Nuclear Physics and the Fundamental Constants of Nature

S.R. Beane and M.J. Savage

An effective field theory with consistent power-counting now exists for nuclear processes involving momentum $p\hspace*{0.2em}\raisebox{0.5ex}{$<$} \hspace{-0.8em}\raisebox{-0.3em}{$\sim$}\hspace*{0.2em}300 {\rm MeV}$ [12], which allows one to perform systematic calculations of some nuclear observables. We used it to compute the leading light quark mass, $m_q$, dependence of observables in the two-nucleon sector, which is a fundamental aspect of strong interaction physics. Partial motivation for this work was the experimental hint that the fundamental constants of nature are time dependent. If this proves to be the case, the predictions of Big Bang Nucleosynthesis (BBN) will differ from present calculations which assume time-independent constants. In order to address BBN in this scenario one needs to know how nuclei and nuclear processes depend upon the constants, including the light-quark masses. We were able to make rigorous predictions for the quark-mass dependence of the deuteron binding energy and the scattering length in the ${}^1\kern -.14em S_0$-channel [13]. It is interesting to note that BBSvK counting [12] allowed us to derive an analytic expression for the ${}^1\kern -.14em S_0$ scattering length as a function of $m_q$. There are uncertainties in the calculations arising from local four-nucleon $m_q$-dependent interactions and from uncertainties in the pion-nucleon interaction in the single nucleon sector. It is hoped that the four-nucleon $m_q$-dependent interactions will be determined in lattice simulations at some point in the future, and that higher precision experiments and calculations will reduce the uncertainty arising from the single nucleon sector.

Figure 1: The left (right) panel shows the scattering length in the ${}^1\kern -.14em S_0$-channel ( ${}^3\kern -.14em S_1$-channel) as a function of the pion mass. The light gray region corresponds to $\eta =1/5$ and the black region corresponds to $\eta =1/15$. In the ${}^3\kern -.14em S_1$-channel the parameter $\overline {d}_{16}$ is taken to be in the interval $-2.61 {\rm GeV}^{-2} < \overline{d}_{16} < -0.17 {\rm GeV}^{-2}$ and $\overline{d}_{18}=-0.51 {\rm GeV}^{-2}$.