Observation of ππ Scattering in KL→3π0 Decays 1by KTeVEd Blucher
University of Chicago••••

Motivation to study KL→π0π0π0 Dalitz Plot
Overview of Analysis
Results
Summary

KTeV: Arizona, Chicago, Colorado, Elmhurst, Fermilab, Osaka, Rice,Sao Paolo, UCLA, Virginia, Wisconsin
9 June 2009

KAON 09, Tsukuba, Japan2Before 2004:“Measurement of the quadratic slope parameter in theKL→ 3π0 decay Dalitz plot”• S. Somalwar et al. (E731), PRL 68, 2580 (1992)• A. Lai et al. (NA48), PL B515, 261 (2001)
Density on Dalitz plot:
2M 000 ∝ 1 + h000 RD2 ,where RD is the distance from the center of the Dalitz plot.
(Term with linear dependence on RD is zero because ofidentical particles in final state.)

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NA48/2 observed “cusp”
in K±→π±π0π0 decayscollected during 2003

2004: Cabibbo pointed out that the π0π0mass spectrum in K±→π±π0π0 could be
used to measure the difference in ππscattering lengths between I=0 and I=2states, a0-a2 − can be precisely calculated
in chiral perturbation theory.

Rescattering process:K±→π±π+π−→π±π0π0The same rescattering affects dynamics of KL→π0π0π0 decays, buteffect is expected to be much smaller.

YD ~ E2cm

KL→3π0 Dalitz plot will show effect of two contributions:~ E1cmIntrinsic KL→3π0 dynamics
M 000 ∝ 1 + h000 RD2 (RD2 = X D2 + YD2 )Rescattering
KL→π+π−π0→π0π0π0(PDG: h000 = –0.005)(shown with h000=0)2Previous results on h000 (E731 & NA48) ignored rescattering;KTeV presents first measurement of h000 that accounts forrescattering.

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Data sample: 68 million KL→π0π0π0 decays collected for

5acceptance studies as part of KTeV ε´ analysis.

This analysis takes advantage of years ofwork to calibrate CsI calorimeter for ε´/εanalysis (σE/E < 1%)

6Event Reconstruction• KL→π0π0π0 reconstruction
identical to KL→π0π0• To improve resolution inDalitz plot variables, we fit 6Eγs in each event using mK andmπ constraints:
σ(RD2)=0.070→0.014

7KL→π0π0π0 Data – Monte Carlo Comparisonsfit 2(E−E2ii )χE = ∑2σi =1i6Raw Dalitz plot: 68 million events

10% variation is mostly from acceptance effects; physics effects
give ~1% variations,89Dalitz Plot Projections

10Dalitz Plot Projections

no obvious cusp effect as in K±

Cusp in KL→π0π0π011

Raw Dalitz Density
MC Phase Space
Visible cusp

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• We fit our data using model of Cabibbo and Isidori: JHEP503, 21 (2005) – includes all one and two loop rescattering
processes.
• h000 and a0−a2 are two free parameters for KL→π0π0π0We perform two fits:
1. Fixing a0-a2 to the NA48 value: m + ( a0 − a2 ) = 0.268 ± 0.017
π2. Floating both h000 and a0−a2

13Good agreementwith model
except for mπ 0 π 0< 0.274 GeV / c 2

14Good agreementwith model
except for mπ 0 π 0< 0.274 GeV / c 2This region isexcluded forcentral values offits, but is included
in systematic error.

Fit Results
1. Using NA48 result m + ( a0 − a2 ) = 0.268 ± 0.017,
πh000 = (+0.59 ± 0.20 stat ± 0.48 syst ± 1.06 ext ) × 10 −3 = (+0.59 ± 1.19) × 10 −3

χ 2 / dof = 2805.3 / 2765 (all pixels)
χ 2 / dof = 125.3 / 130 (edge pixels)

2. Floating both h000 and a0−a2:h000 = (−2.09 ± 0.62 stat ± 0.72 syst ± 0.28 ext ) × 10 −3 = (−2.09 ± 0.99) × 10 −3
m + (a0 − a2 ) = 0.215 ± 0.014 stat ± 0.025 syst ± 0.006 ext = 0.215 ± 0.031πχ 2 / dof = 2790.6 / 2764 (all pixels)
χ 2 / dof = 126.3 / 130 (edge pixels)

ChPT (Colangelo et al.): m + ( a0 − a2 ) = 0.265 ± 0.004
π1516Comparison with Other Results}

x 10–3

Ignoredrescattering

17Summary•Rescattering effect observed in KL→3π0•Data well described by model of Cabbibo and Isidori, exceptfor mππ < 0.274 GeV/c2•Measured a0−a2 consistent with but less precise than NA48
measurement in K±→π±π0π0 decays (isospin decomposition
favors K± over K0)•After including rescattering effect, no evidence for nonzero
h000
Results published in E. Abouzaid et al. [KTeV Collaboration],Phys. Rev. D 78, 032009 (2008).