# Kaon Semi-Leptonic Form Factor

**Principal Investigator:** Enno E. Scholz, Institut für Theoretische Physik, Universität Regensburg (Germany)

**HPC Platform:** SuperMUC of LRZ

**Date Published: **July 2014

**LRZ Project ID: **pr89ti

In the Standard Model (SM) of particle physics the interactions between the elementary particles are mediated by the strong and electro-weak forces. The strong forces are described by the theory of Quantum Chromodynamics (QCD). QCD forces are mediated by gluons between the quarks, which are the fundamental building blocks of all hadrons, especially the proton and the neutron, and therefore of most matter around us.

Six different quark flavors grouped in 3 generations have been observed in Nature (up and down, charm and strange, top and bottom), which differ, e.g., in their masses but also their electric charges. The electro-weak forces are described by another gauge field theory, the electro-weak theory of which for example Quantum Electrodynamics mediating the electric forces via photons is a subgroup. Since the quarks carry electric charges, the electro-weak forces act via photons between different quarks. But there are also the W- and Z-bosons as further force carriers in the electro-weak theory being responsible for more interactions between the elementary particles, also including the leptons (electron, muon, tau and their respective neutrinos).

The Cabibbo-Kobayashi-Maskawa (CKM) matrix describes the mixing between the mass eigenstates and electroweak eigenstates of the different quark flavors in the Standard Model of Particle Physics. Tests of the unitarity of the CKM matrix might reveal deviations from the Standard Model and consequently will be a sign of new physics beyond the Standard Model. The CKM matrix elements can be obtained, e.g., from experimental measurements of certain decay modes like the kaon decaying into a pion and a lepton plus anti-neutrino pair (Kl3 decay) if the form factors for such a decay are known. The calculation will address the kaon semi-leptonic form factor needed for the determination of the matrix element |V_us| from the Kl3 decay rates.

The form factor will be calculated non-perturbatively from lattice QCD simulations carried out with 2+1 flavors of dynamical SLiNC-fermions, where pion masses down to 210 MeV have been reached. These configurations were generated beforehand by the QCDSF-Coll. and resources of the SFB-TRR 55 "Hadron Physics from Lattice QCD". On these ensembles the researchers calculate two- and three-point correlation functions from which the form factor between a kaon and a pion state at zero or near-zero momentum transfer can extracted. Numerically this requires the inversion of large sparse matrices to obtain the propagators between certain quarks making it necessary to perform these calculations on HPC installations. The inverter used and optimized for running on the SuperMUC architecture is a multi-grid domain-decomposition solver. Typically, for the lattice sizes between 32^3x64 and 48^3x96 applied in this project, partition sizes of 1,024 nodes on SuperMUC are employed, but scaling of the used inverter code would have allowed the use of larger partition sizes as well.

Copyright: © Institut für Theoretische Physik, Universität Regensburg/Germany

This project was made possible through the Partnership for Advanced Computing in Europe. (PRACE)

**Researchers:**

Gunnar Bali, Vladimir Braun, Alessio Burello, Benjamin Gläßle, Rudolf Rödl, Enno E. Scholz (PI), Wolfgang Söldner

Enno E. Scholz

Institut für Theoretische Physik

Universität Regensburg

Universitätsstr. 31, D-93053 Regensburg/Germany

e-mail: enno.scholz@physik.uni-regensburg.de

*July 2014*