1. 1 Measuring Im( t ) using K S - K L Interference in  0 e + e - Hogan Nguyen Fermilab November 10 th, 2009 Project X Physics Workshop Work presented here can be found in FERMILAB-TM-2438-PPD

2. 2 Motivated by NA48 Discovery of K S   0 e + e - in 2003 and the realization that K L   0 e + e - is dominated by indirect and direct CP violation K L ~  K 1 + K 2 0e+e-0e+e- Indirect CPV Direct CPV CP Conserving CP Conserving Term is Small (helicity suppression) Direct CPV gives access to Im( t ), where t = V ts *V td Indirect CPV Term can be calibrated from K S   0 e + e -, up to a sign ambiguity. Take advantage of K S -K L interference from target K 0 ’s to amplify the Direct CPV term

3. 3 From NA62 Physics-Handbook: Christopher Smith

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6. 6 Some Formulas NA48 Discovery Phys. Lett. B576,43 (2003) Im( t ) in units of 10 -4 Sign of A S must be determined via other methods: 1. Theory 2. K L   0  0 l + l - 3. Lepton energy Asymmetry in K L   0  +  - F. Mescia, C. Smith, S. Trine, JHEP 08 (2006) 088.

7. 7 Rate of  0 e + e - from target K 0, K 0 incoherent with respect to each other. Pure K L Interference Term affecting K S term Number of  S lifetimes from target Non-resonant K L  ee Interference Term D is the dilution factor. For very high energy protons, D = 0.3.

8. 8 For T p ~2.1 GeV, D ~ 1 (pure K 0 ). N. Mokhov

9. 9 The Sign of A S is very important Im( t )/A S = -1.3/1.06 Im( t )/A S = +1.3/1.06 Im( t ) = 0 Im( t ) in units of 10 -4 For Im( t )/A S = +1.3/1.06 there is a great loss of resolution in extracting Im( t )

10. 10 Fit Results for Im( t ) for D = 1.0 (pure K 0 ) N(6  S <  < 16  S ) Fitted Im( t ) Fit Error 25K 1.14 0.10 100K 1.26 0.05 400K 1.29 0.02 25K (D=0.3) 0.97 0.22 Simple  2 fit biases Im( t ) Have not studied fit biases Input in MC generator Im( t ) = 1.3 (units of 10 -4 ) A S =  1.06 Perfect Detector Dilution = 1.0

11. 11 Very Rough Beam Rate Estimates T p = 2.6 GeV P K = 300 MeV - 1000 MeV Acceptance Angle Range = 17  to 23  ~ 3 x 10 -4 K 0 ’s produced per incident proton onto deuterium (from N. Mokhov’s study) Using only  > 6  S rejects all but 0.25% of K S Realistic detector acceptance ~ 5% (KTeV) ? BR( K S   0 e + e - ) = 5.8 x 10 -9 Useable K 0 Yield per incident 2.6 GeV proton onto deuterium (3 x 10 -4 ) x (2.5 x 10 -3 ) x (0.05) x (5.8 x 10 -9 ) = 2.17 x 10 -16 Number of Protons Error on Im( t ) 1.15 x 10 23 0.10 4.60 x 10 23 0.05 Detector Length Considerations (c  S = 2.6 cm) P K (GeV)   Z(6  S ) Z(16  S ) 0.3 0.51 1.17 18.3 cm 48.6 cm 1.0 0.89 2.23 34.7 cm 92.7 cm A very compact detector 10 -3 interaction length gas target

12. 12 Other Nice Things about K S - K L  0 e + e - interference - Fully Constrained Decay - An Open Geometry Detector - More forgiving in accidentals -  0 is really tough. We will need confirmation from other modes More realism needed - in practice, we may not know the dilution very well. We have to extract from data using other means (K2pi decays)