Direct CP violation and the $\Delta I=1/2$ rule in $K\to\pi\pi$ decay from the standard model

Abbott, R.; Blum, T.; Boyle, P.A.; Bruno, M.; Christ, N.H.; Hoying, D.; Jung, C.; Kelly, C.; Lehner, C.; Mawhinney, R.D.

doi:10.1103/PhysRevD.102.054509

Direct CP violation and the $\Delta I=1/2$ rule in $K\to\pi\pi$ decay from the standard model

RBC and
UKQCD

Collaborations

•

R. Abbott
(
- Columbia U.
)

Apr 20, 2020

95 pages

Published in:

Phys.Rev.D 102 (2020) 5, 054509

Published: Sep 18, 2020

e-Print:

2004.09440 [hep-lat]

DOI:

10.1103/PhysRevD.102.054509

Report number:

CERN-TH-2020-058,
MIT-CTP/5197

Experiments:

LATTICE-UKQCD

View in:

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Abstract: (APS)

We present a lattice QCD calculation of the ΔI=1/2, K→ππ decay amplitude A0 and ϵ′, the measure of direct CP violation in K→ππ decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a 323×64 lattice with an inverse lattice spacing of a-1=1.3784(68) GeV. However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the ππ ground state and more accurately relate the lattice operators to those defined in the standard model. We find Re(A0)=2.99(0.32)(0.59)×10-7 GeV and Im(A0)=-6.98(0.62)(1.44)×10-11 GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result Re(A0)=3.3201(18)×10-7 GeV. These results for A0 can be combined with our earlier lattice calculation of A2 [2] to obtain Re(ϵ′/ϵ)=21.7(2.6)(6.2)(5.0)×10-4, where the third error represents omitted isospin breaking effects, and Re(A0)/Re(A2)=19.9(2.3)(4.4). The first agrees well with the experimental result of Re(ϵ′/ϵ)=16.6(2.3)×10-4. A comparison of the second with the observed ratio Re(A0)/Re(A2)=22.45(6), demonstrates the standard model origin of this “ΔI=1/2 rule” enhancement.

Note:

Updated to published version. 95 pages, 12 figures

Lattice field theories, lattice QCD
CP: violation
operator: lattice
experimental results
lattice field theory
ground state
enhancement
statistical
statistics
kinematics

References(81)

Figures(25)

[1]

Standard Model Prediction for Direct CP Violation in K→ππ Decay

RBC and
UKQCD

Collaborations

•

Z. Bai
(
- Columbia U.
)

et al.

- Phys.Rev.Lett. 115 (2015) 21, 212001
•
e-Print:
- 1505.07863
•
DOI:
- 10.1103/PhysRevLett.115.212001

[2]

$K \rightarrow \pi\pi$ $\Delta I=3/2$ decay amplitude in the continuum limit

T. Blum
(
- Connecticut U. and
- RIKEN BNL
)
,
P.A. Boyle
(
- Edinburgh U.
)
,
N.H. Christ
(
- Columbia U.
)
,
J. Frison
(
- Edinburgh U.
)
,
N. Garron
(
- Cambridge U., DAMTP and
- Plymouth U.
)

et al.

- Phys.Rev.D 91 (2015) 7, 074502
•
e-Print:
- 1502.00263
•
DOI:
- 10.1103/PhysRevD.91.074502

[3]

CP Violation in the Renormalizable Theory of Weak Interaction

Makoto Kobayashi
(
- Kyoto U.
)
,
Toshihide Maskawa
(
- Kyoto U.
)

- Prog.Theor.Phys. 49 (1973) 652-657,
- Also in *Lichtenberg, D. B. (Ed.), Rosen, S. P. (Ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 218-223.
•
DOI:
- 10.1143/PTP.49.652