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Quarks, the building blocks of protons and neutrons, usually pair up or form trios. But sometimes they assemble into larger, unstable combinations that live for mere fractions of a second. Two such particles, Bs0* and Bs1, have long been a puzzle: calculations hinted they should be bound, but the precision wasn't enough to say so with confidence.

Now a team of physicists used lattice QCD, a method where space and time are divided into tiny cells. Inside each cell, quarks interact according to the laws of the strong force, and the computer sums millions of such interactions. The key trick was tuning the heavy b-quark's parameters with a neural network, which adjusts values so that errors don't accumulate. This removed the main source of inaccuracy from previous work.

The result: the binding energy of Bs0* relative to the BK threshold is -65.9 MeV, and that of Bs1 relative to B*K is -60.6 MeV. For comparison, the binding energy of a deuterium nucleus is about 2.2 MeV, so these exotic mesons are bound tens of times more tightly. For the first time, it was shown that the binding persists even as the lattice spacing approaches zero — the so-called continuum limit. This check is critical: if the particles fell apart at an infinitely fine grid, all previous conclusions would be computational artifacts.

Why does this matter? Understanding how quarks stick together in unusual combinations sheds light on the nature of the strong force — the most powerful force in the microcosm. Perhaps even more exotic states exist deep inside neutron stars, and lattice calculations could help predict them.