**2.3 For theory-computing**

For theory-computing, we study flavor physics based on lattice gauge theory, which enables large-scale numerical simulations on a supercomputer. The theory of strong interactions in the Standard Model is Quantum Chromo Dynamics (QCD). In phenomena related to the Cabibbo-Kobayashi-Maskawa (CKM) matrix, the theoretical values of the interaction amplitudes also have factors that cannot be obtained in a perturbative way since the strong coupling constant becomes strong at a low energy scale as QCD, as a non-abelian gauge theory, predicts. The only way that one can calculate the non-perturbative quantities with a controlled error is the lattice method, in which we put strongly interacting particles, quarks and gluons, on a lattice and calculate quantities directly from first principles. Fig. 9 shows the baryon based on lattice QCD.

We use the staggered fermions, which are one of the more popular lattice fermion schemes for full QCD lattice simulations. The staggered fermion scheme has the advantage that its

The e-Science Paradigm for Particle Physics 87

extracted from the three-point correlation function whose interpolating operators are

In this method, we have to generate quark propagators first. In order to create the desired meson states (kaon or pion) with non-zero spatial momenta, we use random U(1) sources with momentum phases. We also use the PxP operator insertion method (generally called sequential source) in order to create or annihilate the other meson state. Next, we contract

From a Ward identity, we can convert the matrix elements of the vector current operator to those of the scalar density operator. This gives another method to calculate the form factor. The way to obtain correlation function data is similar to that found for the vector current method. Since the two methods are connected by a Ward identity, we can check if the data is

The kaon and pion decay constants can also be used to determine Vus. Since the ratio fK/fπ is related to Vus/Vub, we can obtain Vus if Vub is precisely known. From these quantities, we calculate the two point function of axial vector current and pseudo-scalar operator in the

We have introduced the concept of an e-Science paradigm for experiment-computing-theory for particle physics. Computing-experiment collaborative research offers not only an e-Science research environment including data production, data processing and data analysis, but also a data handling system for the Belle II experiment. The e-Science research environment enables us to research particle physics anytime and anywhere in more efficient way. Experiment-theory collaborative research provides a way to study the standard model and new physics. Theory-Computing collaborative research enables lattice gauge theory

composed by the pseudo-scalar operator and the conserved vector current operator.

these quark propagators properly and obtain three-point correlation function data.

consistent.

Fig. 10. Kaon semi-leptonic decay.

same way as the form factor.

**3. Conclusions** 

**2.3.2 Kaon and pion decay constants** 

tools using supercomputing at KISTI.

Fig. 9. Baryon based on lattice QCD.

computational cost is cheaper than other lattice fermion models while preserving remnant chiral symmetry. However, this scheme suffers from taste symmetry breaking in finite lattice spacing. Tastes are the remaining species that originate from the fermion doubling problem. Taste symmetry breaking complicates the analysis using lattice data. Thus, in order to reduce taste symmetry breaking effects, we use the HYP-smeared staggered fermions as valence quarks.

Lattice calculations cannot be done in the physical quark mass regime. In order to overcome this limitation, we calculate quantities with several non-physical quark masses and extrapolate the result to a physical regime. In this procedure, the staggered chiral perturbation theory guides the extrapolation.

This study can be extended to heavy flavor physics and other hadronic phenomena. In addition to physics research, we have developed new algorithms that enhance precision and utilize new hardware such as Graphic Processing Unit (GPU), which overcomes the limitation of CPU computing power.
