Title: Searching for New Fundamental Interactions via Isotopic Shifts in Molecular Lattice Clocks

Abstract: Precision measurements with ultracold atoms and molecules are primed to probe beyond-the-Standard Model physics. Isotopologues of homonuclear molecules are a natural testbed for new Yukawa-type mass-dependent forces at nanometer scales, complementing existing mesoscopic-body and neutron scattering experiments. Here we propose using isotopic shift measurements in molecular lattice clocks to constrain these new interactions from new massive scalar particles in keV$/c^2$ range: the new interaction would impart an extra isotopic shift to molecular levels on top of one predicted by the Standard Model. For the strontium dimer, a Hz-level agreement between experiment and theory could constrain the coupling of the new particles to hadrons by up to an order-of-magnitude over the most stringent existing experiments.