm-anticharm pair, it must also contain an up quark and an anti-down quark.”

Reference article

Interpreting the nature of X(3872) and other exotic hadrons found later is a challenge for physicists working in quantum chromodynamics (QCD), the theory that describes the action of quarks and their interactions.

Nielsen and her colleague Fernando Silveira Navarra, also a Full Professor at IF-USP, are participants in the Quarkonium Working Group (QWG), an international network dedicated to the field, alongside some 70 researchers from the world’s leading universities.

“Heavy quarkonium: progress, puzzles, and opportunities”, a paper by this international group published in the European Physical Journal in 2011, has become a reference in the field, receiving more than 700 citations.

The researchers at IF-USP made a significant contribution to this study. “One of the methods used to do calculations in this field is the so-called quantum chromodynamics sum rules, or QCDSR, with which we’ve been working for years. With the help of this method, we were able to gain a better understanding of exotic states,” Navarra said.

“Some [exotic particles] may be better understood as tetraquarks, others as massive quark mesons like the charmonium, and yet others as a quantum mixture of the charmonium and tetraquarks.”

In a quantum mixture, the wave function associated with the object in question has two components: one that describes the charmonium and another that describes the tetraquark. In a large number of observations, the object will be observed as either one or the other, in accordance with a certain probabilistic distribution.

“The proliferation of new states has created a situation that to some extent resembles the situation that existed before Gell-Mann and Zweig proposed the quark model. There are several particles apparently with connections to one another, challenging researchers to group them together based on some criterion. We have also made our contribution here, showing that certain states can be correctly interpreted as excitations of others,” Navarra said.

The scenario to which physicists were accustomed and now consider simplistic, consisting of baryons (three quarks) and mesons (quark-antiquark), corresponds to the energy levels of the everyday world, or those that could be reached in laboratories until recently. As new machines capable of reaching ever-higher energy states are built, exotic objects are increasingly being detected, demanding fresh efforts at theoretical interpretation.

“In a sense, the new discoveries corroborate quantum chromodynamics because this theory establishes the configurations of quarks that can exist and those that cannot. The simplest ones are the triad of quarks and the quark-antiquark pair,” Nielsen said.

“However, other more complex configurations are also possible. There’s a famous saying in quantum mechanics: ‘Everything not forbidden is compulsory’. What we’re achieving now, thanks to the new energy levels reached by accelerators like the LHC, is the capacity to observe other possible states.”