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Investigations of Semileptonic Kaon Decays at the NA48 Еxperiment Milena Dyulendarova (University of Sofia “St. Kliment Ohridski”) for NA48 Collaboration

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Outline of the Talk Theoretical Description NA48 Experiment Analyses of K L →π e ν e (K 0 e3 ) decay modes NA48/2 Experiment Analysis of K ± e3 decay Conclusion

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Theoretical Description Dalitz plot density: where m K - mass of particle i, E * i – energy of i in CoM (center of mass); f S, f V (f + and f - ), f T - scalar, vector and tensor form factors. - four momentum transferred to the lepton pair; The vector form factors can be approximated by Taylor expansion with

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NA48 Experiment Simultaneous near collinear beams of K L and K S with average energy ~110 GeV Designed for measurement of direct CP-violation in the K 0 system

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NA48 Experiment - Detector System Magnet Spectrometer (two drift chambers DCH before and two DCH after the magnet spectrometer) Hodoscope CHOD (time resolution – 200 ps per track) Homogenous electromagnetic calorimeter LKr Hadron calorimeter HAC Muon veto system MUV

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K L →π e ν e (K 0 e3 ) Analysis Experimental data Special run with K L beam - September (1999) ~ 2 TB data recorded 5.6 million K 0 e3 events were selected and analyzed. MC simulation The detector performance is simulated by GEANT package. The radiative corrections in (virtual and real) were generated by PHOTOS routine. Basic Selection Criteria Two tracks with different charges coming from a common vertex Vertex located in the decay region Tracks in detector aperture Time difference of the tracks

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K 0 e3 Analysis (continued) Minimal momentum of each track p min = 10 GeV Minimal distance between tracks Identification of the particles in the final state 0.93 < E/p < 1.1 for one of the tracks (e ± ) & E/p < 0.9 for the other one (π ± ) No MUV signal around the event time (± 6 ns) Background BgK µ3 K3πK3π K e4 K e3 (misidentification) <1 x 10 -4 3 x 10 -5 2 x 10 -5

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Experimental Results for K 0 e3 Assuming only V-A couplings: the linear dependence of the K 0 e3 vector form factor on q 2 is: in addition a quadratic term is admitted: Admitting scalar and tensor couplings in addition to V-A currents linear slope of the f + (q 2 ): and the following form factor values: polar parametrization : K * (892)

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World results NA48: f S /f + (0) < 0.028 f T /f + (0) < 0.09 PDG: f S /f + (0) < 0.04 f T /f + (0) < 0.23

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NA48/2 Experiment – Charged Beam Formation Simultaneous K + and K - beams with average energy ~ 60 GeV Two achromat systems – two dipole magnets with opposite polarities Kaon Beam Spectrometer (KABES)

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Analysis of K ± e3 Decay DATA 56 hours special run taken in 2002. About 4 million K ± e3 events were selected. MC The NA48/2 detector response is simulated by MC program based on GEANT. The radiative corrections in K ± e3 were generated by using Ginsberg and PHOTOS routine. Basic Selection Criteria 1 charged track forming a vertex with the z-axis Vertex in decay region Detector geometry acceptance Minimum momentum of the P tr > 5 GeV e ± and 0 identification Event in Dalitz plot region

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Analysis of K ± e3 Decay Background Reducing main K 0 background - region excluded: 55 GeV < E K < 65 GeV 234 MeV < E* < 264 MeV M K 12 MeV around the PDG value Comments Summing all sources the systematic error is less 1% (maximal possible value) The systematic uncertainty is < 0.5% Dalitz plot distribution from Ginsberg+PHOTOS simulation

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Conclusion The K 0 e3 results are in agreement with the linear approximations tested in former experiments. The slope in the vector form factor is measured with a high precision The scalar and tensor form factors are consistent with zero, the measurement is the most precise up to now The results are consistent with a lack of quadratic term in the vector form factor, and at the same time consistent with a Taylor expansion of a pole- dominance form factor with a pole mass of M V =859±18 MeV. K ± e3 decay mode is under detailed investigation.

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