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

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

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

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

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

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

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 x x 10 -5

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)

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

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)

Analysis of K ± e3 Decay DATA 56 hours special run taken in 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

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

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.