The parity-violating nucleon-nucleon force in the 1/N_c expansion

Abstract

Several experimental investigations have observed parity violation in nuclear systems-a consequence of the weak force between quarks. We apply the $1/N_c$ expansion of QCD to the P-violating T-conserving component of the nucleon-nucleon (NN) potential. We show there are two leading-order operators, both of which affect $\vec{p}p$ scattering at order $N_c$. We find an additional four operators at $O(N_c^0{\sin }^2{\theta }_W)$ and six at $O(1/N_c)$. Pion exchange in the PV NN force is suppressed by $1/N_c$ and ${\sin }^2{\theta }_W$, providing a quantitative explanation for its non-observation up to this time. The large-$N_c$ hierarchy of other PV NN force mechanisms is consistent with estimates of the couplings in phenomenological models. The PV observed in $\vec{p}p$ scattering data is compatible with natural values for the strong and weak coupling constants: there is no evidence of fine tuning.

5 pages, 2 figures. New version accepted for publication in Physical Review Letters. It incorporates responses to referee comments and has been cut to comply with the PRL length limit

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• Fundamental Neutron Physics: a White Paper on Progress and Prospects in the US