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The spectroscopy of molecular 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 $\mu=m_p/m_e$ over cosmological history. Investigation of some ten of such absorbers in the redshift range $z= 2.0-4.2$ yields a constraint of $|\Delta\mu/\mu|< 5 \times 10^{-6}$ at 3$\sigma$, as was recently reported in a review [1]. Observation of H$_2$ from the photospheres of white dwarf stars inside our Galaxy delivers a constraint of similar magnitude on a dependence of $\mu$ on a gravitational potential $10^4$ times as strong as on the Earth's surface [2].
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 [3]. Similarly, precision measurements of high-overtone vibrational transitions of HD$^+$ ions, also result in transition frequencies fully consistent with calculations including QED corrections [4].
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 [5] and of higher dimensions [6], phenomena describing physics beyond the Standard Model.
[1] W. Ubachs, J. Bagdonaite, E.J. Salumbides, M.T. Murphy, L. Kaper, Rev. Mod. Phys. 88, 021003 (2016).
[2] J. Bagdonaite, E.J. Salumbides, S.P. Preval, M.A. Barstow, J.D. Barrow, M.T. Murphy, W. Ubachs, Phys. Rev. Lett. 113, 123002 (2014).
[3] W. Ubachs, J.C.J. Koelemeij, K.S.E. Eikema, E.J. Salumbides, J. Mol. Spectr. 320, 1 (2016).
[4] J. Biesheuvel, J.-Ph. Karr, L. Hilico, K.S.E. Eikema, W. Ubachs, J.C.J. Koelemeij, Nat. Comm. 7, 10385 (2016).
[5] E.J. Salumbides, J.C.J. Koelemeij, J. Komasa, K. Pachucki, K.S.E. Eikema, W. Ubachs,
Phys. Rev. D87, 112008 (2013).
[6] E.J. Salumbides, A.N. Schellekens, B. Gato-Rivera, W. Ubachs, New. J. Phys. 17, 033015 (2015).
