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

TL;DR

This study directly evaluates K -> pi pi decay matrix elements at NLO in the chiral expansion, revealing significant NLO effects and providing stable results for electroweak penguin operators through a hybrid extrapolation method.

Contribution

First direct lattice evaluation of DI=3/2 K -> pi pi matrix elements at NLO, with a hybrid chiral extrapolation approach to handle non-conforming data.

Findings

Stable results for electroweak penguin operators in the NDR-MSbar scheme at 2 GeV.

NLO corrections significantly impact matrix element values, around 30%.

Challenges in reliably extrapolating O_4 matrix elements due to many Low-Energy Constants.

Abstract

We present the first direct evaluation of DI = 3/2 K -> pi pi 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 -> pi pi 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 behaviour 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 (<pi pi (I=2)|O_8|K^0>= (0.68 +- 0.09) GeV^3 and <pi pi (I=2)|O_7|K^0>= (0.12 +- 0.02) GeV^3 in the NDR-MSbar scheme at the scale 2 GeV), but not for the matrix elements of O_4 (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.