Abstract
It has been customary to use data from the Oklo natural nuclear reactor to place bounds on the change that has occurred in the electromagnetic fine structure constant α over the last 2 billion years. Alternatively, an analysis could be based on a recently proposed expression for shifts in resonance energies which relates them to changes in both α and the average m q of the u and d current quark masses, and which makes explicit the dependence on mass number A and atomic number Z. (Recent model independent results on hadronic \({\sigma}\)-terms suggest sensitivity to the strange quark mass is negligible.) The most sophisticated analysis, to date, of the quark mass term invokes a calculation of the nuclear mean-field within the Walecka model of quantum hadrodynamics. We comment on this study and consider an alternative in which the link to low-energy quantum chromodynamics and its pattern of chiral symmetry-breaking is more readily discernible. Specifically, we investigate the sensitivity to changes in the pion mass \({M_\pi}\) of a single nucleon potential determined by an in-medium chiral perturbation theory (\({\chi}\)PT) calculation which includes virtual \({{\Delta}}\)-excitations. Subject to some reasonable assumptions about low-energy constants, we confirm that the m q -contribution to resonance shifts is enhanced by a factor of 10 or so relative to the \({\alpha}\)-term and deduce that the Oklo data for Sm imply that \({|m_q({\rm Oklo})- m_q({\rm now})| \lesssim 10^{-9}m_q({\rm now})}\).
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Davis, E.D. Implications of the Oklo Phenomenon in a Chiral Approach to Nuclear Matter. Few-Body Syst 56, 431–437 (2015). https://doi.org/10.1007/s00601-014-0909-0
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DOI: https://doi.org/10.1007/s00601-014-0909-0