Apparently noninvariant terms of U(N)×U(N)U(N)\times U(N) nonlinear sigma model in the one-loop approximation

We show how the Apparently Noninvariant Terms (ANTs), which emerge in perturbation theory of nonlinear sigma models, are consistent with the nonlinearly realized symmetry by employing the Ward-Takahashi identity (in the form of an inhomogeneous Zinn-Justin equation). In the literature the discussions on ANTs are confined to the SU(2) case. We generalize them to the U(N) case and demonstrate explicitly at the one-loop level that despite the presence of divergent ANTs in the effective action of the "pions", the symmetry is preserved.Comment: two paragraphs added in Introduction, typos in Eqs. fixe

More about the Wilsonian analysis on the pionless NEFT

We extend our Wilsonian renormalization group (RG) analysis on the pionless nuclear effective theory (NEFT) in the two-nucleon sector in two ways; on the one hand, (1) we enlarge the space of operators up to including those of $\mathcal{O}(p^4)$ in the $S$ waves, and, on the other hand, (2) we consider the RG flows in higher partial waves ($P$ and $D$ waves). In the larger space calculations, we find, in addition to nontrivial fixed points, two ``fixed lines'' and a ``fixed surface'' which are related to marginal operators. In the higher partial wave calculations, we find similar phase structures to that of the $S$ waves, but there are \textit{two} relevant directions in the $P$ waves at the nontrivial fixed points and \textit{three} in the $D$ waves. We explain the physical meaning of the $P$-wave phase structure by explicitly calculating the low-energy scattering amplitude. We also discuss the relation between the Legendre flow equation which we employ and the RG equation by Birse, McGovern, and Richardson, and possible implementation of Power Divergence Subtraction (PDS) in higher partial waves.Comment: 39 pages, 5 figures, the final versio

Polarity in Bending Deformation in InSb Crystals : II. Theory and Supplementary Experiments(Physics)

A geometrical consideration of the configuration of {111} tetrahedra in a bent crystal having the sphalerite structure shows that the type of bending is reversed between the primary slip plane and some of the secondary slip planes. This explains why the secondary slip is activated and the primary slip plane becomes forest-rich in β-bending. Two types of experiments establish the origin of the higher flow stress in β-bending compared with α-bending. It is concluded that the difference in the flow stress between the two types of bending in the deformation stage after the lower yield point originates mainly from the difference in the activity of the secondary slip system, while that in the early stage of deformation originates from the difference in the rate of increase in the density of screw dislocations due to the difference in the mobility between α-dislocations and β-dislocations moving on the primary slip plane

Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons

Low-energy effective field theory describing a nonrelativistic three-body system is analyzed in the Wilsonian renormalization group (RG) method. No effective auxiliary field (dimeron) that corresponds to two-body propagation is introduced. The Efimov effect is expected in the case of an infinite two-body scattering length, and is believed to be related to the limit cycle behavior in the three-body renormalization group equations (RGEs). If the one-loop property of the RGEs for the nonrelativistic system without the dimeron field, which is essential in deriving RGEs in the two-body sector, persists in the three-body sector, it appears to prevent the emergence of limit cycle behavior. We explain how the multi-loop diagrams contribute in the three-body sector without contradicting the one-loop property of the RGEs, and derive the correct RGEs, which lead to the limit cycle behavior. The Efimov parameter, $s_{0}$, is obtained within a few percent error in the leading orders. We also remark on the correct use of the dimeron formulation. We find rich RG-flow structure in the three-body sector. In particular, a novel nontrivial fixed point of the three-body couplings is found when the two-body interactions are absent. We also find, on the two-body nontrivial fixed point, the limit cycle is realized as a loop of finite size in the space of three-body coupling constants when terms with derivatives are included.Comment: 19 pages, 28 figures, one section added with three figure

Interstellar Extinction Law toward the Galactic Center II: V, J, H, and Ks Bands

We have determined the ratios of total to selective extinction directly from observations in the optical V band and near-infrared J band toward the Galactic center. The OGLE (Optical Gravitational Lensing Experiment) Galactic bulge fields have been observed with the SIRIUS camera on the IRSF telescope, and we obtain A(V)/E(V-J)=1.251+-0.014 and A(J)/E(V-J)=0.225+-0.007. From these ratios, we have derived A(J)/A(V) = 0.188+-0.005; if we combine A(J)/A(V) with the near-infrared extinction ratios obtained by Nishiyama et al. for more reddened fields near the Galactic center, we get A(V) : A(J) : A(H) : A(Ks) = 1 : 0.188 : 0.108 : 0.062, which implies steeply declining extinction toward the longer wavelengths. In particular, it is striking that the Ks band extinction is \approx 1/16 of the visual extinction A(V) much smaller than one tenth of A(V) so far employed.Comment: 8 pages, 7 figures, Accepted for publication in Ap

Polarity in Bending Deformation of InSb Crystals : I. Experiments(Physics)

Deformation characteristics of InSb crystals subjected to α-bending or β-bending are observed as a function of the strain rate and the temperature. Difference in the characteristics between the two types of bending is demonstrated. Higher flow stresses are observed in β-bending as compared with α-bending. No difference is found between the two types of bending in the magnitudes of parameters which characterize the strain rate and the temperature sensitivities of the yield stresses. Observations on slip bands as well as those of dislocation etch-pits show that dislocations on the secondary slip system are activated in β-bending. It is suggested that this is the cause of the observed higher flow stresses. It is shown that the motion of screw dislocations of the primary slip system controls the deformation rate in both types of bending