This paper reports a new lattice calculation of the charm and bottom quark masses using a “step‑scaling” strategy. The main idea is to do the renormalization and heavy‑quark tuning in physically small boxes where the bottom quark can be treated relativistically. The small‑volume results are then connected, step by step, to large‑volume ensembles that include physical light and strange quark masses. The authors say this approach yields precise masses with systematic errors that are different from, and therefore complementary to, those of standard large‑volume methods.

What the researchers did: they computed heavy‑light meson masses in a series of finite volumes. They simulated with three flavors of O(a)‑improved Wilson quarks and the Lüscher–Weisz improved gauge action. Small‑volume runs use the Schrödinger functional setup with massless sea quarks in volumes L1≈0.5 fm and L2≈2L1≈1.0 fm. Large‑volume results come from CLS ensembles that lie on a chiral trajectory and include simulations at physical light and strange masses. The authors also simulated down to very fine lattice spacings (as small as a≈0.0078 fm) and used two discretizations for the static limit based on HYP‑smeared gauge fields.

How the method works at a high level: the calculation builds finite‑volume “step‑scaling” functions that record how a heavy‑light meson mass changes when the box size doubles. One function, σm(L1), measures the change between L1 and 2L1. Another, ρm(L2), connects the finite‑volume result to the effectively infinite‑volume meson mass. These finite‑volume differences can be computed both with relativistic heavy quarks and in the static limit of Heavy Quark Effective Theory (HQET). Combining the relativistic data, the static limit, and a non‑perturbative renormalized heavy mass in the small box produces the renormalization‑group‑invariant heavy‑quark mass.