When in school, we learned that atoms are made up of three kinds of subatomic particles - electrons, protons and neutrons. We imagined tiny negatively charged electrons as excitable entities that were always zipping around, restrained by positively charged protons that kept things together, while neutrons, cohabiting with protons in the nucleus, passively looked on. However, this cartoon version of the atom sweeps over an incredible complexity of interactions. After more than a century of research in quantum physics, we have a more nuanced understanding of the anatomy of an atom and continue to explore its landscape.
While the concept of an atom as the fundamental unit of matter was prevalent for hundreds of years, the discovery of electrons at the turn of the twentieth century showed that it was possible to break atoms down further. Various models of an atom were proposed, from Joseph John Thomson’s model of electrons embedded in a positively charged pudding to Erwin Schrödinger’s model where electrons are an effervescent cloud surrounding the nucleus. In the 1970s, the Standard Model of particle physics broke down subatomic particles even further to come up with an assorted box of elementary particles. Those making up matter are known as fermions and others that impart mass or carry force are called bosons.
Atomic models through the ages. From left to right: JJ Thomson’s plum pudding model, Ernest Rutherford’s nuclear model, Niels Bohr’s planetary model and Erwin Schrödinger’s quantum model. Image by Ville Takanen shared under a CC by 3.0 license.
Fermions, the elementary particles making up matter, are of two types, quarks and leptons. They have an alter ego in an antimatter particle, which has the same mass but other contrasting properties. Two types of quarks, named up and down, make up protons and neutrons, which are among six different kinds or ‘flavours’ of quarks. Composites of quarks are more generally called hadrons. Baryons are a subclass of hadrons made up of an odd number of (anti)quarks. The two lightest members of the baryon family (represented as \(qqq\), where \(q\) is a quark and \(qqq\) is a triplet of quarks) are the proton, which consists of two up quarks and one down quark, and the neutron, comprising of one up quark and two down quarks. Mesons, made up of a quark-antiquark pair (\(q \bar q\), where \(\bar q\) is an antiquark), form the other class of hadrons, which are unstable and usually observed in particle collision experiments.
Ordinary hadrons are composed of a quark-antiquark pair (meson) or a triplet of quarks (baryon). Image by Bhabani Sankar Tripathy.
Quarks have a fractional electric charge, and depending on how they are combined, may impart a resultant charge to the hadrons they are part of. For example, a proton gets one unit of positive charge since it is made up of two up quarks, each with a two-thirds positive charge, and a down quark with a one-third negative charge. Up and down quarks are the building blocks of most matter around us. There are two more quark pairs (charm-strange, top-bottom) analogous to up-down except for each pair's progressively increasing mass, and rarity. Leptons, such as electrons and neutrinos, are much lighter matter particles, which have two additional analogous generations of lepton-pairs (muon-muon neutrino, tau-tau neutrino) much like quarks.
The Standard Model of elementary particles.
The force determining how quarks within protons and protons within a nucleus stick together, despite repelling electric forces, is known as the strong force. Quantum ChromoDynamics (QCD) is a well-accepted theory of strong force that explains how elementary particles within hadrons interact with each other. QCD argues that apart from the electric charge, a quark carries another kind of charge called ‘colour’ charge, which can be either red, green or blue. This has nothing to do with colours in the visible spectrum, but is used to describe a specific property of quarks, which makes them sensitive to the strong force. The three constituent quarks within each proton or neutron belong to three different colours to render the resulting composite colourless. A quark’s property of colour makes it responsive to the strong force, where quarks of different colours are held together by force-carrying particles called gluons. Gluons in strong force are equivalent to photons in electromagnetic force, with the exception that gluons carry a colour charge, while photons do not carry an electric charge.
The strength of the strong force increases with distance, such that it can be considered very small at distances less than one-tenths of a femtometer (\(10^{-16}\) meters), but is large at greater distances. The strong force gets its name because its strength is many orders of magnitude greater than the other fundamental forces (gravitation, electromagnetism, weak interaction). When quarks are pulled apart to large distances, the energy expended in separating them is high enough to give rise to a new quark-antiquark pair that bunks with the existing one. Quarks, therefore, cannot be isolated and are never observed alone.
Quarks and gluons are the building blocks of protons and neutrons. Within these, three differently coloured quarks interact using strong forces mediated by gluons. Image by Bhabani Sankar Tripathy.
The presence of a colour charge on gluons mediating the strong force, and the relationship of strong force with distance makes it unique among the fundamental forces. These properties make it impossible to study strong interactions at large distances by solving equations to find exact solutions. Instead, researchers use computationally intensive numerical simulations such as Lattice Quantum ChromoDynamics (Lattice QCD). In this framework, space-time is discretized into a grid on which the theory of QCD is defined and quark-gluon interactions are monitored using Markov chain Monte Carlo simulations. The input parameters to these calculations are related to quark mass and coupling strength. These virtual numerical experiments provide predictions that can be tested against real-world experimental observations.
In particle collision experiments, such as in the Large Hadron Collider (LHC) at CERN - the European Organization for Nuclear Research in Switzerland, Belle II at KEK - The High Energy Accelerator Research Organization in Japan, and Beijing Spectrometer III in the Beijing Electron–Positron Collider II at the Institute of High Energy Physics in China, particles are smashed at very high velocities to offer clues about the interactions between elementary particles. Scientists use theoretical predictions to interpret the data emerging from these experiments.
Reconstruction of particle tracks detected from high energy proton collision experiments at the Large Hadron Collider. Image by ATLAS Collaboration, CERN.
Until 2003, experiments around the globe uncovered the existence of a handful of hadrons, most of which fit into the simplest picture of baryons (\(qqq\)) and mesons (\(q \bar q\)). Since then, experimental facilities have been discovering exotic hadrons - complex quark composites with a fleeting existence (\(\sim10^{-23}\) seconds), which challenge this traditional picture. “\(X(3872)\) was the first exotic hadron to be discovered at Belle II, whose origin remains an open question till today,” says M. Padmanath who leads the hadron physics group at The Institute of Mathematical Sciences (IMSc), Chennai. Another discovery that has spiked recent scientific interest is the \(T_{cc}\) tetraquark reported by the LHCb collaboration, suggested to be made of two charm quarks and an up and a down antiquark, he adds. LHCb and Belle II continue to investigate documented exotic hadrons and discover novel ones, while emerging facilities, such as the Electron-Ion Collider at the Brookhaven National Laboratory, can give us a detailed picture of quark-gluon interactions and allow us to test theoretical predictions of exotic hadrons. “Lattice QCD simulations play an important role in gathering evidence for the existence of these composite particles and the conditions under which they come to be,” Padmanath explains.
Exotic hadrons are fleeting complex composites of quarks discovered in particle collision experiments, which can be investigated using Lattice QCD simulations. Image by Bhabani Sankar Tripathy.Exotic hadrons detected in the Large Hadron Collider beauty experiment at CERN. Here, the mass of each exotic hadron (in giga-electron volt) is plotted against its year of discovery. The colour codes indicate the quark composition of a hadron. In the figure legend: \(u\) - up, \(d\) - down, \(c\) - charm, \(s\) - strange, and the corresponding antiquarks are represented by bars over the symbols. Image by the Quarkonium Working Group Exotics hub.
“Our research explores exotic hadron features such as tetraquarks, pentaquarks and hexaquarks using lattice QCD simulations,” says Padmanath. “We collaborate with global researchers and utilize powerful High-Performance Computing facilities in India (Indian Lattice Gauge Theory Initiative at the Tata Institute of Fundamental Research Mumbai, IMSc), Germany (University of Regensburg, Gauss Centre for Supercomputing and the John von Neumann Institute for Computing in Jülich) and Slovenia (Vega IIS) to study hadronic interactions at the femtoscale (\(10^{-15}\) meters)”.
Recent work by IMSc’s M. Padmanath and collaborators predicted the existence of a new tetraquark (\(T_{bc}\)) using numerical scattering experiments with bottom mesons (\(\bar B^{*}\)) and charmed mesons (\(D\)). Image by Archana Radhakrishnan.
Their recent work, in collaboration with German and Slovenian scientists, involved virtual numerical scattering experiments of mesons to recreate the tetraquark and study its properties [1, 2]. They also predicted the existence of a new heavy di-baryon \(D_{6b}\) [3] and a heavy tetraquark \(T_{bc}\) [4] along with scientists from TIFR Mumbai. “Looking ahead, we plan to perform advanced calculations to deepen our understanding of quark-level interactions within hadrons and their implications in subnuclear physics and beyond,” says Padmanath.
References:
1. Padmanath, M., & Prelovsek, S. (2022). Signature of a doubly charm tetraquark pole in \(DD^{*}\) scattering on the lattice. Physical Review Letters, 129(3), 032002. https://doi.org/10.1103/PhysRevLett.129.032002
2. Collins, S., Nefediev, A., Padmanath, M., & Prelovsek, S. (2024). Toward the quark mass dependence of \(T_{cc}\) from lattice QCD. Physical Review D, 109(9), 094509. https://doi.org/10.1103/PhysRevD.109.094509
3. Mathur, N., Padmanath, M., & Chakraborty, D. (2023). Strongly bound dibaryon with maximal beauty flavor from lattice QCD. Physical Review Letters, 130(11), 111901. https://doi.org/10.1103/PhysRevLett.130.111901
4. Padmanath, M., Radhakrishnan, A., & Mathur, N. (2024). Bound isoscalar axial-vector \(bc \overline u \overline d\) tetraquark \(T_{bc}\) from lattice QCD using two-meson and diquark-antidiquark variational basis. Physical Review Letters, 132(20), 201902. https://doi.org/10.1103/PhysRevLett.132.201902
