Bern 7 march CP,T symmetries in K e4 (K ± →  ± e ± ) B. Peyaud CEA/DSM/DAPNIA Bern meeting 7 March 2007

Bern 7 march K e4 charged decays : formalism Cabibbo-Maksymowicz define 5 kinematic variables to described Ke4 decay: s  (M 2  ), s e (M 2 e ), cos  , cos  e and  The form factors of the decay rate are determined from a fit to the experimental data distribution of the 5 variables. Several formulations of the form factors appear in the literature: Pais and Treiman ( Phys.Rev. 168 (1968) ) form factors,  phase shift Lee and Wu ( Ann. Rev. Nucl. Sci. 16 (1966) ) form factors,  phase shift, symmetries Amoros and Bijnens ( J.Phys. G25 (1999) ) form factors,  phase shift dipion dilepton

Bern 7 march d  5 = G F 2 |Vus| 2 N(s ,se) D 5 (s ,s e,  ,  e,  ) ds  dse dcos   dcos  e d  D 5 =I1+I2cos2  e +I3sin 2  e cos2  +I4sin2  e cos  +I5sin  e cos  + I6cos  e + I7sin  e sin  + I8sin2  e sin  + I9sin 2  e sin2  intensity functions I1….I9 depend on 3 Form Factors F1, F2 and F3 I1= 1/2{|F1| 2 +3/2[|F2| 2 + |F3| 2 ] sin2   }I2= -1/2{|F1| 2 -1/2[|F2| 2 + |F3| 2 ] sin2   } I3= -1/2{|F2| 2 - |F3| 2 } sin2   I4= 2Re{F1* F2} sin   I5= -2Re{F1* F3} sin   I6= -2Re{F2* F3} sin2   I7= -2Im{F1* F2} sin   I8= Im{F1* F3} sin   I9= -Im{F2* F3} sin2    15 terms tan(  )= ½ / =2 / D 5 K- = D 5 K+ (s ,s e,  ,  -  e,  +  ) kinematic factors:  = – (PL) Q/ (M 2 √s  ),  = Q√se/M 2 and  = X/M 2 take  pg as phase reference and let  =  sf  pg,  f =  pf -  pg and  2 =  ph –  pg On the s- and p-wave hypothesis F1,F2,F3 are expanded in the form F1=  f s exp(i  +  f p cos   exp(i  f ) +  cos   = gf s exp(i  ) +  cos  {g+  f p /  exp(i  f )} and F2=  g and F3=  ghexp(i  2 ) fs, fp, g, h and  = Pais-Treiman parameterization Partial rates for K ± (p) →  +  - e ± e

Bern 7 march Lee-Wu vs Pais-Treiman amplitudes à la Lee-Wu: if CPT holds:  A =A,  B 0 = B 0,  B + = B -,  B - = B + furthermore                p  s  if CP holds independent of either CPT or T: then  A  A,  B 0 =B 0,  B - =B +,  B + = B -,              →  1 (K + ) =  1 (K - ) and  2 (K + ) =  2 (K - ) if CPT        p  s if T holds independent of either CPT or CP : then        p  s →  1 =  2 = 0

Bern 7 march K e4 amplitudes and phases without T, CP violation fsfs gpgp fpfp fp/fp/ g’ p hphp  K-K- CP CPT T fsfs gpgp fpfp fp/fp/ g’ p hphp  K+K+

Bern 7 march K e4 amplitudes and phases with T and CP violation fsfs gpgp fpfp fp/fp/ g’ p hphp  ff 11 22 ff K+K+ fsfs gpgp fpfp fp/fp/ hphp   f  1  2  f K-K- / CPCPT / T  1 (K - ) = -  1 (K + ) and  2 (K - ) = -  2 (K + )

Bern 7 march Standard Ke4 parameters g=0.92, g’ =0.84, h =0.37, a00=0.25,  1 =0,  2 =0 Sensitivity to  1 Variation of fit parameters operates on Ji The 5d shape decay rate is distributed ~ bins Sensitivity to 

Bern 7 march LogJiBi T violating amplitude J 13 B 13 for  fp = Phase of fp LogJiBi J 13 B 13 = O(10 -3 ) this is a Monte Carlo exercise

Bern 7 march 20079

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Bern 7 march Summary NA48/2 sensitivity to T violating phases  1,2 is unique: statistics + both K + and K - Our K e4 samples total ~10 6 K + and K - i.e. x20 larger than those of the last experiment with 3559 K+ and 3311 K-… E.W. Beier et al. PRL 29, 8(1972)  signal of T and CP violation is at reach … Question to theorists:  1(fp)  2(h) phases within SM and beyond? Excerpt from Lee Wu paper Ann. Rev. Nucl. Sci. (1966): … it seems reasonably certain that some violation of time reversal invariance should be present in these weak decays (Ke4), but the degree of such violation remains unclear.