title: Emerging understanding of the ΔI=1/2 rule from lattice QCD.
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→ππ 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.
authors.affiliation: SUPA, School of Physics, The University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom.
authors.forename: P A
authors.initials: PA
authors.lastname: Boyle
authors.affiliation: Physics Department, Columbia University, New York, New York 10027, USA.
authors.forename: N H
authors.initials: NH
authors.lastname: Christ
authors.affiliation: School of Mathematics, Trinity College, Dublin 2, Ireland.
authors.forename: N
authors.initials: N
authors.lastname: Garron
authors.affiliation: School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom.
authors.forename: E J
authors.initials: EJ
authors.lastname: Goode
authors.affiliation: School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom.
authors.forename: T
authors.initials: T
authors.lastname: Janowski
authors.affiliation: RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA.
authors.forename: C
authors.initials: C
authors.lastname: Lehner
authors.affiliation: Physics Department, Columbia University, New York, New York 10027, USA.
authors.forename: Q
authors.initials: Q
authors.lastname: Liu
authors.affiliation: School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom.
authors.forename: A T
authors.initials: AT
authors.lastname: Lytle
authors.affiliation: School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom.
authors.forename: C T
authors.initials: CT
authors.lastname: Sachrajda
authors.affiliation: Brookhaven National Laboratory, Upton, New York 11973, USA.
authors.forename: A
authors.initials: A
authors.lastname: Soni
authors.affiliation: Physics Department, Columbia University, New York, New York 10027, USA.
authors.forename: D
authors.initials: D
authors.lastname: Zhang