Toward the excited meson spectrum of dynamical QCD

Abstract: We present a detailed description of the extraction of the highly excited isovector meson spectrum on dynamical anisotropic lattices using a new quark-field construction algorithm and a large variational basis of operators. With careful operator construction, the combination of these techniques is used to identify the continuum spin of extracted states reliably, overcoming the reduced rotational symmetry of the cubic lattice. Excited states, states with exotic quantum numbers (0+-, 1-+ and 2+-) and states of high spin are resolved, including, for the first time in a lattice QCD calculation, spin-four states. The determinations of the spectrum of isovector mesons and kaons are performed on dynamical lattices with two volumes and with pion masses down to ~ 400 MeV, with statistical precision typically at or below 1% even for highly excited states.

Toward the Excited Meson Spectrum of Dynamical QCD

The paper, "Toward the excited meson spectrum of dynamical QCD," presents a comprehensive examination of the spectrum of highly excited mesons using lattice QCD with two flavors of light quarks and one strange quark. The authors employ anisotropic lattices and a refined operator basis to address challenges related to reduced symmetries inherent in lattice computations.

The researchers introduce innovative techniques, notably the use of "distillation" methods for quark-field construction, which enable efficient computation of correlation functions, crucial for extracting spectroscopic information. This approach utilizes a variational method across an extensive operator basis to achieve robust extraction of excited states, including those of high spin and exotic quantum numbers like $0^{+-}$, $1^{-+}$, and $2^{+-}$.

An important part of their methodology involves assigning continuum spins to states. This is done by comparing overlaps of subduced operators on the lattice, where the subduction process respects the symmetry reduction imposed by cubic lattice structure. Identification of continuum spins is achieved even for high-spin states (up to spin-four), making it a distinctive contribution of this work.

The numerical results show a detailed spectrum that hints at features predicted by quark model classifications as well as hybrid states indicated by overlaps onto operators reflecting non-trivial gluonic field configurations. It identifies non-exotic hybrid mesons likely involved in strong mixing with conventional $q\bar{q}$ states, especially at higher masses.

Consistency across different lattice volumes and pion masses is shown, with results exhibiting anticipated features of QCD bound states. Despite these successes, two-meson states appear suppressed, potentially due to a combination of weak operator overlap and dynamical characteristics of confinement. This indicates a need for more targeted operator design in future studies, potentially including higher-dimensional multi-hadron operators.

In conclusion, the paper demonstrates how refined lattice techniques can probe complex dynamics within the QCD meson spectrum. While some theoretical ambiguities remain, particularly in connecting lattice results to physical resonances, the groundwork laid herein points towards increasingly refined lattice methodologies in capturing strong interaction physics effectively. Future research paths include exploring multi-particle interactions and further elucidating resonant states with broader operator bases, extending insights from studies like GlueX into lattice simulations.