Parity-Violating Nucleon-Nucleon Force in the1/NcExpansion

Abstract

Several experimental investigations have observed parity violation in nuclear systems-a consequence of the weak force between quarks. We apply the 1/Nc expansion of QCD to the P-violating T-conserving component of the nucleon-nucleon (NN) potential. We show there are two leadingorder operators, both of which affect pp scattering at order Nc. We find an additional four operators at order N 0 c sin 2 θW and six at O(1/Nc). Pion exchange in the PV NN force is suppressed by 1/Nc and sin 2 θW , providing a quantitative explanation for its non-observation up to this time. The large-Nc hierarchy of other PV NN force mechanisms is consistent with estimates of the couplings in phenomenological models. The PV observed in pp scattering data is compatible with natural values for the strong and weak coupling constants: there is no evidence of fine tuning. The strong-nuclear and electromagnetic forces play the most prominent role in proton-proton (pp) scattering. There are also parity-violating (PV) pp interactions, which manifest the presence of weak interactions between the quarks inside each proton. Measurements of longitudinal beam asymmetries ∼ 10 and TRIUMF [3] demonstrate that PV nucleon-nucleon (NN) forces exist. PV in NN systems is also probed via an asymmetry in the reaction np → dγ [4,5]. And ab initio calculations of few-nucleon systems allow us to take models of the PV NN force and predict, e.g., the longitudinal asymmetry in 3 He( n, p) 3 H [6], which is soon to be measured [7]. Nuclear parity violation is also observed in, e.g., the radiative decay of the first excited state of 19 F, but there theoretical uncertainties in the relationship between the observable and the model of the PV NN force are harder to quantify. Much work has gone into constraining the PV NN force from a variety of nuclear experiments, see Refs. [8,9] for recent reviews.The prevailing paradigm in such analyses is based on single-meson exchange between nucleons, most commonly in the framework developed by Desplanques, Donoghue, and Holstein (DDH) [10]. The quantum numbers of the exchanged mesons determine the operator structures that contribute, while operator coefficients involve products of strong and weak meson-nucleonnucleon coupling constants. In this paper we show that Standard Model (SM) couplings and the 1/N c expansion of QCD predict the operators, and the sizes of the associated coefficients, which appear in the PV NN potential.An alternative framework-suitable for studying PV at very low energies-that systematizes pioneering studies [11,12] has recently emerged [13][14][15], but has, as yet, been applied to far fewer experiments. The extension of chiral perturbation theory to few-nucleon systems, χEFT [16] has also been invoked [17][18][19][20][21]. In χEFT the one-pion-exchange piece of the PV NN force dominates, with all other effects suppressed by two orders in the chiral expansion.One-pion exchange gives the long-distance parityconserving potential, and drives many of the properties of light nuclei. But, thus far, experiment...

Time-reversal-invariance-violating nucleon-nucleon potential in the1/Ncexpansion

“…In both cases first corrections are suppressed by a single power of 1/N c . However, to the order we considered, the expansion in a given isospin sector is in 1/N 2 c , as it is in the TCPV and TCPC cases [25]. In terms of a meson-exchange picture, the LO in N c TVPV potential corresponds to π and ω exchanges.…”

“…There pion exchange constitutes the sole LO contribution to the potential in the chiral counting, but the analysis of Ref. [25] shows it is actually suppressed by sin 2 θ W /N c compared to other mechanisms.…”

“…This prevents spurious factors of m N ∼ N c from appearing in the expression for the potentials; see Ref. [25] for an analogous discussion for the TCPV case. The TVPV potential derived from these Lagrangians is given in Refs.…”

“…Now, using the known large-N c scalings of the strong couplings, it is possible to determine the constraints that the large-N c analysis places on the TVPV meson-nucleon couplings. The N c scaling of the strong couplings is [23,25,28] …”

“…The large-N c analysis was first applied to the TCPC NN potential in Refs. [22,23], and more recently to three-nucleon forces [24] and to the TCPV potential [25,26]. The large-N c expansion analysis allows us to capture dominant QCD effects of embedding the fundamental TV interactions in the nonperturbative environment of the nucleon.…”