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Scattering Lengths and Decays: NA48/2 Experiments on Kaon Ke4 and 3p Decays

Explore NA48/2 experiment findings on Kaon decays, including preliminary results, form factor fits, cusp evidence, and comparisons, presented at HADRON07. Discussion includes data analysis, interpretations, fits to data, and conclusions drawn from the research. The NA48/2 detectors, selection criteria, and kinematics variables for Ke4 decays are emphasized in the presentation. The presentation also covers the pp scattering lengths and their relation with data findings. Concluding remarks highlight the agreement between NA48/2 results and provide insights into the observed phenomena.

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Scattering Lengths and Decays: NA48/2 Experiments on Kaon Ke4 and 3p Decays

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  1. ppscattering lengths from Kaon Ke4 and 3p decays by NA48/2 M.Lenti INFN Sezione di Firenze On behalf of the NA48 collaboration HADRON07, Frascati 8-13 October 2007

  2. Plan of the presentation • The NA48/2 experiment • The Cusp (K±→p±p0p0) - Data 2003+2004: preliminary results - p+p-→p0p0 rescattering • Ke4 (K±→p+p-e±n) - Data 2003: preliminary results - Form factors fits • Conclusions HADRON 07

  3. The CERN NA48/2 experiment 7×1011ppp SPS protons at 400 GeV/c Kaon beam at 60±3 GeV/c momentum K+/K-~1.8 HADRON 07

  4. The NA48 detectors • 2003 run: 50 days • 2004 run: 60 days • 1997-2001: NA48 KLKS (e’/e) • 2002: NA48/1 KS • 2003-2004: NA48/2 K± (Dg) • 2007: NA62 K± (Ke2/Km2) • 2011: NA62 K+→p+nn K± HADRON 07

  5. K±→p0p0p±:selection • 1 tracks, 4 e.m. Clusters • clusters pairing: all possible combinations (3) • p0→gg vertex by imposing p0 mass • choose combination with closest vertices • K decay vertex: average of p0vertices • Calculate p0p0 invariant mass p0p0 inv.mass resolution 3p invariant mass (2004) HADRON 07

  6. Cusp evidence 2004: 43.6 M events 2003: 16.0 M events Change of slope at the p+p-threshold HADRON 07

  7. + K+ 0 0 N.Cabibbo, PRL 93 (2004) 121801 Cusp interpretation: 1 Loop No M1 amplitude M1 amplitude present:13% depletionunder the threshold HADRON 07

  8. N.Cabibbo and G.Isidori, JHEP 503 (2005) 21 Cusp interpretation: 2 Loops • All 1- and 2-loops rescattering processes • 5 S-wave scattering lengths expressed as linear comb. of a0 and a2 • Isospin symmetry breaking effect in • No radiative corr. : 5% precision on a0-a2 Subleadingeffect No rescatteringamplitude Leading effect M2(00), (GeV/c2)2 HADRON 07

  9. Cusp: fit to the data 5 parameters fit (g, h’, m+(a0-a2), m+a2, N) 7 bins excluded from the fit 2003+2004 data HADRON 07

  10. Cusp: results (1) HADRON 07

  11. Cusp: result (2) HADRON 07

  12. Ke4 (K±→p+p-e±n): selection • 3 tracks • missing energy and pt • E/p for electron PID Background estimated from Wrong sign events: 0.5% level 440000 from K+ 240000 from K- 2003 data set HADRON 07

  13. Ke4: kinematics variables Decay amplitude described by two axial (F, G) and one vector (H) form factors which can be partial wave expanded (s and p wave; d neglected): and further expanded in powers of q2: HADRON 07

  14. Ke4: form factors fit Fs, Fp, Gp, Hp and d are extracted from a fit to 10(Mpp)×5(Men)×5(cosqe)×5(cosqp)×12(f) = 15000 equi-populated bins • Data - MC Men(GeV/c2) Mpp(GeV/c2) • • K+ • K- cosqp cosqe f(rad) HADRON 07

  15. Ke4: form factors fit HADRON 07

  16. Ke4: fit results Preliminary (2003 data) HADRON 07

  17. Ke4: d dependence Use Roy equations in order to relate the d variation and the pp scattering lengths The Universal band center line parametrization corresponds to a 1-parameter fit with a fixed relation between a2 and a0 HADRON 07

  18. Ke4: pp scattering lengths HADRON 07

  19. Cusp and Ke4: comparison HADRON 07

  20. Conclusions • Preliminary 2003+2004 measurement of a2-a0 in 3p decay presented • Preliminary 2003 measurement of a2, a0 and form factors in Ke4 presented • General agreement between the NA48/2 results above HADRON 07

  21. Spare Slides HADRON 07

  22. Only s-wave possible Preliminary 2003+2004 40000 evts, bck 2-3% HADRON 07

  23. Dalitz plot slopes of K±→p±p0p0 HADRON 07

  24. Dalitz plot slopes of K±→p±p+p- HADRON 07

  25. Ke4: Transition Amplitude HADRON 07

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