  String theory predicts that the couplings of Nature descend from dynamical
fields. All known string-motivated particle physics models also come with a
wide range of possible extra sectors. It is common to posit that such moduli
are frozen to a background value, and that extra sectors can be nearly
completely decoupled. Performing a partial trace over all sectors other than
the visible sector generically puts the visible sector in a mixed state, with
coupling constants drawn from a quantum statistical ensemble. An observable
consequence of this entanglement between visible and extra sectors is that the
reported values of couplings will appear to have an irreducible variance.
Including this variance in fits to experimental data gives an important
additional parameter that can be used to distinguish this scenario from the
case where couplings are treated as fixed parameters. There is a consequent
interplay between energy range and precision of an experiment that allows an
extended reach for new physics.
