Time-Reversal-Invariance Violation in the $Nd$ System and Large-$N_C$

Abstract

A minimal set of five low energy constants (LECs) for time-reversal and parity violating ($/T/P$) nucleon-nucleon ($NN$) interactions at low energies ($E<m_{\pi }^2/M_N$) is given. Using a large-$N_C$ (number of colors in QCD) analysis we show that one linear combination of LECs is $\mathcal{O}(N_C)$, three LECs are $\mathcal{O}(N_C^0)$, and one linear combination of LECs is $\mathcal{O}(N_C^{-1})$. We also calculate the $/T/P$ observables of neutron spin rotation through a polarized deuteron target and a spin correlation coefficient in nucleon-deuteron scattering using pionless effective field theory. Using the large-$N_C$ analysis we show that the spin correlation coefficient and the neutron spin rotation are predominantly determined by same two LECs in the large-$N_C$ basis.

Comments: 22 pages, 3 figures