Control samples for tracking efficiency Km2 and Ke3 control samples selected without requiring a kink:

0) Tagging -> reconstruction of kaon flight path

1) Km2 : calorimeter cluster E>100 MeV ; Pm from a kinematic fit (Eclu, tclu ,PK ) with

constraints on muon TOF and extrapolation position, Emiss=Pmiss

2) Ke3 : 3 clusters + p0-> gg decay 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(Pm ) = 5 MeV s(Rvtx) = 2 cm background free

s(Pe ) = 20 MeV s(Rvtx) = 2 cm 3% bkg with cuts (or fit)

correction on kink reconstruction efficiency

(data/MC)m2 (data/MC)e2

= 0.952(3)

Km2-Ke3 control samples: momentum resolution

Dp (MeV)

Ke3Km2

Dp (MeV)

RMS = 4.4 RMS = 19.2

Km2 – Ke3 control samples: vtx resolution

DR (cm)

Ke3Km2

DR (cm)

s = 2.2 cms = 2.2 cm

Km2 – Ke3 control samples: efficiencies data/MC

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”)

Ke3Km2

Km2 – Ke3 control samples: efficiencies data/MC

RT RT

θ2xy θ2xy

Ke3Km2

The correction is evaluated in 5x5 bins and folded with Km2 and ke2 spectra

Km2 – Ke3 control samples: further investigations

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 – Pext and trajectory in x-y

Secondary split probability as for K

Km2 control sample: K vs m efficiencies 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”)

RT RT

θ2xy θ2xy

Kaon efficiency muon efficiency

Km2 control sample: K vs m efficiencies 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”)

RT RT

θ2xy θ2xy

muon efficiency kink efficiency

Km2 control sample: K vs m split probabilities 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”)

RT RT

θ2xy θ2xy

Kaon split probability muon split probability

Km2 control sample: m effi vs split A clear correlation is observed between the muon reconstruction efficiency and its splitting probabilityWe 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 )

θ’2xy

Efficiency

split prob

dataMC

K split probabilities: Km2 vs Ke3

data/MC Km2

θ’2xy

data/MC Ke3

θ’2xy

1.054(6) 1.023(24)

Secondary split probabilities: Km2 vs Ke3

θ’2xy

data/MC Km2 data/MC Ke3

θ’2xy

0.975(23)1.068(6)

effi(data)/effi(MC) Km2effi(data)/effi(MC) Ke3

Kaon0.991(2)

secondary0.968(2)

Check with a toy MC25% difference assumed between electron and muon dE/dxuniform cell illumination; 40 hits

R (cm)

Kaon split probabilitys(cm)

muon

electronpull

Check with a toy MCwe assume:- 25% difference between electron and muon dE/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