1. Search for CP violation in  decays R. Stroynowski SMU Representing CLEO Collaboration

2. Symmetry The word “symmetry” derives from greek “  ” (same measure, Polykleitos 5 th century BC describing left and right sides of animals). In Physics, it describes an invariance under a set of transformations. Continuous symmetries: Translation invariance (homogeneity of space) Rotation invariance (isotropy of space) Boost invariance (special relativity) Discrete symmetries Space reflection(Parity, P)(x,y,z)  (-x,-y,-z) Particle-antiparticle symmetry (Charge conjugation, C) Time reversal (T) t  -t

3. P and C is separately violated in weak interactions. The violation is maximal CP describes particle-antiparticle symmetry. In relativistic Field Theory CPT theorem implies that CP is equivalent to T

4. Motivation Particle physics CP violation has been observed in the quark sector where it is due to the structure of the quark mixing matrix. Recent observation of neutrino oscillations imply existence of the neutrino mixing matrix and thus allow for a possible CP violation in the neutrino sector. Is the analogous mixing matrix exist in the charged lepton sector it must be mostly diagonal, since there are strict limits on the lepton number violating decays. Such matrix – if it exists – could also lead to CP violation. Many extensions of the Standard Model allow for the CP violation in the lepton sector.

5. Cosmology The expectation that Big Bang should result in a symmetry between matter and antimatter is not confirmed by the astronomical observations. The electron-positron annihilation line is not observed at the rate expected even for the widely separate clumps of matter and antimatter. Thus the initial symmetry is violated. Although it is possible to ascribe this as due to initial condition, it would be much more elegant to describe it as due to observable processes. CP violating decays are natural candidates for such processes. CP violation has been observed in weak decays of s and b quarks but its magnitude is insufficient to explain cosmological problems.

6. CP Violation If CP symmetry is exact than there is no difference between a given process and its CP-conjugated one. CP violation generates a difference between the partial decay widths. Any kinematical variable associated with the decay can be described as a sum  even  odd with the corresponding probability density P=P even +P odd For CP violation expect <  #0. Expected deviation is small  must optimize choice. Atwood and Soni: smallest statistical error for  =P odd /P even  must have a model for P  deviation from zero independent of the model, but interpretation of the value (limit) is model dependent.

7. Procedure: select the model, e.g., multi-Higgs-doublet-model Grossman (1994), Weinberg ((1976),Grossman,Nir,Ratazzi (1997) calculate matrix element construct CP-odd observable Two decay modes with similar sensitivity to new physics:      Scalar coupling suppressed by isospin   K   W coupling Cabbibo suppressed

9. Need 3 vectors to construct CP-odd variables For      use spin correlations for tau pairs each decays decaying to the same final state  direction reconstructed with 2-fold ambiguity  use both solutions and study the bias Vector formfactor approximated by  (770) Breit-Wigner Scalar formfactor: 1, a 0 (980), a 0 (1450)

10. Analysis Use 13.3 fb -1 of CLEOII data (12.2 x 10 6     pairs) Standard CLEO selection criteria to reconstruct signal Background estimate (9.9%) from MC and from the data  Dominant background from other  decays. f s =1 f s =a 0 (980) f s =a 0 (1450) Shape depends on formfactor NO ASYMMETRY

11. Estimate of limits for Im(  ) is model dependent. Since all odd powers of Im(  ) are allowed, Monte Carlo calibration method is used to extract the limits. Results depend also on the choice of the formfactor. f s Im(  ) 1-0.0008+/-0.0014-0.012+/-0.021 ao(980)-0.0006+/-0.0024-0.001+/-0.004 a 0 (1450) 0.0002+/-0.0017 0.001+/-0.012 Systematics: 2-fold ambiguity in reconstructing  direction, background contribution to the asymmetry, tracking   Im(  )=0.003 Result: Limits on scalar coupling constant -0.046<Im(  )<0.022 at 90% CL

12. Search for CP violation in   K 0   decays Single  decays  spin averaged terms only No  direction reconstruction P 2 ~ |f v | 2 (2(qQ)(kQ)-(kq)Q 2 ) + |  | 2 |f s |2(qk) + 2Re(  )Re(f s f v * )m  (Qk) – 2Im(  )Im(f s f v * )m  (Qk) q -  four-vector, k – four-vector, Q 2 = 2m  2 +2m K 2 -[m had 4 +(m  2 -m K 2 ) 2 ]/m had 2 Obtain (qQ),(kQ),(qk) from experimentally measured parameters using prescription by Kuhn and Mirkes Use fv=BW (K*(890)) and fs=BW(K*(1430))  = P odd /P even

13. Analysis CLEOII data - 13.3 fb -1. signal:   K 0 s  with K 0 s   +  - tag:   single prong, i.e., l l , h(  0 )  background: (41.3%): other  decays+ small qq contribution 11970 events K*(890) peak with 4.7+/- MeV mass shift no evidence for scalar K*(1430)

14. Results Data Monte Carlo with Im(  )=1 Expect enhancement due to K(890)-K(1430) interference Systematics: background studied via Monte Carlo tracking efficiency scalar form-factor parametrization Overall multiplicative error - 15%

15. Results No CP violation observed In the range: 0.85 GeV/c 2 < M(K  ) < 1.45 GeV/c 2 = -2.0+/-1.8 x 10 -3 Im(  ) = (-0.046+/-0.044+/-0.019)(1+/-0.15) -0.172 < Im(  ) < 0.067 at 90% CL

16. Summary No CP violation has been observed      : -0.046 < Im(  ) < 0.022 at 90% CL   K   : -0.172 < Im(  ) < 0.067 at 90% CL      provides most restrictive limit on Im(  )   K   provides a limit on the lightest of charged Higgs in MHDM m H > 2.1 GeV/c 2