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The scattering and spectroscopic properties of molecular halo states canserve as sensitive probes of the constancy of the electron-to-proton mass ratio$\beta=m_e/m_p$. Since halo states are formed by resonant $s$-waveinteractions, their properties exhibit universal correlations that are fairlyindependent of the interactions at short distances. For diatomic molecules,these properties depend on a single parameter only, and so this `universality'means that all the characteristics of a diatomic halo state can be determinedwith high precision if only one parameter is accurately known. Furthermore,this knowledge can be used to establish the respective property masssensitivities for investigating the stability of $\beta$. Here, we show for thehalo states of the helium dimers that the relationship between the probedproperties and their mass sensitivity can be derived from numerically exactsolutions of suitable radial Schr\"{o}dinger equations for a set of effectivepotential energy curves. The resulting relations exhibit a weak dependence onthe short-range part of the used potentials and a near-negligible dependence onthe `higher-order' nonadiabatic, relativistic, QED and residual retardationeffects. The presented approach is thus a robust alternative to otherliterature approaches, particularly in cases where a lack of experimental dataprevents an accurate interaction potential from being determined.

Universal behaviour of diatomic halo states and the mass sensitivity of their properties