Implications of the Oklo phenomenon in a chiral approach to nuclear matter [CL]

http://arxiv.org/abs/1406.7394


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 $\alpha$ 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 $\alpha$ 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 (QCD) 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 $\mathrm{\Delta}$-excitations. Subject to some reasonable assumptions about low-energy constants (LECs), 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 $|m_q(\mathrm{Oklo})- m_q(\mathrm{now})| \lesssim 10^{-9}m_q(\mathrm{now})$.

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E. Davis
Tue, 1 Jul 14
27/70

Comments: 11 pages, contribution to Light Cone 2014, Raleigh, North Carolina, USA (May 26-30), submitted to Few-Body Systems