Defining the Nambu--Jona-Lasinio Model by Higher Derivative Kinetic Term

Usual treatment of the Nambu--Jona-Lasinio (NJL) model using loop momentum cutoff suffers from ambiguities in choosing the loop momenta to be cut off and violation of (external) gauge invariance. We define the NJL model from the starting Lagrangian level by using a higher derivative fermion kinetic term with a cutoff parameter $\Lambda$. This definition is free from such ambiguities and manifestly keeps the chiral symmetry as well as the gauge invariance. Quantization of this higher derivative system, current operators and calculational method are discussed in some detail. Calculating the pion decay constant and $\pi^0\rightarrow 2\gamma$ decay amplitude, we explicitly demonstrate that the low energy theorem holds. It is observed that the NJL mass relation $m_\sigma = 2 m_0$ between the $\sigma$ meson and fermion masses no longer holds in this model. We also present a simplified calculational method which is valid when the cutoff parameter $\Lambda$ is much larger than the energy scale of physics.Comment: 31 pages, phyzzx, 3 uuencoded epsf figures, KUNS-126

Evolution of cosmological perturbations in a stage dominated by an oscillatory scalar field

In the investigation of the evolution of cosmological perturbations in inflationary universe models the behavior of perturbations during the reheating stage is the most unclear point. In particular in the early reheating phase in which a rapidly oscillating scalar field dominates the energy density, the behavior of perturbations are not known well because their evolution equation expressed in terms of the curvature perturbation becomes singular. In this paper it is shown that in spite of this singular behavior of the evolution equation the Bardeen parameter stays constant in a good accuracy during this stage for superhorizon-scale perturbations except for a sequence of negligibly short intervals around the zero points of the time derivative of the scalar field. This justifies the conventional formula relating the amplitudes of quantum fluctuations during inflation and those of adiabatic perturbations at horizon crossing in the Friedmann stage, except for possible corrections produced by the energy transfer from the scalar field to radiation in the late stage of reheating. It is further shown that outside the above sequence of time intervals the behavior of the perturbations coincides in a good accuracy with that for a perfect fluid system obtained from the original scalar field system by the WKB approximation and a spacetime averaging over a Hubble horizon scale.Comment: Revised version, 23 pages, no figure, plain LaTeX, minor errors in some equations are corrected, no change in the main results and the conclusio

Manifestly gauge invariant theory of the nonlinear cosmological perturbations in the leading order of the gradient expansion

In the full nonlinear cosmological perturbation theory in the leading order of the gradient expansion, all the types of the gauge invariant perturbation variables are defined. The metric junction conditions across the spacelike transition hypersurface are formulated in a manifestly gauge invariant manner. It is manifestly shown that all the physical laws such as the evolution equations, the constraint equations, and the junction conditions can be written using the gauge invariant variables which we defined only. Based on the existence of the universal adiabatic growing mode in the nonlinear perturbation theory and the $\rho$ philosophy where the physical evolution are described using the energy density $\rho$ as the evolution parameter, we give the definitions of the adiabatic perturbation variable and the entropic perturbation variables in the full nonlinear perturbation theory. In order to give the analytic order estimate of the nonlinear parameter $f_{NL}$, we present the exponent evaluation method. As the models where $f_{NL}$ changes continuously and becomes large, using the $\rho$ philosophy, we investigate the non-Gaussianity induced by the entropic perturbation of the component which does not govern the cosmic energy density, and we show that in order to obtain the significant non-Gaussianity it is necessary that the scalar field which supports the entropic perturbation is extremely small compared with the scalar field which supports the adiabatic perturbation

Long wavelength limit of evolution of nonlinear cosmological perturbations

In the general matter composition where the multiple scalar fields and the multiple perfect fluids coexist, in the leading order of the gradient expansion, we construct all of the solutions of the nonlinear evolutions of the locally homogeneous universe. From the momentum constraint, we derive the constraints which the solution constants of the locally homogeneous universe must satisfy. We construct the gauge invariant perturbation variables in the arbitrarily higher order nonlinear cosmological perturbation theory around the spatially flat Friedmann-Robertson-Walker universe. We construct the nonlinear long wavelength limit formula representing the long wavelength limit of the evolution of the nonlinear gauge invariant perturbation variables in terms of perturbations of the evolutions of the locally homogeneous universe. By using the long wavelength limit formula, we investigate the evolution of nonlinear cosmological perturbations in the universe dominated by the multiple slow rolling scalar fields with an arbitrary potential. The tau function and the N potential introduced in this paper make it possible to write the evolution of the multiple slow rolling scalar fields with an arbitrary interaction potential and the arbitrarily higher order nonlinear Bardeen parameter at the end of the slow rolling phase analytically. It is shown that the nonlinear parameters such as fNL and gNL are suppressed by the slow rolling expansion parameters

Evolution of Cosmological Perturbations in the Long Wavelength Limit

The relation between the long wavelength limit of solutions to the cosmological perturbation equations and the perturbations of solutions to the exactly homogeneous background equations is investigated for scalar perturbations on spatially flat cosmological models. It is shown that a homogeneous perturbation coincides with the long wavelength limit of some inhomogeneous perturbation only when the former satisfies an additional condition corresponding to the momentum constraint if the matter consists only of scalar fields. In contrast, no such constraint appears if the fundamental variables describing the matter contain a vector field as in the case of a fluid. Further, as a byproduct of this general analysis, it is shown that there exist two universal exact solutions to the perturbation equations in the long wavelength limit, which are expressed only in terms of the background quantities. They represent adiabatic growing and decaying modes, and correspond to the well-known exact solutions for perfect fluid systems and scalar field systems.Comment: 16 pages, no figure, submitted to PR

Long wavelength limit of evolution of cosmological perturbations in the universe where scalar fields and fluids coexist

We present the LWL formula which represents the long wavelengh limit of the solutions of evolution equations of cosmological perturbations in terms of the exactly homogeneous solutions in the most general case where multiple scalar fields and multiple perfect fluids coexist. We find the conserved quantity which has origin in the adiabatic decaying mode, and by regarding this quantity as the source term we determine the correction term which corrects the discrepancy between the exactly homogeneous perturbations and the $k \to 0$ limit of the evolutions of cosmological perturbations. This LWL formula is useful for investigating the evolutions of cosmological perturbations in the early stage of our universe such as reheating after inflation and the curvaton decay in the curvaton scenario. When we extract the long wavelength limits of evolutions of cosmological perturbations from the exactly homogeneos perturbations by the LWL formula, it is more convenient to describe the corresponding exactly homogeneous system with not the cosmological time but the scale factor as the evolution parameter. By applying the LWL formula to the reheating model and the curvaton model with multiple scalar fields and multiple radiation fluids, we obtain the S formula representing the final amplitude of the Bardeen parameter in terms of the initial adiabatic and isocurvature perturbations Keywords:cosmological perturbations,long wavelength limit,reheating,curvaton PACS number(s):98.80.CqComment: Page:4

Evolution of Cosmological Perturbations in the Universe dominated by Multiple Scalar Fields

By efforts of several authors, it is recently established that the dynamical behavior of the cosmological perturbation on superhorizon scales is well approximated in terms of that in the long wavelength limit, and the latter can be constructed from the evolution of corresponding exactly homogeneous universe. Using these facts, we investigate the evolution of the cosmological perturbation on superhorizon scales in the universe dominated by oscillating multiple scalar fields which are generally interacting with each other, and the ratio of whose masses is incommensurable. Since the scalar fields oscillate rapidly around the local minimum of the potential, we use the action angle variables. We found that this problem can be formulated as the canonical perturbation theory in which the perturbed part appearing as the result of the expansion of the universe and the interaction of the scalar fields is bounded by the negative power ot time. We show that by constructing the canonical transformations properly, the transformed hamiltonian becomes simple enough to be solved. As the result of the invetigation using the long wavelength limit and the canonical perturbation theory, under the sufficiently general conditions, we prove that for the adiabatic growing mode the Bardeen parameter stays constant and that for all the other modes the Bardeen parameter decays. From the viewpoint of the ergodic theory, it is discussed that as for the Bardeen parameter, the sigularities appear probabilistically. This analysis serves the understanding of the evolution of the cosmological perturbations on superhorizon scales during reheating.Comment: 31 Pages; Latex, No figure

Human bone marrow VCAM-1+ macrophages provide a niche for reactive and neoplastic erythropoiesis

Resident bone marrow macrophages provide a microenvironment for erythropoiesis, forming erythroblastic islands (EBIs) via adhesion molecules. In this study, we examined vascular cell adhesion molecule-1 (VCAM-1) expression in human bone marrow specimens using immunohistochemistry. VCAM-1 was strongly expressed in CD169+ macrophages in EBIs and weakly in sinusoidal vascular endothelial cells. In reactive erythropoiesis, including hemolytic and megaloblastic anemia, the extended cytoplasm of VCAM-1+ CD169+ macrophages circumscribed the erythroid cells. The strong affinity between VCAM-1+ macrophages and erythroid cells was also observed in polycythemia vera (PV), essential thrombocythemia (ET), and chronic myelogenous leukemia (CML). VCAM-1 density was significantly higher in PV than in ET and CML (p < 0.001), and correlated with blood erythrocyte count in all three neoplasms (p < 0.001). In ET, the VCAM-1 density was higher in cases with the JAK2 mutation than with the CALR mutation. In myelodysplastic syndrome with erythroid predominance but unclear EBI formation, punctate VCAM-1+ cytoplasmic processes of macrophages were seen between erythroblasts, similar to those seen between granulocytic precursors in CML, suggesting incomplete contact of VCAM-1+ macrophages with dysplastic erythroid cells. These results suggest that VCAM-1+ macrophages create a niche for reactive and neoplastic erythropoiesis and may be a therapeutic target in PV

ダイガクセイ ノ ソイネ ニ タイスル イメージ ト オモイデ ニ ツイテ : テキスト マイニング ホウ オ モチイテ

It aimed at conducting detailed analysis for the text by free description about the image and recollections to co−sleeping using text−mining method in this research. Question paper investigation was conducted for a total of 424 college students, and graduate students. When the portion of the free description about the image of co−sleeping and the recollections of co−sleeping was analyzed by text−mining method, five image groups have been surveyed greatly. Physical comfort and mental comfort were suggested from the image group of co−sleeping. From the recollections group of co−sleeping, it was suggested that co−sleeping is one of the communications of the parent and child at the time of sleeping. In the position of co−sleeping, a negative word was hardly looked at by the image of co−sleeping also at recollections about those who were doing co−sleeping “next to the mother”, either