# K{yields}{pi}{pi} Amplitudes from Lattice QCD with a Light Charm Quark

## Abstract

We compute the leading-order low-energy constants of the {delta}S=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite-volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a {delta}I=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the {delta}I=1/2 amplitude, our computation suggests large QCD contributions to the physical {delta}I=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm-quark mass in K{yields}{pi}{pi} amplitudes. The use of fermions with an exact chiral symmetry is an essential ingredient in our computation.

- Authors:

- Department of Physics, CERN, TH Division, CH-1211 Geneva 23 (Switzerland)
- Departamento de Fisica Teorica and IFIC, Universidad de Valencia, E-46071 Valencia (Spain)
- Faculty of Physics, University of Bielefeld, D-33501 Bielefeld (Germany)
- DESY, Notkestrasse 85, D-22603 Hamburg (Germany)
- Institut fuer Kernphysik, Universitaet Mainz, D-55099 Mainz (Germany)

- Publication Date:

- OSTI Identifier:
- 20957677

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevLett.98.082003; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; APPROXIMATIONS; CHIRAL SYMMETRY; CHIRALITY; CORRELATION FUNCTIONS; HAMILTONIANS; KAONS; MASS; MEV RANGE; PERTURBATION THEORY; PIONS; QUANTUM CHROMODYNAMICS; QUARKS

### Citation Formats

```
Giusti, L., Pena, C., Hernandez, P., Laine, M., Wennekers, J., and Wittig, H.
```*K{yields}{pi}{pi} Amplitudes from Lattice QCD with a Light Charm Quark*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVLETT.98.082003.

```
Giusti, L., Pena, C., Hernandez, P., Laine, M., Wennekers, J., & Wittig, H.
```*K{yields}{pi}{pi} Amplitudes from Lattice QCD with a Light Charm Quark*. United States. doi:10.1103/PHYSREVLETT.98.082003.

```
Giusti, L., Pena, C., Hernandez, P., Laine, M., Wennekers, J., and Wittig, H. Fri .
"K{yields}{pi}{pi} Amplitudes from Lattice QCD with a Light Charm Quark". United States.
doi:10.1103/PHYSREVLETT.98.082003.
```

```
@article{osti_20957677,
```

title = {K{yields}{pi}{pi} Amplitudes from Lattice QCD with a Light Charm Quark},

author = {Giusti, L. and Pena, C. and Hernandez, P. and Laine, M. and Wennekers, J. and Wittig, H.},

abstractNote = {We compute the leading-order low-energy constants of the {delta}S=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite-volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a {delta}I=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the {delta}I=1/2 amplitude, our computation suggests large QCD contributions to the physical {delta}I=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm-quark mass in K{yields}{pi}{pi} amplitudes. The use of fermions with an exact chiral symmetry is an essential ingredient in our computation.},

doi = {10.1103/PHYSREVLETT.98.082003},

journal = {Physical Review Letters},

number = 8,

volume = 98,

place = {United States},

year = {Fri Feb 23 00:00:00 EST 2007},

month = {Fri Feb 23 00:00:00 EST 2007}

}