Lattice QCD Reveals Phase Shifts for Doubly Charmed and Bottomed Tetraquarks

The search for exotic particles composed of multiple quarks continues to push the boundaries of particle physics, and a new study focuses on the potential existence of tetraquarks, particles made of four quarks. Masato Nagatsuka and Shoichi Sasaki, both from Tohoku University, along with their colleagues, investigate the interactions between quarks to determine if stable tetraquark combinations can form, specifically looking at systems containing charm and bottom quarks. Their work employs a sophisticated computational technique, utilising lattice quantum chromodynamics with twisted boundary conditions, to map out the forces between these quarks at various energies. This method allows researchers to explore a continuous range of interaction strengths, revealing subtle signals of bound states, and the team reports evidence for a shallowly bound state in the charm quark system, potentially shedding light on the composition and stability of these elusive particles.

The T+cc and T−bb states represent hadronic bound states, with the T+cc state previously observed as a peak near the DD* threshold. The T−bb state is a theoretically predicted tetraquark containing heavier bb̄ud quark flavours. Researchers employ Lüscher’s finite-size method to calculate how hadrons scatter, a well-established approach within lattice QCD simulations. Numerous studies have used simulations with periodic boundaries to determine scattering at specific energies for the DD* system.

Lattice QCD Calculations of Hadron Structure

This research centres on lattice quantum chromodynamics (LQCD), a non-perturbative approach to solving the equations governing the strong force that binds quarks together. The work investigates hadron physics, focusing on particles containing heavier quarks like charm and bottom, and studies hadron masses, decay characteristics, and interactions to understand their structure. A key focus is identifying hadron resonances, short-lived excited states, and potential molecular states, such as those formed by multiple hadrons bound together. The team carefully accounts for the effects of simulating particles within a limited space, ensuring accurate results.

Researchers perform large-scale lattice QCD simulations using complex mathematical descriptions of the gluon field, calculating correlation functions to determine hadron properties. Interpolating operators create and detect hadrons within the simulations, and the choice of these operators is crucial for accuracy. Applying Lüscher’s formula connects energy levels in a limited space to scattering in an infinite space, allowing researchers to extract scattering parameters from the simulation data. Calculations often begin with light quark masses, then extrapolate to physical quark masses using chiral perturbation theory, modelling the dependence of hadron properties on quark masses with functions like Pade approximants and assessing uncertainties with Bayesian statistical methods.

The researchers have achieved precise determinations of hadron masses and decay constants, analysing scattering amplitudes to search for resonances and determine interaction strengths, finding evidence for certain hadron resonances and potentially confirming previously observed states. The team investigates the possibility of exotic molecular states, such as tetraquarks or pentaquarks, focusing on controlling systematic uncertainties arising from the discretization of spacetime, the choice of operators, and extrapolating to physical quark masses. Results are compared with experimental data to validate calculations and test predictions of the Standard Model, aiming to improve calculations, explore new physics, and refine our understanding of hadron structure.

Tetraquark Stability Studied with Twisted QCD

Researchers have developed a sophisticated method for investigating tetraquarks, particles composed of four quarks, specifically those containing charm and bottom quarks. This investigation uses lattice quantum chromodynamics (LQCD), a powerful computational approach for studying the strong force. The team precisely calculates particle interactions to determine if combinations are stable enough to form bound states, potentially representing a new form of matter. A key innovation is the application of “twisted boundary conditions” within the lattice QCD simulations, allowing researchers to explore a wider range of energies and momenta than previously possible, improving the precision with which they can predict the formation of bound states.

By manipulating the boundaries of the simulation, they can effectively scan for tetraquark states that might otherwise be missed, which is particularly important when searching for particles with subtle interactions or those close to breaking apart. Results indicate a potential shallow bound state within the charm quark system, with a binding energy measured in kiloelectronvolts, suggesting that certain combinations of charm quarks may be stable enough to form a tetraquark. The team’s calculations demonstrate that this method is significantly more sensitive than previous approaches, allowing them to probe energy levels with greater accuracy. Furthermore, the researchers have shown that their method accurately predicts particle interactions, providing a valuable tool for understanding the strong force. This work represents a significant step forward in the search for exotic hadrons and provides new insights into the fundamental building blocks of matter, promising to be instrumental in unraveling the mysteries of the strong force and discovering new forms of matter beyond protons and neutrons.

Shallow Charm Tetraquark State Identified

This research investigates the potential existence of tetraquark particles containing heavy quarks, specifically charm and bottom quarks. Using Lüscher’s finite-size method within lattice quantum chromodynamics (LQCD), the team calculated the interactions between these heavy quarks to search for evidence of bound states. This method allows researchers to determine how particles scatter and interact, even at very low energies, by simulating conditions with limited space and manipulating the boundaries of the simulation. Results indicate a shallow bound state exists in the charm quark system, with a very small binding energy, suggesting a weakly bound tetraquark particle.

While deeper, more strongly bound states have been previously identified in bottom quark systems, this research represents the first detailed investigation into shallow bound states in the charm quark system using this particular method. The authors acknowledge that identifying these shallow states is challenging and requires precise calculations of the scattering phase shifts near the interaction threshold. It is important to note that the identification of these states relies on extrapolating data from the simulations, and the observed binding energy is small, meaning further investigation is needed to confirm the existence and properties of this tetraquark particle with greater certainty. Nevertheless, this research provides valuable insights into the complex interactions of heavy quarks and contributes to the ongoing search for exotic forms of matter beyond protons and neutrons.