Gradient flow and the renormalization group

We investigate the renormalization group (RG) structure of the gradient flow. Instead of using the original bare action to generate the flow, we propose to use the effective action at each flow time. We write down the basic equation for scalar field theory that determines the evolution of the action, and argue that the equation can be regarded as a RG equation if one makes a field-variable transformation at every step such that the kinetic term is kept to take the canonical form. We consider a local potential approximation (LPA) to our equation, and show that the result has a natural interpretation with Feynman diagrams. We make an $\varepsilon$ expansion of the LPA and show that it reproduces the eigenvalues of the linearized RG transformation around both the Gaussian and the Wilson-Fisher fixed points to the order of $\varepsilon$.Comment: 11 pages, 1 figure; v2, v3: typos corrected, some discussions improve

Studies on the Wear Resisting Properties of Spheroidal Graphite Cast Steel Having Various Matrices

On dry abrasion, the wear resisting properties of the spheroidal graphite cast steel having various matrices which were obtained by different heat-treatments such as normalizing, oil quenching and tempering have been studied. The upper specimens have various heat treated matrices and the lower specimen has the normalizing structure, The results obtained can be summarized as follows : 1. Surface hardness after abrasion showed the difference by each of the matrices, but it had a tendency to attain constant value along with the increase of running distance. 2. Although the surface of specimens was adjusted constant by mechanical finishing before wearing test, surface roughness approached to the characteristic curves in each combination of matrices between upper and lower specimens. 3. The lustrous degenerative layer as seen samples tempered at low temperature was produced by physical factors such as work hardening and tempering effects. 4. On the contrary, the greyish layer as seen on samples tempered at high temperature was very thin and was produced by chemical factors such as oxidizing or nitriding. 5. The upper specimens having much greyish areas did not so much wear the lower specimens, but they showed themselves less wear resisting. On the contrary, the specimens which were covered with lustrous degenerative layer, showed more wear resisting, but the wearing amounts of the lower specimens were increased. Therefore, the combination of the extremely different matrices and the identical matrices must be avoided

Leptonic CP asymmetry and Light flavored scalar

We consider a situation where right-handed neutrinos couple to a light scalar which is possibly a Nambu-Goldstone boson resulting from high-energy symmetry breaking. Its coupling is typically complex-valued and flavor-dependent. In this work, we investigate the possibility of the leptonic asymmetry generation in the Universe from tree-level right-handed neutrino decay to flavorful light scalar. Furthermore a new source of asymmetry generation from a single decay process is pointed out, which is characteristic of the present setting.Comment: 28 pages, 10 figure

Electroweak axion string and superconductivity

We study the axion strings with the electroweak gauge flux in the DFSZ axion model and show that these strings, called the electroweak axion strings, can exhibit superconductivity without fermionic zero modes. We construct three types of electroweak axion string solutions. Among them, the string with $W$-flux can be lightest in some parameter space, which leads to a stable superconducting cosmic string. We also show that a large electric current can flow along the string due to the Peccei-Quinn scale much higher than the electroweak scale. This large current induces a net attractive force between the axion strings with the same topological charge, which opens a novel possibility that the axion strings form Y-junctions in the early universe.Comment: 35 pages, 8 figures; v3: published versio

Wear Resisting Properties of Cast Irons Having Different Shapes of Graphite

The wear resisting properties of cast irons having different shapes of graphite have been studied on dry wearing without lubricant, by using Fukao-type dry wear tester. It was found that the specimens consisting of ferrite matrix are remarkably less wear resistive in comparison with that of pearlite matrix, and that the wearing amounts increase with the order of shapes of wormy flake, small nodular and eutectic graphite

Quark masses and CKM hierarchies from S4′S_4^\prime modular flavor symmetry

We propose models to explain the hierarchies of the quark masses and mixing by utilizing the $S_4^\prime$ modular flavor symmetry. The hierarchy is realized by the modulus $\tau$ stabilized at $\mathrm{Im}\,\tau \gg 1$, where the residual $Z_4^T$ symmetry is approximately unbroken and the Froggatt-Nielsen mechanism works. It is found that the quark hierarchies are realized only in a few cases of quark representations. We study two models with assigning the modular weights, so that the observed quark hierarchies are explained in the cases of both small and large ratios of the top to bottom Yukawa couplings. We also argue that $\mathcal{O}({0.1})$ hierarchies of the $\mathcal{O}({1})$ coefficients can be explained by imposing another $S_3$ modular symmetry.Comment: 13 pages, 3 tables; ver2 comments on CP violation adde

Quantum current dissipation in superconducting strings and vortons

In this work, the current stability is discussed for cosmic strings with the bosonic superconductivity. A non-vanishing curvature of string generally induce the quantum instability of the current-carrying particle. Its decay rates are explored for various types of model parameters, curved string shapes, and decay processes. As a cosmological application, the stability is examined for superconducting strings in the string network and also for cosmic vortons by evaluating their cosmological evolution. The zero mode and hence the vorton cannot be stable in various cases, e.g., with a hierarchy between the current-carrying particle mass off the string and the string tension or with sizable couplings of the current-carrying particle to light species such as the Standard Model particles.Comment: 42 pages, 14 figures, 1 tabl