Hadron spectroscopy and interactions

Abstract

In recent years, lattice QCD calculations of hadron spectroscopy have concentrated on resonances and shallow bound states detected via poles in two- and three-hadron scattering amplitudes. Hadron interactions have therefore become a key focus. In these proceedings, I review the current state of the art and recent advances in methods for studying hadron interactions via finite-volume spectroscopy and finite-volume quantization conditions. I will also review recent spectroscopy studies and results presented at Lattice 2025, with a focus on charmed mesons, the doubly charmed tetraquark, and the doubly bottom tetraquark.

Figures (5)

• Figure 1: Locations of physical scattering and possible poles for a two-particle partial wave amplitude. Left: on the complex centre-of-mass energy plane, which has physical and unphysical Riemann sheets resulting from a branch cut starting at threshold. Right: on the complex scattering momentum plane, which opens the cut via $\sqrt{s}=\sqrt{m_1^2+p^2}+\sqrt{m_2^2+p^2}$.
• Figure 2: Difference between the ground-state effective energy of a $DD^*$ system and the sum of effective masses of a $D$ and a $D^*$ meson. Blue circles are obtained from solving a GEVP for a symmetric correlator matrix with $N_\text{op}=23$; orange diamonds are obtained from a single asymmetric correlation function with local creation operator and bilocal annihilation operator.
• Figure 3: Analytic structure of the $NN$ scattering amplitude: (a) poles and cuts at fixed scattering angle and (b) cuts after partial-wave projection. Standard two-body quantization conditions only deal with the elastic two-particle branch cut. Reproduced from Ref. Raposo:2023oru under the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/).
• Figure 4: Low-lying $D$ and $D_s$ mesons for various $J^P$. Blue circles and orange squares indicate light and strange states listed in the PDG ParticleDataGroup:2024cfk; green diamonds show the two-pole structures in the UChPT analysis of Ref. Du:2017zvv.
• Figure 5: Lattice calculations of the $T_{bb}$ binding energy, determined using finite-volume spectroscopy Leskovec:2019ioaMohanta:2020eedHudspith:2023loyAlexandrou:2024iwiColquhoun:2024jzhTripathy:2025vaoVujmilovic:2025czt (blue circles) and potentials via the Born-Oppenheimer Brown:2012tmBicudo:2015vtaBicudo:2016ooe and HAL QCD Aoki:2023nzp methods (orange squares for single channel and green squares for coupled channel). Open symbols indicate a single lattice spacing or a single pion mass was used. Some earlier calculations that have been superseded Bicudo:2012qtFrancis:2016huiJunnarkar:2018twb are omitted from this figure.