This paper reports new lattice QCD results on how heavy quarks and their bound states behave in hot matter. The Fastsum collaboration used anisotropic lattices — grids with finer steps in (imaginary) time than in space — to study bottomonium (bound states of a bottom quark and antiquark), open‑beauty mesons (B mesons), and the static quark potential at temperatures around and above the QCD transition temperature Tc.

The authors ran simulations with Nf = 2+1 quark flavors on two sets of ensembles called Gen2 and Gen2L. These ensembles use pion masses of about 380 MeV (Gen2) and 240 MeV (Gen2L), spatial lattice spacings of about 0.1205 fm and 0.1121 fm, and an anisotropy parameter as/ aτ ≈ 3.45. They changed the temperature by varying the number of time slices. Heavy bottom quarks were treated with a nonrelativistic effective action (NRQCD) including O(v4) corrections. To extract real‑time information from Euclidean lattice data they compared many analysis methods: direct correlator fits and moments, a generalized eigenvalue approach, linear methods (Tikhonov, Backus–Gilbert, Hansen–Lupo–Tantalo), and Bayesian reconstructions (maximum entropy and the BR method).

For bottomonium (the Υ(1S) ground state) the different methods give a consistent picture of a small but robust negative thermal mass shift and a thermal broadening. The negative mass shift reaches up to about 40 MeV compared with the corresponding zero‑temperature result. All methods show an increasing thermal width with temperature, but they disagree on its size, so the authors currently place only an upper bound on the width rather than a precise value. They also note that the linear reconstruction methods have much larger uncertainties and are not optimized to resolve narrow peaks.

These proceedings present the first lattice results for B‑meson masses and spectral functions at high temperature. Masses extracted from exponential fits show a clear negative thermal mass shift already for temperatures above roughly 140 MeV, which is below the chiral transition temperature Tc in these ensembles. Spectral reconstructions with the BR method indicate that the ground‑state peak for the B meson disappears around Tc, while a matched zero‑temperature correlator truncated to the same time extent still shows a peak. The authors interpret this as evidence that there is no bound B‑meson state above Tc in these simulations. They caution that their light quarks are heavier than physical, so the absolute masses are larger than experiment.