Constraining Extra Space Dimensions using Precision Molecular Spectroscopy

Highly accurate measurements of quantum level energies in molecular systems provide a test ground for new physics, as such effects could manifest themselves as minute shifts in the quantum level structures of atoms and molecules. For the lightest molecular systems, neutral molecular hydrogen (H${}_2$, HD and D${}_2$) and the molecular hydrogen ions (H${}_2^{+}$, HD${}^{+}$ and D${}_2^{+}$), weak force effects are several orders weaker than current experimental and theoretical results, while contributions of Newtonian gravity and the strong force at the characteristic molecular distance scale of 1 \AA
can be safely neglected. Comparisons between experiment and QED calculations for these molecular systems can be interpreted in terms of probing large extra space dimensions, under which gravity could become much stronger than in ordinary 3-D space. Under this assumption, using the spectra of H${}_2$ we have derived constraints on the compactification scales for extra dimensions within the Arkani-Hamed-Dimopoulos-Dvali (ADD) framework, and constraints on the brane separation and bulk curvature within the Randall-Sundrum (RS-I and RS-II) frameworks.