1. Progress on BR(K L  p + p - ) using a double-tag method A. Antonelli, M. Antonelli, M. Dreucci, M. Moulson CP working group meeting, 25 Feb 2003

2. Event tag: K S  p + p - vertex Decay tag: 1 track + cluster opposite Vertex not required K L tag Analytic track extrapolation Tag cuts: Track residual Cluster residual p* (CM frame of KL tag) N 1 = 2 e 1 S + B 1 N 2 = e 1 2 (1 -r )S + B 2 S = 4(1 -r )N 1 2 /N 2 e = 2N 2 /[N 1 (1 -r )] Input from MC: Background (B 1, B 2 ) Dominantly from K m3 Shape from MC Sideband/fit normalization Tagging correlation (1 - r ): (1 -r ) = e 2 MC /( e 1 MC ) 2 Analytic cluster extrapolation T0T0 The double-tag method

3. Data and MC samples Data: 5230 dk0 DST’s for 2001-2002 runs total K L tags found 429 pb -1 according to VLAB MC Signal: 500K K S  p + p -, K L  p + p - events generated (cpv_cksh) Equivalent to 338 pb -1 (assuming s f = 3.1 m b) MC Background: 119M K S  p + p -, K L  all events generated (kspcklbc) Equivalent to 166 pb-1 (assuming s f = 3.1 m b)

4. Systematic investigation of track cuts Possible cuts: d PCA distance to tagging line s Extrapolation length FV Fiducial volume L Track length Use these cuts to select the “right” tree for each sign of charge Old method: Impose cuts on d, s, FV, even EmC cuts to make list of candidate trees Choose tree of each charge sign with best value of p* New method: Choose tree with smallest value of d Impose cuts on d, s, FV, L in a fiducial sense Cuts don’t percolate (relaxing cuts doesn’t change trees selected)

5. Track residual cut MC signal events All tag candidates Red: wrong candidates MC signal events Only MC true candidates Contamination in sample of selected trees: Ordering by d:12% Ordering with cuts:8% Significant contribution to resolution on d from angular resolution on p L : 95% inclusive cut for all r (  r xyz ): d < 0.0425r + 0.6 cm

6. Extrapolation length cut Originally motivated to assist in selection of “right” tree Unreconstructed vertices at p - m kinks: p has smaller s Not very powerful Impose as fiducial cut to reduce interference from K S Reduces contamination in sample of selected trees: 8%  5% However, cuts about 10% of single tags MC signal events All tag candidates Red: wrong candidates Same, with cuts on d, FV MC true tags

7. Fiducial volume Define FV to: Exclude regenerations Exclude interference from reentrant tracks from EmC Maintain high, constant reconstruction efficiency Conditional efficiency: 2N 2 /N 1 e FV = 0.2479  0.0006 from MC truth Conditional efficiencies with cuts on d, s, L

8. Track length cut Estimates of d (useful for selecting “right” tag) and p* (analysis variable) degrade with decreasing track length L > 40 cm eliminates 2% of events after FV cut, decreases contamination to 3% For significant effect on tails of p* distribution, a harder cut would be required MC true tags

9. Signal extraction by HMCMLL fit to MC signal + background : Fit parameters: N 1, B 1 Fit interval: |p*| < 30 MeV Statistical error includes MC statistics N 1 = 74462  603 Problems with p* spectrum from MC MC spectra smeared: s = 0.33 MeV Population under(over)estimated at low(high) p* c 2 = 320 for N dof = 148 Solid: MC Markers: data Analysis of single-tag p* spectrum MC signal + background, fit for |p*| < 30 MeV p* (MeV)

10. N 2 = 21544  226 c 2 = 504 for N dof = 398 Analysis of double-tag p* spectrum Fit analogous to single-tag fit No convolution performed Solid: fit Markers: data p 1 * (MeV) p 2 * (MeV) bin

11. MC signal sample: 82978 tagged K L  p + p - in FV 70395 single tags 20465 double tags Tagging efficiency: e 1 = N 1 /2N KLFV = 0.424  0.002 e 2 = N 2 /N KLFV = 0.247  0.002 Correlation: 1 -r = e 2 / e 1 2 = 1.371  0.012 MC efficiencies and correlation Cross checks: Tagging efficiency from “data” e 1 = 2N 2 /N 1 (1 -r ) 0.422  0.006 Conditional tag efficiency: R 21 = 2N 2 /N 1 = e 1 (1 -r ) 0.581  0.003 MC 0.579  0.005 Data Safe systematic error on ( 1-r ): Entire difference in R 21 (0.35%)

12. Summary (stat. error only): N 1 = 3658  123 (210 datarec pb) N 2 = 996  34 (57 datarec pb) 1-r = 1.259  0.012 e tag = 2N 2 /N 1 (1 - r ) = 0.433  0.019 N p+p- = N 1 /2 e tag = 4226  287 N KS = 7441626 e FV = 0.2653  0.0009 f = 0.945  0.002 Single tag6.7% Double tag3.4% Sample correlation - 3.4% Tag correlation0.9% Fiducial volume*0.3% Statistical error6.8% Conditional track efficiency3.8% Tag bias2.8% Fit interval2.0% Resolution MC/data3.0% Systematic error5.9% Total error9.1% BR(K L  p + p - ) for 2000 data (Elba) BR(K L  p + p - ) = fN p+p- /N KS e FV = (2.02  0.19) × 10 -3

13. Summary (stat. error only): N 1 = 74462  603 (173 datarec pb) N 2 = 21544  226 (50 datarec pb) 1-r = 1.371  0.012 e tag = 2N 2 /N 1 (1 - r ) = 0.422  0.006 N p+p- = N 1 /2 e tag = 88192  1788 N KS = 174 383 220 e FV = 0.2479  0.0006 f = not yet evaluated Single tag1.6% Double tag1.0% Sample correlation - 0.8% Tag correlation0.9% Fiducial volume*0.2% Statistical error2.0% Conditional track efficiency0.4% Tag bias? Fit interval? Resolution MC/data? Systematic error? Total error? 2001-2002 estimate of BR(K L  p + p - ) BR(K L  p + p - )/f = N p+p- /N KS e FV = (2.04  0.04) × 10 -3

14. Conclusions Analysis of 429 pb -1 of 2001-2002 data in progress Current statistical error: 2.0% Statistical significance limited to ~160 pb-1 by MC statistics With full MC statistics, statistical error would be well under 1.5% KS cuts to clean up tag bias may hurt statistics by a similar amount Systematics yet to be evaluated MC/data efficiencies agree much better for 2001-2002 (0.4%) data than they did for 2000 data (4%) Serious issues with shape of p* spectrum in MC New, improved MC production may help considerably