Parity-Violating Neutron Spin Rotation in Hydrogen and Deuterium and the Predictive Power of EFT

One of the least-explored sectors of the Standard Model is the weak part of the nuclear force. Experiments on hadronic parity-violation (PV) at low energies require one comprehensive theoretical framework with reliable error-estimates to: check data consistency; subtract binding effects; and extract the PV interaction strengths. ``Pion-less'' Effective Field Theory is such a method with minimal theoretical bias. Different PV parameters are probed in $np$ and $nd$ spin rotation. Using na\"ive dimensional analysis, the signal for standard target densities is $\left|\frac{\mathrm{d} \phi_{\mathrm{PV}}}{\mathrm{d} l}\right|\approx [10^{-7}\cdots10^{-6}]\frac{\mathrm{rad}}{\mathrm{m}} $. An estimate of the numerical and systematic uncertainties of our calculations indicates excellent convergence. We also show that PV 3-nucleon interactions are suppressed in the $nd$-system, despite the non-perturbative renormalisation of parity-conserving 3-nucleon interactions. Therefore, few-nucleon experiments can dis-entangle PV 2-nucleon interactions at the 10\%-level without introducing new unknowns.\\[4pt] [1] H. W. Grie{\ss}hammer, M. R. Schindler and R. P. Springer, Eur. Phys. J. A 48 (2012) 7. \newline [2] H. W. Grie{\ss}hammer and M. R. Schindler, Eur. Phys. J. A 46 (2010) 73