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Emerging understanding of the ΔI = 1/2 rule from lattice QCD

Emerging understanding of the ΔI = 1/2 rule from lattice QCD
Emerging understanding of the ΔI = 1/2 rule from lattice QCD
There has been much speculation as to the origin of the ΔI = 1/2 rule (ReA0/ReA2 ~ 22.5). We find that the two dominant contributions to the ΔI = 3/2, K → π π correlation functions have opposite signs, leading to a significant cancelation. This partial cancelation occurs in our computation of ReA2 with physical quark masses and kinematics (where we reproduce the experimental value of A2) and also for heavier pions at threshold. For ReA0, although we do not have results at physical kinematics, we do have results for pions at zero momentum with mπ ~ 420 MeV [ReA0/ReA2 = 9.1 (2.1)] and mπ ~ 330 MeV [ReA0/ReA2 = 12.0 (1.7)]. The contributions which partially cancel in ReA2 are also the largest ones in ReA0, but now they have the same sign and so enhance this amplitude. The emerging explanation of the ΔI = 1/2 rule is a combination of the perturbative running to scales of O (2 GeV), a relative suppression of ReA2 through the cancelation of the two dominant contributions, and the corresponding enhancement of ReA0. QCD and electroweak penguin operators make only very small contributions at such scales.
152001-152006
Boyle, P.A.
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Christ, N.H.
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Garron, N.
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Goode, E.J.
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Janowski, T.
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Lehner, C.
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Liu, Q.
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Lytle, A. T.
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Sachrajda, C.T.
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Soni, A.
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Zhang, D.
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Boyle, P.A.
deafc6c3-3d18-4199-84f5-6f20cd03e311
Christ, N.H.
bca5b070-bac5-4160-b12c-826a608a12b4
Garron, N.
4652f982-8723-41c1-9bf7-46bc5c54c2db
Goode, E.J.
29354b98-c117-4ace-9ca4-1d3ad531485f
Janowski, T.
a2f6e700-6ae9-4a93-93f9-095cbe0ca850
Lehner, C.
f5ed25c1-68c1-4a5f-9e01-73233639caae
Liu, Q.
9c3579c5-8fa0-402b-ad8e-83f4542b1b05
Lytle, A. T.
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Sachrajda, C.T.
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Soni, A.
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Zhang, D.
1c04f0f4-c07c-4671-8fd0-fa07a685fea2

Boyle, P.A., Christ, N.H., Garron, N., Goode, E.J., Janowski, T., Lehner, C., Liu, Q., Lytle, A. T., Sachrajda, C.T., Soni, A. and Zhang, D. (2013) Emerging understanding of the ΔI = 1/2 rule from lattice QCD. Physical Review Letters, 110 (15), 152001-152006. (doi:10.1103/PhysRevLett.110.152001). (PMID:25167252)

Record type: Article

Abstract

There has been much speculation as to the origin of the ΔI = 1/2 rule (ReA0/ReA2 ~ 22.5). We find that the two dominant contributions to the ΔI = 3/2, K → π π correlation functions have opposite signs, leading to a significant cancelation. This partial cancelation occurs in our computation of ReA2 with physical quark masses and kinematics (where we reproduce the experimental value of A2) and also for heavier pions at threshold. For ReA0, although we do not have results at physical kinematics, we do have results for pions at zero momentum with mπ ~ 420 MeV [ReA0/ReA2 = 9.1 (2.1)] and mπ ~ 330 MeV [ReA0/ReA2 = 12.0 (1.7)]. The contributions which partially cancel in ReA2 are also the largest ones in ReA0, but now they have the same sign and so enhance this amplitude. The emerging explanation of the ΔI = 1/2 rule is a combination of the perturbative running to scales of O (2 GeV), a relative suppression of ReA2 through the cancelation of the two dominant contributions, and the corresponding enhancement of ReA0. QCD and electroweak penguin operators make only very small contributions at such scales.

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PhysRevLett.110.152001 - Version of Record
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Published date: 9 April 2013
Organisations: Theoretical Partical Physics Group

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Local EPrints ID: 350975
URI: http://eprints.soton.ac.uk/id/eprint/350975
PURE UUID: cb8d8481-05a3-4678-b1e9-68bb6924ddb8

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Date deposited: 11 Apr 2013 14:01
Last modified: 20 Nov 2021 14:22

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Contributors

Author: P.A. Boyle
Author: N.H. Christ
Author: N. Garron
Author: E.J. Goode
Author: T. Janowski
Author: C. Lehner
Author: Q. Liu
Author: A. T. Lytle
Author: C.T. Sachrajda
Author: A. Soni
Author: D. Zhang

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