The chiral SUð3Þ Lagrangian with charmed baryons of spin J P ¼ 1=2 þ and J P ¼ 3=2 þ is analyzed. We consider all counterterms that are relevant at next-to-next-to-next-to-leading order (N 3 LO) in a chiral extrapolation of the charmed baryon masses. At N 2 LO we find 16 low-energy parameters. There are three mass parameters for the antitriplet and the two sextet baryons, six parameters describing the mesonbaryon vertices and seven symmetry breaking parameters. The heavy-quark spin symmetry predicts four sum rules for the meson-baryon vertices and degenerate masses for the two baryon sextet fields. Here a large-N c operator analysis at next-to-leading order (NLO) suggests the relevance of one further spin-symmetry breaking parameter. Going from N 2 LO to N 3 LO adds 53 ¼ 17 þ 36 parameters. For the leading symmetry conserving two-body counterterms involving two baryon fields and two Goldstone boson fields we find 36 terms. While the heavy-quark spin symmetry leads to 36 − 16 ¼ 20 sum rules, an expansion in 1=N c at NLO generates 36 − 7 ¼ 29 parameter relations. A combined expansion leaves six unknown parameters only. For the symmetry breaking counterterms we find 17 terms, for which there are 17 − 9 ¼ 8 sum rules from the heavy-quark spin symmetry and 17 − 5 ¼ 12 sum rules from a 1=N c expansion at NLO.

We consider a dynamical system of phantom scalar field under exponential potential in background of loop quantum cosmology. In our analysis, there is neither stable node nor repeller unstable node but only two saddle points, hence no Big Rip singularity. Physical solutions always possess potential energy greater than magnitude of the negative kinetic energy. We found that the universe bounces after accelerating even in the domination of the phantom field. After bouncing, the universe finally enters oscillatory regime.Comment: 8 pages, 6 figures, Revtex 4, Figures and References added. Version accepted by Physical Review D1

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...