Constraints on extra dimensions from precision molecular spectroscopy

Abstract

Accurate investigations of quantum-level energies in molecular systems are shown to provide a testing ground to constrain the size of compactified extra dimensions. This is made possible by recent progress in precision metrology with ultrastable lasers on energy levels in neutral molecular hydrogen (H 2 , HD, and D 2 ) and molecular hydrogen ions (H 2 + , HD + , and D 2 + ). Comparisons between experiment and quantum electrodynamics calculations for these molecular systems can be interpreted in terms of probing large extra dimensions, under which conditions gravity will become much stronger. Molecules are a probe of spacetime geometry at typical distances where chemical bonds are effective (i.e., at length scales of an Å). Constraints on compactification radii for extra dimensions are derived within the Arkani-Hamed-Dimopoulos-Dvali framework, while constraints for curvature or brane separation are derived within the Randall-Sundrum framework. Based on the molecular spectroscopy of D 2 molecules and HD + ions, the compactification size for seven extra dimensions (in connection to M-theory defined in 11 dimensions) of equal size is shown to be limited to μ < R 0.6 m 7 . While limits on compactification sizes of extra dimensions based on other branches of physics are compared, the prospect of further tightening constraints from the molecular method is discussed.

High-precision spectroscopy of the HD+ molecule at the 1-p.p.b. level

“…level, and a test of molecular QED at the level of 2.7 × 10 −4 , which are the most stringent tests performed so far. Second, it allows us to put new bounds on the existence of hypothetical fifth forces, and put new limits on the compactification radius of higher dimensions, as described in detail in [3,4,12]. Third, the result presented here can be used to obtain a new value the proton-to-electron mass ratio with a precision of 2.9 p.p.b.…”

“…At close range r, the electric field of the ion polarizes the neutral molecule which results in an attractive interaction potential U(r) = −αQ 2 /(8πǫ 0 r) 4 . Here α denotes the polarizability volume (in m 3 ) 1 of the molecule, ǫ 0 is the electric constant, and Q is the elementary charge.…”

“…The analysis of the spectroscopic data, systematic frequency shifts, and the results are discussed in Sect. 4, followed by the conclusions in Sect. 5.…”

“…Because of their relative simplicity, molecular hydrogen ions such as H + 2 and HD + are benchmark systems for molecular theory [1,2], and suitable probes of fundamental physical models [3,4]. Already four decades ago, Wing et al [5] performed measurements of ro-vibrational transitions in HD + and conjectured that such measurements could be used to test quantum electrodynamics (QED) theory in molecules and lead to an improved value of the proton-to-electron mass ratio, μ.…”

“…In this article, we present the result of a high-precision frequency measurement of the ro-vibrational transition (v, L):(0, 2)→ (8,3) in the HD + molecule and compare it with state-of-the-art molecular theory to find excellent agreement. From this comparison, we subsequently derive new constraints on the size of effects due to possible new physics (in the form of hypothetical fifth forces or compactified higher dimensions [3,4,12]) in HD + , and we determine a value of μ for the first time from a molecular system [12].…”