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K to ?? decay amplitudes from lattice QCD

K to ?? decay amplitudes from lattice QCD
K to ?? decay amplitudes from lattice QCD
We report a direct lattice calculation of the K to ?? decay matrix elements for both the ?I=1/2 and 3/2 amplitudes A0 and A2 on 2+1 flavor, domain wall fermion, 163×32×16 lattices. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are nonperturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this paper, we take a major step toward the computation of the physical K??? amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422 MeV at rest in the kaon rest frame. With this simplification, we are able to resolve Re(A0) from zero for the first time, with a 25% statistical error and can develop and evaluate methods for computing the complete, complex amplitude A0, a calculation central to understanding the ?=1/2 rule and testing the standard model of CP violation in the kaon system.

1550-7998
114503-1-114503-22
Blum, T.
29e11a5b-96d3-4b8d-a17c-ec4b836ceead
Boyle, P.
a12661a4-a1da-4fdc-9207-db20087bfaba
Christ, N.
bafeb9b1-3dd1-4027-8690-1d99257b2c8e
Garron, N.
4652f982-8723-41c1-9bf7-46bc5c54c2db
Goode, E.
29354b98-c117-4ace-9ca4-1d3ad531485f
Izubuchi, T.
4ee5b26a-e913-4a6b-8a2f-80159b3219b2
Lehner, C.
f5ed25c1-68c1-4a5f-9e01-73233639caae
Liu, Q.
9c3579c5-8fa0-402b-ad8e-83f4542b1b05
Mawhinney, R.
871ec3e5-7501-4c79-a815-95b147eb1907
Sachrajda, C.
0ed6568b-f52f-4314-8677-4aeeb925d6f7
Soni, A.
7a4196ff-0f6b-429e-af54-d1036e9c433b
Sturm, C.
5ccbb81f-c09b-4b32-9871-fc6b13bfacc4
Yin, H.
04f9aabf-323a-4a34-a432-66511811790a
Zhou, R.
fbf82787-d075-4c24-96ac-633e045534f2
Blum, T.
29e11a5b-96d3-4b8d-a17c-ec4b836ceead
Boyle, P.
a12661a4-a1da-4fdc-9207-db20087bfaba
Christ, N.
bafeb9b1-3dd1-4027-8690-1d99257b2c8e
Garron, N.
4652f982-8723-41c1-9bf7-46bc5c54c2db
Goode, E.
29354b98-c117-4ace-9ca4-1d3ad531485f
Izubuchi, T.
4ee5b26a-e913-4a6b-8a2f-80159b3219b2
Lehner, C.
f5ed25c1-68c1-4a5f-9e01-73233639caae
Liu, Q.
9c3579c5-8fa0-402b-ad8e-83f4542b1b05
Mawhinney, R.
871ec3e5-7501-4c79-a815-95b147eb1907
Sachrajda, C.
0ed6568b-f52f-4314-8677-4aeeb925d6f7
Soni, A.
7a4196ff-0f6b-429e-af54-d1036e9c433b
Sturm, C.
5ccbb81f-c09b-4b32-9871-fc6b13bfacc4
Yin, H.
04f9aabf-323a-4a34-a432-66511811790a
Zhou, R.
fbf82787-d075-4c24-96ac-633e045534f2

Blum, T., Boyle, P., Christ, N., Garron, N., Goode, E., Izubuchi, T., Lehner, C., Liu, Q., Mawhinney, R., Sachrajda, C., Soni, A., Sturm, C., Yin, H. and Zhou, R. (2011) K to ?? decay amplitudes from lattice QCD. Physical Review D, 84 (11), 114503-1-114503-22. (doi:10.1103/PhysRevD.84.114503).

Record type: Article

Abstract

We report a direct lattice calculation of the K to ?? decay matrix elements for both the ?I=1/2 and 3/2 amplitudes A0 and A2 on 2+1 flavor, domain wall fermion, 163×32×16 lattices. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are nonperturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this paper, we take a major step toward the computation of the physical K??? amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422 MeV at rest in the kaon rest frame. With this simplification, we are able to resolve Re(A0) from zero for the first time, with a 25% statistical error and can develop and evaluate methods for computing the complete, complex amplitude A0, a calculation central to understanding the ?=1/2 rule and testing the standard model of CP violation in the kaon system.

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Published date: 14 December 2011
Organisations: Theoretical Partical Physics Group

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Local EPrints ID: 339269
URI: https://eprints.soton.ac.uk/id/eprint/339269
ISSN: 1550-7998
PURE UUID: f1cf8c5f-1532-481b-8262-a701bee58759

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Date deposited: 28 May 2012 13:01
Last modified: 16 Jul 2019 22:02

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Contributors

Author: T. Blum
Author: P. Boyle
Author: N. Christ
Author: N. Garron
Author: E. Goode
Author: T. Izubuchi
Author: C. Lehner
Author: Q. Liu
Author: R. Mawhinney
Author: C. Sachrajda
Author: A. Soni
Author: C. Sturm
Author: H. Yin
Author: R. Zhou

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