Revised and Improved Value of the QED Tenth-Order Electron Anomalous Magnetic Moment

In order to improve the theoretical prediction of the electron anomalous magnetic moment $a_e$ we have carried out a new numerical evaluation of the 389 integrals of Set V, which represent 6,354 Feynman vertex diagrams without lepton loops. During this work, we found that one of the integrals, called $X024$, was given a wrong value in the previous calculation due to an incorrect assignment of integration variables. The correction of this error causes a shift of $-1.25$ to the Set~V contribution, and hence to the tenth-order universal (i.e., mass-independent) term $A_1^{(10)}$. The previous evaluation of all other 388 integrals is free from errors and consistent with the new evaluation. Combining the new and the old (excluding $X024$) calculations statistically, we obtain $7.606~(192) (\alpha/\pi)^5$ as the best estimate of the Set V contribution. Including the contribution of the diagrams with fermion loops, the improved tenth-order universal term becomes $A_1^{(10)}=6.678~(192)$. Adding hadronic and electroweak contributions leads to the theoretical prediction $a_e (\text{theory}) =1~159~652~182.032~(720)\times 10^{-12}$. From this and the best measurement of $a_e$, we obtain the inverse fine-structure constant $\alpha^{-1}(a_e) = 137.035~999~1491~(331)$. The theoretical prediction of the muon anomalous magnetic moment is also affected by the update of QED contribution and the new value of $\alpha$, but the shift is much smaller than the theoretical uncertainty.Comment: 32 pages, 1 figure, references adde

Higher Order Terms of Improved Mean Field Approximation for IIB Matrix Model and Emergence of Four-dimensional Space-time

The spontaneous breakdown of SO(10) symmetry of the IIB matrix model has been studied by using the improved mean field approximation (IMFA). In this report, the eighth-order contribution to the improved perturbative series is obtained, which involves evaluation of 20410 planar two-particle irreducible vacuum diagrams. We consider SO(d)-preserving configurations as ansatz (d=4,7). The development of plateau, the solution of self-consistency condition, is seen in both ansatz. The large ratio of the space-time extent of d-dimensional part against the remaining (10-d)-dimensional part is obtained for SO(4) ansatz evaluated at the representative points of the plateau. It would be interpreted as the emergence of four-dimensional space-time in the IIB matrix model.Comment: 13 page

I=2I=2 ππ\pi\pi potential in the HAL QCD method with all-to-all propagators

In this paper, we perform the first application of the hybrid method (exact low modes plus stochastically estimated high modes) for all-to-all propagators to the HAL QCD method. We calculate the HAL QCD potentials in the $I=2$ $\pi\pi$ scattering in order to see how statistical fluctuations of the potential behave under the hybrid method. All of the calculations are performed with the 2+1 flavor gauge configurations on $16^3 \times 32$ lattice at the lattice spacing $a \approx 0.12$ fm and $m_{\pi} \approx 870$ MeV. It is revealed that statistical errors for the potential are enhanced by stochastic noises introduced by the hybrid method, which, however, are shown to be reduced by increasing the level of dilutions, in particular, that of space dilutions. From systematic studies, we obtain a guiding principle for a choice of dilution types/levels and a number of eigenvectors to reduce noise contaminations to the potential while keeping numerical costs reasonable. We also confirm that we can obtain the scattering phase shifts for the $I=2$ $\pi\pi$ system by the hybrid method within a reasonable numerical cost, which are consistent with the result obtained with the conventional method. The knowledge we obtain in this study will become useful to investigate hadron resonances which require quark annihilation diagrams such as the $\rho$ meson by the HAL QCD potential with the hybrid method.Comment: 20 pages, 10 figures, published version in PTE

Configuration sampling in multi-component multi-sublattice systems enabled by ab Initio Configuration Sampling Toolkit (abICS)

Simulation of the intermediate levels of disorder found in multi-component multi-sublattice systems in various functional materials is a challenging issue, even for state-of-the-art methodologies based on first-principles calculation. Here, we introduce our open-source package ab Initio Configuration Sampling Toolkit (abICS), which combines high-throughput first-principles calculations, machine learning, and parallel extended ensemble sampling in an active learning setting to enable such simulations. The theoretical background is reviewed in some detail followed by brief notes on usage of the software. In addition, our recent applications of abICS to multi-component ionic systems and their interfaces for energy applications are reviewed as demonstration of the power of this approach.Comment: 25 pages, 6 figure

Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant

This paper presents the complete QED contribution to the electron g-2 up to the tenth order. With the help of the automatic code generator, we have evaluated all 12672 diagrams of the tenth-order diagrams and obtained 9.16 (58)(\alpha/\pi)^5. We have also improved the eighth-order contribution obtaining -1.9097(20)(\alpha/\pi)^4, which includes the mass-dependent contributions. These results lead to a_e(theory)=1 159 652 181.78 (77) \times 10^{-12}. The improved value of the fine-structure constant \alpha^{-1} = 137.035 999 174 (35) [0.25 ppb] is also derived from the theory and measurement of a_e.Comment: 4 pages, 2 figures. Some numbers are slightly change

Exploring walking behavior in SU(3) gauge theory with 4 and 8 HISQ quarks

We present the report of the LatKMI collaboration on the lattice QCD simulation for the cases of 4 and 8 flavors. The Nf=8 in particular is interesting from the model-building point of view: The typical walking technicolor model with the large anomalous dimension is the so-called one-family model (Farhi-Susskind model). Thus we explore the walking behavior in LQCD with 8 HISQ quarks by comparing with the 4-flavor case (in which the chiral symmetry is spontaneously broken). We report preliminary results on the spectrum, analyzed through the chiral perturbation theory and the finite-size hyperscaling, and we discuss the availability of the Nf=8 QCD to the phenomenology.Comment: 7 pages, Proceedings of 30th International Symposium on Lattice Field Theory, June 24-29, 2012, Cairns, Australi