A direct search for Ks  3  0 decay at KLOE LNF Spring School Frascati, May 17th-21st, 2004 A direct search for Ks  3  0 decay at KLOE M. Martini, INFN Frascati, for the KLOE collaboration.

KS3p0 All KLOE statistics  0.9 signal events produced (e=100%) This decay has never been observed but is allowed by SM [CP violating, CP(3p0)=-1]. From theoretical point of view: All KLOE statistics  0.9 signal events produced (e=100%) Actually published value: BR(KS3p0) < 1.4x10-5 (SND, PL B459 1999) The observation of this decay would confirm CP violation in KS system. Uncertainty on KS3p0 amplitude limits precision on CPT test (Bell-Steinberger relation). M. Martini, LNF Spring School 2004

KS3p0 KS identification: tagging from KL decay KLCRASH b0.22 KLCRASH (e~30%) This algorithm search KL which interact directly on EMC. KLCRASH calorimetric clusters are selected using energy and b*. High bkg rejection needed: major expected background: KS2p0 (BR31%) + 2 fake photons either from shower fragments or accidental overlap with clusters from machine background. M. Martini, LNF Spring School 2004

Photons counting and Kinematic fit DATA=450pb-1 (2001+2002); MC =540pb-1 (all available statistics) Preselected signal sample (KLCRASH and 6 photons): 39728 events Normalization Sample (KLCRASH and 4 photons): 23.5x106 events -- KS3p0 (MC) -- MC BKG  Data A kinematic fit is applied on the Ks side requiring the conservation of 4-momentum (NDOF=11).  c2FIT c2FIT < 30 is not enough (2/3 of bkg rejected)! Other discriminating variable have to be used: (c22p, c23p) M. Martini, LNF Spring School 2004

The c22p The c22p is built selecting 4 out of 6 clusters which better satisfy the kinematics of KS  2p0 The parameters used are: mass distribution opening angle between pions in KS C.M. frame 4-momentum conservation KLCRASH + 4 photons  DATA -- MC The calibration is done using KS2p0 sample. M. Martini, LNF Spring School 2004

The c23p The c23p is based only on  KS3p0 MC  DATA  MCbg The c23p is based only on the 3 “best reconstructed” pion masses M. Martini, LNF Spring School 2004

DATA-MC comparison We define a signal box and 5 control boxes. c23p M. Martini, LNF Spring School 2004

DATA-MC comparison A small fraction of the background (3%) is constituted by fake KLCRASH (KSp+p-) + KL3p0. Our MC well reproduces such fakes. c23p M. Martini, LNF Spring School 2004

Analysis summary To increase bkg rejection we use these analysis cuts: Track veto: to reject events with tracks coming from IP. DECUT: After finding the four photons satisfying the kinematics of KS2p0, the residual energy of the KS is measured: E(KS) = EKs- Eg 2 bodies decay  E(KS) ~ 0 MeV 3 bodies decay  E(KS) ~ Mp Rejecting events with: DE(KS)<10 MeV M. Martini, LNF Spring School 2004

Candidates We have optimized our analysis cuts looking at MC c22p c23p c2FIT DECUT  DATA  MC c22p c23p e = (22.6±0.8)% We count 4 candidates with 3.2±1.4±0.2 expected by MC N3p ≤ 5.76 @90% CL Folding the proper bkg uncertainty. M. Martini, LNF Spring School 2004

Upper Limit determination We derive from our analysis: This improves of a factor ~100 the previous limit. Using PDG values and our limit: Using this upper limit we can calculate some parameters directly related to CP and CPT test. M. Martini, LNF Spring School 2004

Related parameters M. Martini, LNF Spring School 2004 Our limit can be compared with NA48 No KS single beam: detecting interference term between KSKL in the same final state (proportional to Re(h000) and Im(h000)). 90% CL KLOE Im(h000) Re(h000) KLOE KLOE versus NA48 (hep-ph/0310152) 90% CL Assuming CPT invariance Re(h000)=Re(e). We can calculate the contribution of 3p0 decay at Im(d) (Im(d)000) using unitarity relation: with: M. Martini, LNF Spring School 2004

Related parameters The most conservative approach is to assign a phase to a000 which gives the minimum and maximum values of Im(d)000: Im(d)000 f000 (rad) Since these are 2 opposite values, we obtain a range for |Im(d)|000 @ 90% C.L.: This value is obtained using only unitarity, and increases the precision on CPT test, becoming negligible 3p0 uncertainty. M. Martini, LNF Spring School 2004

Additional information

Good agreement DATA-MC in all the regions The c23p  DATA  MCbg The c23p is based only on the 3 reconstructed pion masses “SPLASH” events Due to DAFNE bkg which satisfy the trigger. Reduced by our Splash Filter: rmean > 70 cm Emean > 70 MeV  DATA  MCbg  KS3p0 MC c2FIT < 30 Good agreement DATA-MC in all the regions M. Martini, LNF Spring School 2004

? DATA-MC comparison M. Martini, LNF Spring School 2004 MCbg In the data, a new category of BKG events (not simulated by the standard Kcrash MC) appears. The simulation takes into consideration only KL decaying after a cilinder bigger than DCH and smears the KL MC direction with the Kcrash resolution observed in data. FAKEKCRA M. Martini, LNF Spring School 2004

The Kcrash fake background A small fraction of the background (3%) is constituted by a fake Kcrash and a KL 3p0 decay. The fake KLCRASH is generated mostly by KS p+p- event, where the pions, spiralizing around the pipe, interact on the quadrupoles creating late clusters in the event. We have add the simulation of these events in the MC and calibrated their quantity. M. Martini, LNF Spring School 2004

DATA-MC “fakes” comparison Comparing events with tracks from IP. EKLCRA b* Outside the KLCRASH b* windows DATA are dominated by fakes In the central band there is also a small percentage of KLCRASH. b*  DATA -- MC Fake EKLCRA  MC fakes only (i.e. no Kcrash)  DATA dominated by fakes  DATA -- MC Fake EKLCRA M. Martini, LNF Spring School 2004

The agreement between DATA and MC is better than 10% in all DATA-MC comparison 23844.9  103.8 24396  156 Cdown 11744.1  74.0 11249  106 Cup 5595.1  51.0 5502  74 CSbox 426.5  14.4 382  19 DOWN 479.8  21.2 493  22 UP 309.5  16.3 337  18 SBOX Nev (MC) Nev (Data) Region The agreement between DATA and MC is better than 10% in all the regions. UP SBOX DOWN Cup CSox Cdown c22p c23p M. Martini, LNF Spring School 2004

Monte Carlo calibration -- DATA -- MC -- KCRAMC -- FAKEKCRA c23p < 3.5 FIT data using shapes from MC: ID(DATA) = a1 ID(MC)+ a2 ID(FAKES) 0.949 0.895 1.002 FAKEKCRA 0.447 0.446 KCRAMC Mean (B) (A) Normalized with the full sample Ng=6 Two different regions used: c23p < 3.5 (A) c23p < 8.8 (B) After removing SBOX M. Martini, LNF Spring School 2004

DATA-MC comparison (I) c23p all c23p > 3.5 c23p < 3.5 c23p< 8.8  DATA -- MC Normalization with the mean values of the coefficients M. Martini, LNF Spring School 2004

DATA-MC comparison (II) c22p all c22p > 40 14<c23p<40 c23p< 14 MC KS  3p0, BR=1.4x10-5 Normalization with the mean values of the coefficients M. Martini, LNF Spring School 2004

The track veto All events with tracks from IP are rejected rPCA < 4 cm ; |zPCA| < 10 cm MC Signal DATA MC bkg c22p all c22p > 40 14<c23p<40 c23p< 14 MC signal, BR(KS3p0)=1.4x10-5 M. Martini, LNF Spring School 2004

The topological DECUT -- MCBG no 2fit cut  MCBG 2fit < 30  MCBG 2fit + TRKveto  MCSIG After finding the four photons satisfying the kinematics of KS 2p0, the residual energy of the KS is measured: E(Ks) = Eks- Eg DECUT < 10 MeV Summarizing: c2FIT<30 TRKveto Sbox M. Martini, LNF Spring School 2004

Syst1 =  9% (Calibration) Analysis efficiency and bkg systematics Analysis step Survived events KLCRASH 5211 ACC 2566 ACC  Sbox 1467 ACC  Sbox  Tr 1429 ACC  Sbox  Tr  DECUT 1426 All cuts 1111 Sample of 10 Kevents KS  3p0 e3p = ( 21.30.7stat 0.3syst ) DATA/MC evaluated in Signal and control boxes varying the cut on the kin. Fit: c2FIT = 500, 400, 300, 200, 100 No dependence observed as a function of this cut Syst.error on BKG Syst1 =  9% (Calibration) Syst2 =  10% (Data/MC) Systot =  14 % M. Martini, LNF Spring School 2004

Optimization of UL We have optimized the UL by MC looking at 4 different parameters: c2FIT c22p (both sides) c23p DECUT Optimization is done by minimizing the expected 90% CL upper limit (ref. J.F.Grivaz, F. Le Diberder LAL 92-37) All is done varying cuts on MC only. The best choice of the cuts is the following (CUTMAX): c2FIT < 31 14 < c22p < 60 c23p < 3.7 DECUT > 37 MeV M. Martini, LNF Spring School 2004

NA48 interference function KL decay KS decay Interference KL-KS K0 K0 Dilution factors M. Martini, LNF Spring School 2004

Related parameters The more conservative approach is to give at a000 a phase which maximize Im(D)000: Because there are 2 opposite values, we obtain a range for |Im(D)|000 @ 90% C.L.: Im(D)000 KLOE Im(D)000 CPLEAR Im(D)pln This value is obtained using only unitarity, and increases the precision on CPT test. Im(D)00 PDG 03 Im(D)+- x10-5 M. Martini, LNF Spring School 2004