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An exploratory lattice study of ΔI = 3/2 K → pi pi decays at next-to-leading order in the chiral expansion

An exploratory lattice study of ΔI = 3/2 K → pi pi decays at next-to-leading order in the chiral expansion
An exploratory lattice study of ΔI = 3/2 K → pi pi decays at next-to-leading order in the chiral expansion
We present the first direct evaluation of ΔI =3/2 K ππ matrix elements with the aim of determining all the low-energy constants at NLO in the chiral expansion. Our numerical investigation demonstrates that it is indeed possible to determine the K → ππ matrix elements directly for the masses and momenta used in the simulation with good precision. In this range however, we find that the matrix elements do not satisfy the predictions of NLO chiral perturbation theory. For the chiral extrapolation we therefore use a hybrid procedure which combines the observed polynomial behavior in masses and momenta of our lattice results, with NLO chiral perturbation theory at lower masses. In this way we find stable results for the quenched matrix elements of the electroweak penguin operators (I=2 ⟨ππ|O8|K0⟩ = (0.68 ± 0.09) GeV3 and I=2 ⟨ππ|O7|K0⟩ = (0.12 ± 0.02) GeV3 in the NDR-‾MS scheme at the scale 2 GeV), but not for the matrix elements of O4 (for which there are too many low-energy constants at NLO for a reliable extrapolation). For all three operators we find that the effect of including the NLO corrections is significant (typically about 30%). We present a detailed discussion of the status of the prospects for the reduction of the systematic uncertainties.
0550-3213
175-211
Boucaud, Philippe
b9cf7d17-6e2d-40cb-aa82-e66d202b3bcf
Giménez, Vicent
a7e2c06d-63d3-4972-b884-07bb57d846bb
Lin, C.-J. David
3b3ab1f2-efb6-4bd6-a92f-79a23d4b9945
Lubicz, Vittorio
801148ad-141c-41dc-9128-d0cd748bd5d3
Martinelli, Guido
9ce48c45-c91f-439b-a088-6cdcfb8b41cc
Papinutto, Mauro
e7cba614-180e-44a2-8502-2648f80c68c8
Sachrajda, Chris T.
0ed6568b-f52f-4314-8677-4aeeb925d6f7
Boucaud, Philippe
b9cf7d17-6e2d-40cb-aa82-e66d202b3bcf
Giménez, Vicent
a7e2c06d-63d3-4972-b884-07bb57d846bb
Lin, C.-J. David
3b3ab1f2-efb6-4bd6-a92f-79a23d4b9945
Lubicz, Vittorio
801148ad-141c-41dc-9128-d0cd748bd5d3
Martinelli, Guido
9ce48c45-c91f-439b-a088-6cdcfb8b41cc
Papinutto, Mauro
e7cba614-180e-44a2-8502-2648f80c68c8
Sachrajda, Chris T.
0ed6568b-f52f-4314-8677-4aeeb925d6f7

Boucaud, Philippe, Giménez, Vicent, Lin, C.-J. David, Lubicz, Vittorio, Martinelli, Guido, Papinutto, Mauro and Sachrajda, Chris T. (2005) An exploratory lattice study of ΔI = 3/2 K → pi pi decays at next-to-leading order in the chiral expansion. Nuclear Physics B, 721 (1-3), 175-211. (doi:10.1016/j.nuclphysb.2005.05.025).

Record type: Article

Abstract

We present the first direct evaluation of ΔI =3/2 K ππ matrix elements with the aim of determining all the low-energy constants at NLO in the chiral expansion. Our numerical investigation demonstrates that it is indeed possible to determine the K → ππ matrix elements directly for the masses and momenta used in the simulation with good precision. In this range however, we find that the matrix elements do not satisfy the predictions of NLO chiral perturbation theory. For the chiral extrapolation we therefore use a hybrid procedure which combines the observed polynomial behavior in masses and momenta of our lattice results, with NLO chiral perturbation theory at lower masses. In this way we find stable results for the quenched matrix elements of the electroweak penguin operators (I=2 ⟨ππ|O8|K0⟩ = (0.68 ± 0.09) GeV3 and I=2 ⟨ππ|O7|K0⟩ = (0.12 ± 0.02) GeV3 in the NDR-‾MS scheme at the scale 2 GeV), but not for the matrix elements of O4 (for which there are too many low-energy constants at NLO for a reliable extrapolation). For all three operators we find that the effect of including the NLO corrections is significant (typically about 30%). We present a detailed discussion of the status of the prospects for the reduction of the systematic uncertainties.

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Published date: 15 August 2005

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Local EPrints ID: 57105
URI: https://eprints.soton.ac.uk/id/eprint/57105
ISSN: 0550-3213
PURE UUID: ecef4d7a-9cdd-481f-bafa-3f0a8574497a

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Date deposited: 15 Aug 2008
Last modified: 13 Mar 2019 20:34

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