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Bern 7 march 20071 CP,T symmetries in K e4 (K ± → ± e ± ) B. Peyaud CEA/DSM/DAPNIA Bern meeting 7 March 2007

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Bern 7 march 20072 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

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Bern 7 march 20073 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

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Bern 7 march 20074 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

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Bern 7 march 20075 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+

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Bern 7 march 20076 K e4 amplitudes and phases with T and CP violation fsfs gpgp fpfp fp/fp/ g’ p hphp ff 11 22 ff 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 + )

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Bern 7 march 20077 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 ~ 30000 bins Sensitivity to

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Bern 7 march 20078 LogJiBi T violating amplitude J 13 B 13 for fp =0.2 13 12 Phase of fp LogJiBi J 13 B 13 = O(10 -3 ) this is a Monte Carlo exercise

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Bern 7 march 20079

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Bern 7 march 200711 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.

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