Parity-Violating Three Nucleon Interactions at Low Energies and Large-$N_C$

Abstract

The parity-violating (PV) nucleon-nucleon ($NN$) interaction in the three-nucleon system is investigated using pionless effective field theory ($\mathrm{EFT}(/\pi )$). This work shows that a next-to-leading order (NLO) PV three-body force is necessary in contradiction with a previous claim [Griesshammer and Schindler in Eur. Phys. J. A 46, 73 (2010)]. Including three-body $P$ to $D$-wave transitions PV three-nucleon observables are calculated to higher energies than previously considered. Using the recent large-$N_C$ analysis of the PV $NN$ interaction in $\mathrm{EFT}(/\pi )$ the current understanding of low energy PV few-body measurements is reassessed. The recent measurement of the asymmetry $A_{\gamma }$ in $\vec{n}p\to d\gamma$ from the NPDGamma collaboration [D. Blyth et al. (NPDGamma), Phys. Rev. Lett. 121, 242002 (2018)], gives the value $g_4^{(N_C^{-1})}=(-1.4\pm 0.63(stat.)\pm 0.09(syst.))\times 10^{-10}{\mathrm{MeV}}^{-1}$ for a next-to-next-to-leading order (N${}^2$LO) in large-$N_C$ low energy constant (LEC). Using the large-$N_C$ hierarchy of LECs the sizes of the leading order (LO) in large-$N_C$ LECs are estimated using an experimental bound on a parity violating asymmetry in $\vec{p}d$ scattering at $E_{\mathrm{lab}}=15$ MeV and a measurement of $\overrightarrow{pp}$ scattering at $E_{\mathrm{lab}}=13.6$ MeV. Comparing the size of the resulting LO in large-$N_C$ LECs to the N${}^2$LO in large-$N_C$ LEC $g_4^{(N_C^{-1})}$ shows they are roughly the same size in contradiction with current large-$N_C$ counting.

Comments: fixed typos, updated references