Determination of the S-wave pi pi scattering lengths from a study of K+- -> pi+- pi0 pi0 decays

TL;DR

This study analyzes a large sample of kaon decays to measure pi pi scattering lengths, revealing a cusp anomaly linked to charge exchange scattering, and provides precise determinations of scattering length differences.

Contribution

It presents the most precise measurement of the difference between pi pi S-wave scattering lengths using kaon decay data and theoretical fits, including higher-order rescattering effects.

Findings

Observation of a cusp-like anomaly in the pi0 pi0 invariant mass distribution.

Precise determination of (a0 - a2), the difference in pi pi S-wave scattering lengths.

Independent estimation of a2 including higher-order rescattering terms.

Abstract

We report the results from a study of the full sample of ~ 6.031 10^7 K+- -> pi+- pi0 pi0 decays recorded by the NA48/2 experiment at the CERN SPS. As first observed in this experiment, the pi0 pi0 invariant mass M00 distribution shows a cusp-like anomaly in the region around M00 = 2m+, where m+ is the charged pion mass. This anomaly has been interpreted as an effect due mainly to the final state charge exchange scattering process pi+ pi- -> p0 p0 in K+- -> pi+- pi+ pi- decay. Fits to the M00 distribution using two different theoretical formulations provide the presently most precise determination of (a0 - a2), the difference between the pi pi S-wave scattering lengths in the isospin I=0 and I=2 states. Higher-order pi pi rescattering terms, included in the two formulations, allow also an independent, though less precise, determination of a2.