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1993
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M. Ciuchini, E. Franco, G. Martinelli, L. Reina, Phys. Lett. B301
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M. Ciuchini, E. Franco, G. Martinelli, L. Reina, L. Silvestrini, Z. Phys. C68
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2011

The $K\to(\pi\pi)_{I=2}$ Decay Amplitude from Lattice QCD

Blum, T., Boyle, P. A., Christ, N. H. et al.

Understand

We report on the first realistic \emph{ab initio} calculation of a hadronic weak decay, that of the amplitude $A_2$ for a kaon to decay into two \pi-mesons with isospin 2.

We find Re$A_2=(1.436\pm 0.063_{\textrm{stat}}\pm 0.258_{\textrm{syst}})\,10^{-8}\,\textrm{GeV}$ in good agreement with the experimental result and for the hitherto unknown imaginary part we find {Im}$\,A_2=-(6.83 \pm 0.51_{\textrm{stat}} \pm 1.30_{\textrm{syst}})\,10^{-13}\,{\rm GeV}$.
Moreover combining our result for Im\,$A_2$ with experimental values of Re\,$A_2$, Re\,$A_0$ and $\epsilon^\prime/\epsilon$, we obtain the following value for the unknown ratio Im\,$A_0$/Re\,$A_0$ within the Standard Model: $\mathrm{Im}\,A_0/\mathrm{Re}\,A_0=-1.63(19)_{\mathrm{stat}}(20)_{\mathrm{syst}}\times10^{-4}$.
One consequence of these results is that the contribution from Im\,$A_2$ to the direct CP violation parameter $\epsilon^{\prime}$ (the so-called Electroweak Penguin, EWP, contribution) is Re$(\epsilon^\prime/\epsilon)_{\mathrm{EWP}} = -(6.52 \pm 0.49_{\textrm{stat}} \pm 1.24_{\textrm{syst}}) \times 10^{-4}$.

Built on

M. Lüscher, Commun. Math. Phys. 104 (1986) 177; Commun. Math. Phys. 105 (1986) 153; Nucl. Phys. B354 (1991) 531; Nucl. Phys. B364 (1991) 237
1991
Earlier work this paper cites.
A. J. Buras, M. Jamin, M. E. Lautenbacher, Nucl. Phys. B408
1993
Earlier work this paper cites.
M. Ciuchini, E. Franco, G. Martinelli, L. Reina, Phys. Lett. B301
1993
Earlier work this paper cites.
M. Ciuchini, E. Franco, G. Martinelli, L. Reina, L. Silvestrini, Z. Phys. C68
1995
Earlier work this paper cites.
G. Buchalla, A. J. Buras, M. E. Lautenbacher, Rev. Mod. Phys. 68
1996
Earlier work this paper cites.
L. Lellouch, M. Lüscher, Commun. Math. Phys. 219
2001
Earlier work this paper cites.

Similar

C. Kim, Nucl. Phys. Proc. Suppl. 129
2004
Cited alongside, same era.
C. H. Kim, Nucl. Phys. Proc. Suppl. 140
2005
Cited alongside, same era.
C. T. Sachrajda, G. Villadoro, Phys. Lett. B609
2005
Cited alongside, same era.
P. M. Vranas, Phys. Rev. D74
2006
Cited alongside, same era.
A. J. Buras, D. Guadagnoli,Phys. Rev. D78
Original
2008
Cited alongside, same era.
D. Renfrew, T. Blum, N. Christ, R. Mawhinney and P. Vranas, PoS LATTICE2008
Original
2008
Cited alongside, same era.