**2.3.1 Kaon semi-leptonic decay form factor**

Fig. 10 shows the diagram for kaon semi-leptonic decay. The CKM matrix elements are quark mixing parameters, which can be determined by combining experimental weak decay widths of hadrons and their theoretical calculations. A traditional way to determine Vus is connected with the kaon semi-leptonic decay channels, which include K+ → π0 l+ νl (K+l3 ) and K0 → π− l+ νl (K0l3 ). Using these types of decays, we use the conserved vector current operator and the scalar density operator.

The decay rate of Kl3 is written as the product of |Vus|2 and |f+(0)|2. The vector form factor at zero momentum transfer, f+(0), is defined from the hadronic matrix element of the vector current between kaon and pion states. The matrix elements of the vector current can be 86 Particle Physics

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

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

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

Fig. 10 shows the diagram for kaon semi-leptonic decay. The CKM matrix elements are quark mixing parameters, which can be determined by combining experimental weak decay widths of hadrons and their theoretical calculations. A traditional way to determine Vus is connected with the kaon semi-leptonic decay channels, which include K+ → π0 l+ νl (K+l3 )

The decay rate of Kl3 is written as the product of |Vus|2 and |f+(0)|2. The vector form factor at zero momentum transfer, f+(0), is defined from the hadronic matrix element of the vector current between kaon and pion states. The matrix elements of the vector current can be

l3 ). Using these types of decays, we use the conserved vector current

Fig. 9. Baryon based on lattice QCD.

perturbation theory guides the extrapolation.

**2.3.1 Kaon semi-leptonic decay form factor** 

operator and the scalar density operator.

limitation of CPU computing power.

and K0 → π− l+ νl (K0

fermions as valence quarks.

extracted from the three-point correlation function whose interpolating operators are composed by the pseudo-scalar operator and the conserved vector current operator.

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

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 consistent.

Fig. 10. Kaon semi-leptonic decay.
