Physics beyond the Standard Model from hydrogen spectroscopy

Abstract

Spectroscopy of hydrogen can be used for a search into physics beyond the Standard Model. Differences between the absorption spectra of the Lyman and Werner bands of H 2 as observed at high redshift and those measured in the laboratory can be interpreted in terms of possible variations of the proton-electron mass ratio µ = m p /m e over cosmological history. Investigation of some ten of such absorbers in the redshift range z = 2.0 − 4.2 yields a constraint of |∆µ/µ| < 5 × 10 −6 at 3σ. Observation of H 2 from the photospheres of white dwarf stars inside our Galaxy delivers a constraint of similar magnitude on a dependence of µ on a gravitational potential 10 4 times as strong as on the Earth's surface. While such astronomical studies aim at finding quintessence in an indirect manner, laboratory precision measurements target such additional quantum fields in a direct manner. Laser-based precision measurements of dissociation energies, vibrational splittings and rotational level energies in H 2 molecules and their deuterated isotopomers HD and D 2 produce values for the rovibrational binding energies fully consistent with quantum ab initio calculations including relativistic and quantum electrodynamical (QED) effects. Similarly, precision measurements of high-overtone vibrational transitions of HD + ions, captured in ion traps and sympathetically cooled to mK temperatures, also result in transition frequencies fully consistent with calculations including QED corrections. Precision measurements of inter-Rydberg transitions in H 2 can be extrapolated to yield accurate values for level splittings in the H + 2 -ion. These comprehensive results of laboratory precision measurements on neutral and ionic hydrogen molecules can be interpreted to set bounds on the existence of possible fifth forces and of higher dimensions, phenomena describing physics beyond the Standard Model.

Do extra compactified dimensions of space cause a substructure underlying the expected eigenstates of a molecule?

“…This is setting the upper bound R c <10 −3 μm on the compactification radius R c . This result lowers the upper bound for the compactification radius R c considerably compared to the value R c <0.6 μm reported in [19]. But contrary to the discussion in [19], the model proposed in the present paper does not specify the number n e of the extra dimensions.…”

“…This result lowers the upper bound for the compactification radius R c considerably compared to the value R c <0.6 μm reported in [19]. But contrary to the discussion in [19], the model proposed in the present paper does not specify the number n e of the extra dimensions. As R c depends on the number n e of the extra dimensions, it may be possible to evaluate n e from the result R c <10 −3 μm.…”

“…The ADD-model was applied to diatomic molecules to study the gravitational force between the nuclei in the molecule due to the extra-dimensional gravitational potential suggested by the ADD-model [18,19]. The authors analysed the contribution of the gravitational potential to the splitting of vibrational levels in the HD + ion by combining precision measurements and calculations on the HD + ion.…”

“…The strength of the gravitational potential depends on both R c and n e . The investigations in [19] are setting the upper bound R c <0.6 μm on the compactification radius for the case of n e =7 extra dimensions. This number of extra dimensions is relevant to M-theory.…”

Bounding quantum dark forces

“…Certain of these results have recently been used to bound short distance modifications of gravity, see Refs. [5,[50][51][52].…”