Control samples for tracking efficiency

1. Km2 and Ke3 control samples selected without requiring a kink: 0) Tagging -> reconstruction of kaon flight path Km2 : calorimeter cluster E>100 MeV ; Pm from a kinematic fit (Eclu, tclu ,PK ) with constraints on muon TOF and extrapolation position, Emiss=Pmiss Control samples for tracking efficiency s(Pm ) = 5 MeV s(Rvtx) = 2 cm background free 2) Ke3 : 3 clusters + p0-> ggdecay vertex along the kaon decay path; Pe from a kinematic fit (Eclu, tclu , RVTX , PK ) with constraints on E/P, electron TOF and extrap. point, Emiss=Pmiss s(Pe ) = 20 MeV s(Rvtx) = 2 cm 3% bkg with cuts (or fit) correction on kink reconstruction efficiency (data/MC)m2 = 0.952(3) (data/MC)e2

2. Km2 Ke3 RMS = 4.4 Km2-Ke3 control samples: momentum resolution RMS = 19.2 Dp (MeV) Dp (MeV)

3. Km2 Ke3 Km2 – Ke3 control samples: vtx resolution s = 2.2 cm s = 2.2 cm DR(cm) DR(cm)

4. Data/MC effi ratios as a function of the kaon decay vtx position RT and decay angle θ2xy in the transverse plane (θ2xy > 0 “fish configurations”) Km2 Ke3 Km2 – Ke3 control samples:efficiencies data/MC

5. The correction is evaluated in 5x5 bins and folded with Km2 and ke2 spectra Km2 Ke3 θ2xy θ2xy Km2 – Ke3 control samples:efficiencies data/MC RT RT

6. We reproduced a fraction (25%) of the ntuples adding all track info (tough work!) This allows us to compute efficiencies separately for kaon and secondary track Matching of the kaon track is performed by requiring both first and last hits to be consistent with the estimated kaon trajectory; K split probability is defined as N(K>=2)/N(K>=1) Matching of the secondary is performed by using Pmeas – Pextand trajectory in x-y Secondary split probability as for K Km2 – Ke3 control samples:further investigations

7. We compute separately kaon and muon efficiencies (no kink required) as a function of the kaon decay vtx position RT and the decay angle θ2xy in the transverse plane (θ2xy > 0 “fish configurations”) muon efficiency Kaon efficiency Km2 control sample: K vsmefficiencies θ2xy θ2xy RT RT

8. We compute separately kaon and muon efficiencies (no kink required) as a function of the kaon decay vtx position RT and the decay angle θ2xy in the transverse plane (θ2xy > 0 “fish configurations”) kink efficiency muon efficiency Km2 control sample: K vsmefficiencies θ2xy θ2xy RT RT

9. We compute separately kaon and muon efficiencies (no kink required) as a function of the kaon decay vtx position RT and the decay angle θ2xy in the transverse plane (θ2xy > 0 “fish configurations”) muon split probability Kaon split probability Km2 control sample: K vsmsplit probabilities θ2xy θ2xy RT RT

10. A clear correlation is observed between the muon reconstruction efficiency and its splitting probability We project orthogonal with respect to the direction of the dip in the RT - θ2xy spectrum of the muon split probability (θ’2xy in the following ) Km2 control sample: meffivs split Efficiency data MC split prob θ’2xy

11. data/MC Km2 data/MC Ke3 K split probabilities: Km2 vs Ke3 1.054(6) 1.023(24) θ’2xy θ’2xy

12. data/MC Km2 data/MC Ke3 1.068(6) 0.975(23) Secondary split probabilities: Km2 vs Ke3 θ’2xy θ’2xy effi(data)/effi(MC) Km2 Kaon 0.991(2) secondary 0.968(2) effi(data)/effi(MC) Ke3

13. 25% difference assumed between electron and muondE/dx uniform cell illumination; 40 hits s(cm) Kaon split probability Check with a toy MC muon electron pull R (cm)

14. we assume: • - 25% difference between electron and muondE/dx • - uniform cell illumination; 40 hits • - kink finding algorithm search for deviations in the pull distribution along the track • a 30% worse resolution for the secondary when crossing the kaon track (“fish”) • the same expected resolution is used to normalize the pulls • the toy MC gives: • a X2 enhancement of the splitting probability in the “fish configuration” • A ~10% difference in the splitting prob between electrons and muons Check with a toy MC