Charge symmetry breaking of the nucleon-nucleon interaction: ρ-ω mixing versus nucleon mass splitting

We investigate three models for the charge symmetry breaking (CSB) of the nucleon-nucleon (NN) interaction (based upon ρ-ω mixing, nucleon mass splitting, and phenomenology) that all reproduce the empirical value for the CSB of the ¹S₀ scattering length (Δa_CSB) accurately. We reveal that these models make very different predictions for CSB in ³P_J waves and examine the impact of this on some observable quantities of A>=3 nuclear systems. It turns out that the ³H-³He binding energy difference is essentially ruled by Δa_CSB and not very sensitive to CSB from P waves. However, the Coulomb displacement energies (which are the subject of the Nolen-Schiffer anomaly) receive about 50% of their CSB contribution from NN partial waves beyond ¹S₀. Consequently, the predictions by the various CSB models differ here substantially (10%-20%). Unfortunately, the evaluation of the leading Coulomb contributions carries a large uncertainty such that no discrimination between the competing CSB models can presently be made. To decide the issue we suggest looking into nuclear few-body reactions that are sensitive to CSB of the nuclear force.