arXiv subjects
Publications and source records attributed to Tadashi Ishikawa.
Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are computed numerically. The energy dependence of the integrals is shown explicitly, and a discussion of its behavior is presented.
Numerical calculation of two-loop electroweak corrections to the muon anomalous magnetic moment ($g$-2) is done based on, on shell renormalization scheme (OS) and free quark model (FQM). The GRACE-FORM system is used to generate Feynman diagrams and corresponding amplitudes. Total 1780 two-loop diagrams and 70 one-loop diagrams composed of counter terms are calculated to get the renormalized quantity. As for the numerical calculation, we adopt trapezoidal rule with Double Exponential method (DE). Linear extrapolation method (LE) is introduced to regularize UV- and IR-divergences and to get finite values. The reliability of our result is guaranteed by several conditions. The sum of one and two loop electroweak corrections in this renormalization scheme becomes $a_μ^{EW:OS}[1{\rm+}2{\rm -loop}]= 151.2 (\pm 1.0)\times 10^{-11}$, where the error is due to the numerical integration and the uncertainty of input mass parameters and of the hadronic corrections to electroweak loops. By taking the hadronic corrections into account, we get $a_μ^{EW}[1{\rm+}2 {\rm -loop}]= 152.9 (\pm 1.0)\times 10^{-11}$. It is in agreement with the previous works given in PDG within errors.
The 1-loop effects of the MSSM at the ILC are investigated through numerical analysis. We studied the higgs production processes $e^-e^+\rightarrow Zh$ and $e^-e^+\rightarrow ν\barνh$ at the ILC. It is found that the magnitude of the MSSM contribution through the 1-loop effects is sizable enough to be detected. In the study, three sets of the MSSM parameters are proposed, which are consistent with the observed higgs mass, the muon $g$-$2$, the dark matter abundance and the decay branching ratios of $B$ mesons. In the $e^-e^+\rightarrow Zh$ process, the 1-loop effects of the MSSM are visible and the distinction of the parameter sets is partially possible. For the study of $e^-e^+\rightarrow ν\barνh$, we used the equivalent $\it W$-boson approximation in the evaluation of the 1-loop cross section. While the 1-loop effect of the MSSM is visible, the distinction of the parameter sets might not be possible in this process under the value of realistic luminosity at the ILC.
Interplate megathrust earthquakes have inflicted catastrophic damage on human society. An extremely hazardous megathrust earthquake is predicted to occur along the Nankai Trough off southwestern Japan, an economically active and densely populated area with historical records of megathrust earthquakes. Megathrust earthquakes are the result of a plate subduction mechanism and occur at interplate slip-deficit (or coupling) regions. Many past studies have attempted to capture slip-deficit rate (SDR) distributions for assessing future earthquake disasters. However, they could not capture a total view of the megathrust earthquake source region because they had no seafloor geodetic data. The Hydrographic and Oceanographic Department of the Japan Coast Guard (JHOD) has been developing a highly precise and sustainable seafloor geodetic observation network deployed in this subduction zone to broadly obtain direct information related to offshore SDR. Here, we present seafloor geodetic observation data and an offshore interplate SDR distribution model. Our data suggests that most offshore regions in this subduction zone have positive SDRs. Specifically, our observations indicate previously unknown high-SDR regions that are important for tsunami disaster mitigation and low-SDR regions that are consistent with distributions of shallow slow earthquakes and subducting seamounts. This is the first direct evidence suggesting that coupling conditions are related to these seismological and geological phenomena. These observations provide new fundamental information for inferring megathrust earthquake scenarios and interpreting research on the Nankai Trough subduction zone.
Crustal deformation data obtained by geodetic observation networks are foundations in the fields of geodesy and seismology. These data are essential for understanding plate motion and earthquake sources and for simulating earthquake and tsunami disasters. Although relatively scarce, seafloor geodetic data are particularly important for monitoring the behaviour of undersea interplate boundary regions. Since the mid-1990s, we have been developing the combined Global Navigation Satellite System-Acoustic ranging (GNSS-A) technique for realizing seafloor geodesy. This technique allows us to collect time series of seafloor crustal deformation. Our published data can be used to investigate several seismological phenomena along the subduction zones around Japan, namely the Nankai Trough, Sagami Trough and Japan Trench. These regions are globally important places in geodesy and seismology and are also suitable for comparison with other geophysical datasets. Our intention is for these data to promote further understanding of megathrust zones.
Two-loop electroweak corrections to the muon anomalous magnetic moment are automatically calculated by using GRACE-FORM system, as a trial to extend our system for two-loop calculation. We adopt the non-linear gauge (NLG) to check the reliability of our calculation. In total 1780 two-loop diagrams consisting of 14 different topological types and 70 one-loop diagrams composed of counter terms are calculated. We check UV- and IR-divergences cancellation and the independence of the results from NLG parameters. As for the numerical calculation, we adopt trapezoidal rule with Double Exponential method (DE). Linear extrapolation method (LE) is introduced to regularize UV- and IR- divergence and to get finite values.
Within the framework of the Minimal Supersymmetric Standard Model, we investigate the 1-loop effects of supersymmetric particles on the third-generation fermion-pair production at the ILC. Three sets of the SUSY parameters are proposed which are consistent with the observed Higgs mass, the muon g-2, the Dark Matter abundance and the decay branching ratio of B meson. We discuss on the possibility of discovering the signals consistent with SUSY as well as of experimentally distinguishing the proposed sets of SUSY parameters.
Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate new physics beyond the Standard Model. This indicates that we need to evaluate Feynman loop diagram with multi-loop integral which may require multi-precision calculation. We developed a dedicated accelerator system for multi-precision calculation (GRAPE9-MPX). We present performance results of our system for the case of Feynman two-loop box and three-loop selfenergy diagrams with multi-precision.
This paper describes applications of extrapolation for the computation of coefficients in an expansion of infrared divergent integrals. An extrapolation procedure is performed with respect to a parameter introduced by dimensional regularization. While this treats typical IR singularities at the boundaries of the integration domain, special care needs to be taken in cases where the integrand is singular in the interior of the domain as well as on the boundaries. A double extrapolation is devised for a class of massless vertex integrals. Quadruple precision results are presented, demonstrating high accuracy. The computations are supported by the use of general adaptive integration programs from the QUADPACK package, in iterated integrations with highly singular integrand functions.
We have been developing a program package called GRACE/SUSY-loop which is for the automatic calculations of the MSSM amplitudes in one-loop order. The non-linear gauge (NLG) fixing conditions play the crucial role in the calculations in one-loop order which contain a large number of Feynman diagrams. We present the recent progress in GRACE/SUSY-loop which is obtained by extending the non-linear gauge formalism to the slepton sector.
With an integrated software package {\tt GRACE}, it is possible to generate Feynman diagrams, calculate the total cross section and generate physics events automatically. We outline the hybrid method of parallel computation of the multi-dimensional integration of {\tt GRACE}. We used {\tt MPI} (Message Passing Interface) as the parallel library and, to improve the performance we embedded the mechanism of the dynamic load balancing. The reduction rate of the practical execution time was studied.