For Publisher's use AND DECAYS P. DEBU. DSM/DAPNIA, CEA Saclay, F Gif-Yvette cedex, France.

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1 RECENT EXPERIMENTAL RESULTS ON CP VIOLATING AND RARE K AND DECAYS P. DEBU DSM/DAPNIA, CEA Saclay, F Gif-Yvette cedex, France pdebu@cea.fr Results on rare K and decays obtained since 1998 are summarized. Forthcoming projects are mentioned. Emphasis is put on CP violation. 1 Introduction In the past two years, an impressive amount of experimental results in the K and sectors have been obtained. They cover direct CP violation, CP violating and related rare decays, searches for T violation and for Lepton Flavor Violation. In addition, several very challenging projects are in preparation, and those will also be mentioned in this report. 2 Direct CP violation In the Standard Model (SM) with three quarks and leptons families, CP violation arises through one unique complex parameter in the Cabbibo Kobayashi Maskawa (CKM) quark mixing matrix 1. It allows to accomodate CP violation in the K 0 K 0 mixing, and naturally induces direct CP violation in K! 2 decays. However, the I = 1/2 rule damps the eect, since CP violation in the S = 1 transitions arises from a phase difference between = 1/2 and I = 3/2 decay amplitudes. Direct CP violation in K! 2 decays is parametrized by 0. The theoretical estimate of 0 basically needs three ingredients : The value of the CKM matrix elements combination Im(V td V ts), which isconstrained by the measurements of, the charmless B decays branching ratio, the b! c branching ratio, and the mass difference of neutral B mesons. The resulting relative uncertainty on 0 is of order 15 %. The calculation of the short distance part of the dominant so-called penguin diagrams responsible for direct CP violation has been made at the Next to Leading Order in pertubative QCD. Uncertainties on the t quark mass and on the strength of the QCD coupling constant lead again to a 15 % uncertainty on 0. The uncertainties coming from the Long Distance contributions are fully dominating, the eect being enhanced by a partial cancellation between the electroweak and the gluonic penguin diagrams. Many theoretical groups present results based on the Wilson expansion of the K! 2 amplitude : <jljk 0 >= P 10 i=1 C i()q i () where the Q i 's represent the contributions from 10 eective 4 quark operators, and the C i 's are the Wilson coecients, being the scale at which the C i 's are evaluated. Dierent methods are used to estimate the Q i 's. In principle, calculation on the lattice should be the most satisfying one, but, at present, one of the major contributions, the gluonic penguin operator Q 6, cannot be extracted. Values for 0 = range from small negative values up to.003 or even higher 2. Even though the magnitude of 0 is dif- cult to predict, direct CP violation is naturally present in the standard model. Given the fundamental nature of this symmetry ichep2000: submitted to World Scientic on October 17,

2 breakdown, experimentalists have been trying to establish the existence of direct CP violation for more than two decades. A rst evidence was reported in 1988 by the NA31 collaboration at CERN, which published in 1993 its nal result 3 : 0 = =(23:0 6:5) 10 ;4. Just before, the E731 experiment at FNAL had reported 4 : 0 = =(7:4 5:9) 10 ;4. The NA48 experiment at CERN, E832 at FNAL, and KLOE at Frascati were launched to resolve this ambiguous situation. The basic principles of NA48 and E832 rely on the direct measurement of the double ratio R : R= ;(K L! 0 0 )=;(K S! 0 0 ) ;(K L! + ; )=;(K S! + ; ) =1; 6 Re( 0 =) The use of simultaneous "K L " and "K S " beams reduces systematic uncertainties from K uxes, detector ineciencies, acquisition dead time, losses of events duetoaccidental activity, calibration drifts. High performance data acquisition systems, of order 100 Mbyte/s, allow the recording of several 10 7 K! 2 decays and many more 3 body decays for monitoring and calibration purposes. Most of the background from K L decays is identied with a high resolution spectrometer and a precision electromagnetic calorimeter in both experiments. The comparison of charged and neutral decay rates at a precision below10 ;3 requires a precise matching of the energy scales between both decay modes. This is the most challenging constraint. It lead to the construction of high resolution, linear, ne grain calorimeters. The absolute energy scale for 0 0 decays is xed by the reconstruction of the leading edge of the vertex distribution of K S! 0 0 decays, which is precisely dened by the position of a converter followed by a scintillating counter which denes the beginning of the ducial decay region. Because of their very dierent lifetimes, the vertex distribution of K L and K S decays are not similar. To account for the resulting detector acceptance bias, the E832 collaboration uses a very detailed Montecarlo simulation of their setup. The quality of the simulation is checked by producing pseudo experimental Ke3 and K L! 3 0 decays and comparing the energy and vertex distributions to those of corresponding very large data samples. NA48 uses a dierent technique : they weight K L decay events so that their longitudinal vertex distribution is similar to that of K S decays, reducing to less than 3 10 ;3 the acceptance correction, due to a simple geometrical eect induced by the relative positions and divergences of the K L and K S beams. In 1999, both groups published a result with their rst recorded data : E832 5 : 0 = = (28:0 4:1) 10 ;4 NA48 6 : 0 = = (18:5 7:3) 10 ;4 establishing direct CP violation. The signicance of these results is however impaired by the marginal agreement ofthevarious measurements. The world average reads (21:2 2:8) 10 ;4 with a 2 of 8.4 for three degrees of freedom. This corresponds to a 4 % condence level. In february 2000, NA48 announced a new preliminary result 7 with data taken in 1998 : 0 = =(12:24:9)10 ;4, leading to the combined NA48 0 = = (14:0 4:3) 10 ;4 and the new world average of 0 = =(19:22:5) 10 ;4 and 2 =dof = 10:4=3 (1.5 % CL). Figure 1 shows the spread of those recent measurements. E832 did not present anewvalue, but have measured the charged ratio ;(K L! + ; )=;(K S! + ; ) to be consistent with their published measurement. They have improved the detector simulation, and this reduces signicantly the systematic uncertainty in the acceptance correction in the charged mode, where a slight discrepancy between data and Montecarlo had been found in the vertex distribution of K L! + ; events. ichep2000: submitted to World Scientic on October 17,

3 ε, /ε Gibbons 1993 (E731) Barr 1993 (NA31) Alavi-Harati 1999 (KTeV) Fanti 1999 (NA48) E731 : ( 7.4 ± 5.9) 10-4 NA31 : (23.0 ± 6.5) 10-4 KTEV 99 : (28.0 ± 4.1) 10-4 NA48 99: (18.5 ± 7.3) 10-4 NA48 00: (12.2 ± 4.9) 10-4 NA (prel.) NA48 combined: (14.0 ± 4.3) Figure 1. Recent = results. From data to be analysed, E832 and NA48 will be able to signicantly improve the precision on 0 =. One can hope that this will clarify the present situation. The KLOE experiment at Frascati has started taking data in 1999.! K L K S decays at rest are used to measure 0 = and most of the other phenomenological parameters of the K 0 K 0 system. Given the present luminosity of DANE of about cm 2 s ;1, their objective is to collect the equivalent of1pb ;1 in ayear and reach 10 ;3 precision on 0 =. One can notice that the observed direct CP violation in neutral K to 2 decays is somewhat large. Non Standard Model contributions might be present,and itisimpor- tant to try to search for such new eects. The NA48 collaboration proposes 8 to search for a dierence in the Dalitz plot slope parameters of K +! + + ; and K ;! ; ; + decays with simultaneous K + and K ; beams. Many other measurements can be made with these beams, in particular the study of Ke4 decays. in the nal state of the K! + ; decay. For K L,theinterference of those amplitudes leads to a CP violating polarization of the and to a T-odd term in the dierential decay rate : d;=d=; 1 cos 2 +; 2 sin 2 +; 3 sin 2 where in the angle between the and ee decay planes. The asymmetry parameter A is dened by : A = N(sin 2 > 0) ; N(sin 2 < 0) N(sin 2 > 0) + N(sin 2 < 0) It has been measured by the KTEV collaboration 9 : A =(13:6 2:5 1:2)%, in full agreement with the expectation of 14.4 % from CP violation in K 0 K 0 mixing 10. For K S, the decay is fully dominated by the CP conserving radiative 2 decay, and no signicant asymmetry is expected. The rst observation of the K S! + ; e + e ; decay has been made by NA48 11 : BR(K S! + ; e + e ; )=(5:1:9:3)10 ;5 (prelim.). Figure 2 shows the signal seen in the 1998 and 1999 data. The observed asymmetry is consistent with 0 within a few %. 3.2 K L! 0 e + e ; Direct CP violation can be searched for in K L! 0 e + e ; decays. However3contributions have to be disentangled. The CP conserving one from the 0 intermediate state, the K S π + π - e + e - signal 924 events 3 CP violation and related K decays 3.1 K! + ; e + e ; Like the K! decay, K! + ; e + e ; can proceed through the direct emission of a virtual or the radiative emission by one pion K L π + π - π 0 e + e - (γ) Figure 2. The observation of K S! + ; e + ; e by NA48. ichep2000: submitted to World Scientic on October 17,

4 indirect CP violating one from the K 1 component of the K L state, and the direct CP violating part. The study of K L! 0 decay is used to estimate the rst part. KTEV has published 12 : BR(K L! 0 ) =(1:68 :07 :08)10 ;6, and a V = ;:72:05:06, where a V is the eective vector coupling not accounted for in Chiral Perturbation Theory (P T ) 13. The new NA48 preliminary result is 14 : BR(K L! 0 ) =(1:51 :05 :20) 10 ;6. The indirect CP violating contribution is estimated by using the measured K +! + e + e ; BR and using isospin invariance, but this procedure has large theoretical uncertainties. An improved limit on, or a measurement of, BR(K S! 0 e + e ; ), would x this part. NA48 plans to search for this decay with a 6 10 ;10 SES per year in a dedicated run with a high intensity K S beam. Such a run would allow in addition a measurement of 000 with O(10 ;2 ) precision 15. During a 2 days test run in 99, NA48 already performed a search for K S! 0 e + e ;. They reported 16 a 90 % CL limit on the BR of 1:6 10 ;7, a factor of 10 improvement over the previous limit. The measurement of BR(K L! 0 e + e ; ) is limited by the background from K L! e + e ;. This decay iswell measured by KTEV (BR(K L! e + e ;, E > 5MeV)=(6:31 :14 :43) 10 ;7 (prelim.) 17 ) and NA48 (BR(K L! e + e ;, E > 5 MeV) = (6:32:31:20 :29(normalization)) 10 ;7 (prelim.) 18 ), in good agreement with the Standard Model prediction. The important variables to discriminate 0 e + e ; and e + e ; decays are the angle between the 's in the 0 rest frame and the smallest angle between one and one electron, which should be smaller for the e + e ; decay. In the 1997 data, KTEV nds 2events for 1.1 expected background, leading to the 90 % CL limit 19 : BR(K L! 0 e + e ; ) < 5:1 10 ;10. Plots in gure 3 show m versus m γγ in GeV/c 2 m γγ in GeV/c m eeγγ using m γγ =m π0, in GeV/c m eeγγ assuming m γγ =m π0, in GeV/c 2 Figure 3. KTEV search for K L! 0 e + e ; (see text). m ee after all selection criteria except the phase space ducial cut to suppress the K L!e + e ; background. Events in the central boxes are only plotted in the zoom around the signal region in the bottom plot. 3.3 K L! 0 + ; This decay is similar to the previous one, with an available phase space about a third, but better experimental acceptance and dierent backgrounds ( decay or punch through, smaller + ; BR). KTEV nds 4 K L! + ; events in the 1997 data, with.1 expected background, and gets 20 : BR(K L! + ; ) = (10:4 +7:5 ;4:5 1) 10;9 This is the rst measurement of this branching ratio. They found 2 candidates for K L! 0 + ; with expected background, and published 21 : ichep2000: submitted to World Scientic on October 17,

5 BR(K L! 0 + ; ) < 3:810 ;10 (90 % CL) 3.4 K! () () Data Fitted K S γγ K L γγ γγ background from 2π 0 (MC) These decays are used to test various theoretical models and to estimate the Long Distance contributions to the K L to ee and decays. The short distance contribution to these two FCNC decays is proportional to A 4 (1-) (A and are two parameters of the CKM matrix in the Wolfenstein parametrization 22 ). An improved knowledge of the long distance contributions would allow a better interpretation of the BNL-AGS-E871 results 23 : BR(K L! ) =(7:18 :17) 10 ;9 ( 6200 events) BR(K L! ee) = (8:7 +5:7) ;4:1 10;12 (4 signal events for expected background) This is the smallest branching ratio ever measured. 3.5 K! Three leptonic decays proceed through the intermediate state : K L!4e, K L!e + e ; + ;, K L!4. P T predicts BR(K L!4e) = 3:9 10 ;8. Both KTEV and NA48 have consistent (preliminary) results : KTEV 24 :(3:77 :18 :27) 10 ;8 (436 events) NA48 25 :(3:67 :32 :23 :08) 10 ; Signal Events GeV/c 2 < m µµγ < GeV/c 2 Signal:Background = 41:1 KTeV Preliminary GeV/c 2 µ + µ γ Mass Figure 4. KTEV : invariant mass of K L! + ; candidates γγ signal z v [ cm ] Figure 5. NA48 : longitudinal vertex distribution of K! candidates. (132 events) The last uncertainty for NA48 comes from the branching ratio of the normalization channel (K L! + ; 0 ). D From KTEV, BR(K L!e + e ; + ; ) = (2:50 :41 :15) 10 ;9 (prelim.) 26 with 38 events and.2 background from + ; (converted), + ; 0, D + ; e + e ;. NA48 found 21 candidate events, but did not give a branching ratio. 3.6 K L!! + ;, e + e ; The K L! vertex is parametrized in various models. In the BMS model 27,the amplitude is the sum of a pseudoscalar pseudoscalar transition and a vector vector transition, with a relative strength parametrized by K. In P T, one parameter is introduced to account for a symmetry breaking eect at a scale. In the phenomenological description of D'Ambrosio et al. 28,two parameters and are introduced to describe the K L! form factor. The discussion of these models is outside the scope of this report. The experimental data available are the K L! + ; and the K L!e + e ; branching ratio and the invariant mass distribution of the lepton pair. KTEV has presented 29 : BR(K L! + ; )=(3:70 :04 :07) 10 ;7 with more than 9000 events (see gure 4). With this value and the dimuon mass distribution, they get 29 K = :026, ;:027 in rough agreement with previous measureichep2000: submitted to World Scientic on October 17,

6 ments, although somewhat lower than those from K L! + ;. This might indicate that the BMS model is not adequate to describe the observed spectra. 3.7 K S! One of the most important testof P T is the measurement of the K S! branching ratio. Indeed, this decay is completely dominated by long distance contributions. The P T prediction is (2:4 :2) 10 ;6. The previous measurement was made by NA31 30 : (2:4 :9) 10 ;6. NA48 improved this result (see gure 5) to (2:4 :4 :2) 10 ;6 (prelim.) 31 using data from the short 99 test run in a high intensity K S beam. 3.8 Summary A large amount of new data on K L and K S decays have appeared in the past two years. They are summarized in table 1. Limits on new physics phenomena are pushed and P T is conrmed as an excellent model. In the near future, KTEV and NA48 will keep on providing improved results, since both experiments have on tape data corresponding to about twice the sensitivity for most channels. On a longer term, KLOE and the proposed NA48 extensions (if accepted) will provide interesting measurements on K S and charged K decays. A measurement of this BR would allow a clean determination of the CP violating Wolfenstein parameter of the CKM matrix. The present 90 % CL limit is ;7 33, many orders of magnitude above the expectation. The KEK-PS-E391a experiment is in preparation with the goal to achieve 10 ;10 single event sensitivity (SES). It is meantasa test experiment before launching a more ambitious program at the planned 50 GeV PS at KEK. The KOPIO project at BNL has been recommended. Their objective istodetect about 50 events for a BR of 3 10 ;11. The KAMI collaboration is preparing a proposal with the same kind of sensitivity. The techniques are very dierent : full reconstruction of low energy K decays for KOPIO, measurement of the missing transverse momentum of high energy K's from a carefully designed pencil beam and with a hermetic apparatus for KAMI. The eciency to detect low energy 's is one of the critical parameters. The K +! + decay has somewhat larger theoretical uncertainties than the previous one, but they remain below 10% 32. The BNL E787 experiment has detected one event with negligible background in their 1995 data. They have found no other candidate in their 96 and 97 samples, leading to the updated measurement 34 : 4 K! When the K L! 0 decay appeared in the discussions many years ago, it looked like a "Graal" to experimentalists. This is a CP violating decay, the interest of which lies in the fact that theoretical predictions are very clean. Indeed, the relevant hadronic matrix elements can be extracted by using the measured K +! 0 e + branching ratio. This leads to a few % uncertainty on BR(K L! 0 ), which reads 32 : 310 ;11 (=:39) 2 (m t =170GeV) 2:3 (jv cb j=:04) 4 Figure 6. History of K L! + search. ichep2000: submitted to World Scientic on October 17,

7 Table 1. Rare K L and K S decays results summary. K L decay mode BR or 90 % CL Experiment PDG ; e + e ; (3:63 :18) 10 ;7 FNAL E799 < 4:6 10 ;7 0 (1:68 :11) 10 ;6 FNAL E799 (1:70 :28) 10 ;6 (1:51 :21) 10 ;6 CERN NA48 e + e ; (6:31 :44) 10 ;7 FNAL E799 (6:5 1:2) 10 ;7 (6:32 :47) 10 ;7 CERN NA48 0 e + e ; < 5:1 10 ;10 FNAL E799 < 4:3 10 ;9 + ; (10:4 +7:5 ;4:5 10;9 FNAL E799 ; 0 + ; < 3:8 10 ;10 FNAL E799 < 5:1 10 ;9 + ; (3:70 :08) 10 ;7 FNAL E799 (3:25 :28) 10 ;7 e + e ; (1:06 :05) 10 ;5 CERN NA48 (:91 :05) 10 ;5 e + e ; e + e ; (3:77 :32) 10 ;8 FNAL E799 (4:1 :8) 10 ;8 (3:67 :40) 10 ;8 CERN NA48 e + e ; + ; (2:50 :44) 10 ;9 FNAL E799 (2:9 +6:7 ;2:4 10;9 + ; (7:18 :17) 10 ;9 BNL E871 (7:2 :5) 10 ;9 e + e ; (8:7 +5:7) ;4:1 10;12 BNL E871 < 4:1 10 ;11 K S decay mode + ; e + e ; (5:1 :9) 10 ;5 CERN NA48 ; 0 e + e ; < 1:6 10 ;7 CERN NA48 < 1:1 10 ;6 (2:6 :4) 10 ;6 CERN NA48 (2:4 :9) 10 ;6 BR(K +! + ) =(1:5 +3:4) ;1:2 10;10 This measurement gives a constraint in the ( ) plane. If approved, two projects should bring more information in the future : BNL-E949, which aims at 10 ;10 SES, and CKM at FNAL, with 10 ;12 SES objective. Figure 6 shows the historical progress of this search. To conclude, the K! decays can provide information complementary to the study of B decays, the value of which isat the same level because of the cleanliness of the interpretation of the measurements. It is to be hoped that the experimental eort will match the scientic interest. 5 Non Standard Model T violation It is generally believed that CP violation seen in the K system and interpreted as the presence of an irreducible complex parameter in the CKM matrix is not sucient to account for the observed matter-antimatter asymmetry in the universe. This is a strong motivation to search for violation of the discrete symmetries in phenomena where it is not expected. 5.1 T violation in K 3 decays The transverse polarization P T of the from the K +! 0 + decay, dened as the component of the polarization normal to the plane, is expected to be essentially 0 in the SM, nal state interactions being negligible. With their 1997 data, KEK-PS-E246 has recently published 35 : P T = :0042 :0049 :0009 The precision is already 30 % better than the previous measurement. They should present soon another measurement with their 1998 data, and a new run will start end of year The nal statistical uncertainty should be more than a factor of 2 smaller. ichep2000: submitted to World Scientic on October 17,

8 The present beam intensity is310 5 K + delivered during a.6 s spill every 3 s. They detect K decays at rest, and the transverse polarization is measured by detecting the direction of the e + from the decay. The apparatus has a 12-rotational symmetry. The analysis technique allows a strong cancellation of most systematic uncertainties. They measure the following asymmetry : A T ( (N cw=n ccw ) fwd (N cw =N ccw ) bwd ; 1)=4 where : N (ccw)cw is the number of electrons emitted in the (counter)clockwise direction (N cw =N ccw ) fwd(bwd) is the ratio of these numbers for forward (backward) emitted 0 's. Some extensions of the SM predict a value of P T only one order of magnitude below the attained precision. This motivates the BNL-E923 experiment, under construction, which will use an intense 2 GeV K + beam ( K + every 3.6 s) ! e + e Muons can be produced copiously and hence allow precision tests of the SM and the search for new physics. Two experiments at the Paul Scherrer Institute (R and R-97-06) are dedicated to the measurement of the polarization of the e + from the +! e + e decay. The R experiment (P T ) measures the transverse polarization of the e + from stopped polarized muons : a non zero component orthogonal to the direction of the polarization (P T2 )would be a non ambiguous sign of T violation. The spin is rotated at a frequency!=2, thee + are annihilated in a magnetized foil and the 's are detected in a BGO crystal calorimeter. The distribution of the plane angle with respect to the plane de- ned by themuon polarization direction and the e + momentum direction depends on the e + polarization. An oscillatory dependance of the spectrum at the same frequency for a xed value of is the signal which islooked for. From a rst test run, they have measured < P T2 >= :009 :022, a precision equivalent to the previous measurement. R aims at measurimg the longitudinal polarization of the e + and will look for non SM Michel parameters. Another experiment at TRIUMF, E614, is in preparation. The objective istorecord 10 9 decays and measure all the Michel parameters with precisions three to ten times better than the present ones. More details on the physics of muon decays and on the experimental status can be found in the recent review of Y. Kuno and Y. Okada Lepton Flavor Violation In the SM with massless neutrinos, Lepton Flavor Violation (LFV) is forbidden. It is allowed in the simplest extension with massive neutrinos, but, even with maximal mixing, it would not be measurable for masses of order the ev/c 2. LFV is thus a good place to search for physics beyond the SM at scales well above the TeV. 6.1 LFV in K decays One should rst recall here the limit set by BNL-AGS-E : BR(K L! e) < 4:7 10 ;12 (90 % CL). FNAL-E799 just obtained two new limits (90 % CL) : BR(K L! 0 e) < 3:1 10 ;9 BR(K L!e e ) < 1:36 10 ;10. BNL-AGS-E865 has many new results from their 1996 data. This experiment is dedicated to the search for LFV in K +! + + e ; decay. A spectrometer with 16 planes of proportional chambers provides the measurement of all charged particle momenta. Particle identication, whichisacritical issue in this kind of experiment, relies ichep2000: submitted to World Scientic on October 17,

9 on Cerenkov counters, a 15 r.l. deep "Shashlik" calorimeter, and a 24 planes proportional tube - iron plate range stack. The beam intensity was protons on target, producing 10 8 K + per 1.6 s pulse. This corresponds to 2: K!3 decays seen in the detector. A likelihood analysis is used to evaluate the probability of various hypotheses for selected events, using experimental distributions of the relevant variables to produce the probability density functions. The background comes from 3 decays (the normalizing channel), Dalitz decays and accidentals. It is expected to be Three events survive all cuts. This translates into BR(K +! + + e ; ) < 3:9 10 ;11 (90 % CL). When combined with the 1995 data and the older E777 limit, this leads to : BR(K +! + + e ; ) < 2:8 10 ;11 (90 % CL). The E865 experimental setup allows the search for many other decays with LFV (K +! + e + ;, 0! e + ; ), total lepton number violation ( and ee decays), and eects of Majorana 's in the second generation ( + + ; decay). Table 2 summarizes these results LFV in decays The best limit on the most simple! e decay has been obtained by the LANL MEGA collaboration 40 : BR < 1:2 10 ;11 (90 % CL). The total ux of stopped muons was 1: The limiting factor of the experiment was the instantaneous muon intensity of 2: s ;1 with 6% duty factor. A new proposal at PSI (R99-05) has been approved, aiming at a 10 ;14 SES. Data taking should start in The main improvements are : A 100 % duty factor continuous beam, leading to same instantaneous beam intensity as in MEGA for a factor 16 increase in the total number of available muons. A liquid xenon calorimeter. A constant bending radius spectrometer : a superconducting coil is arranged to produce a graded magnetic eld in which the e + from the! e decay follows a trajectory with a radius independant of the emission angle. This allows to only install drift chambers in the outer part of the solenod volume, reducing by several orders of magnitude the rate of Michel positrons in the detector (see gure 7). Muons also allow to search for LFV in looking at ; N! e ; N conversion of a muonic atom. The BNL MECO experiment aims at a 10 ;16 sensitivity in the process ; +Al! e ; +Al. The present best limit is BR( ; +Ti! e ; +Ti) < 6:1 10 ;13 (90 % CL). If the e form factors relevant to the! e process are also dominant in the muonic atoms conversion, the relation BR( ; N! e ; N) = (B(A,Z)/400) BR( ;! e ; ) can be established, where B(A,Z) is a correction factor of order unity (1.2 for Al, 1.8 for Ti). It is convenient to compare the sensitivity ofvarious experiments. No new result has been presented on these processes. Perspectives for muon physics are good since several R&D programs dedicated to the development of very high intensity proton sources have been launched worldwide. They can be used to produce intense muon beams, with a large number of applications, including a neutrino factory or a muon collider in the far future. 7 Final remarks Direct CP violation is now established by many precise measurements, although with a large spread of results. Those have stimulated a lot of theoretical eorts, but lattice QCD, the cleanest method, in principle, cannot yet provide a solid prediction for 0 =. KTEV and NA48 have still a lot of data to analyze, which hopefully will clarify soon the ichep2000: submitted to World Scientic on October 17,

10 Table 2. Recent E865 results : BR's or 90 % CL limits. Decay mode E865 PDG98 39 K +! + ee (2:94 :14) 10 ;7 (2:7 :2) 10 ;7 K +! + (9:2 :6) 10 ;8 (5 1) 10 ;8 K +! + + e ; < 2:8 10 ;11 < 2 10 ;10 0! + e ; < 3:8 10 ;10 < 1:6 10 ;8 K +! + + ; < 3 10 ;9 < 1:5 10 ;4 K +! e + e + ; < 6:3 10 ;10 < 1 10 ;8 K +! + e + ; < 5:1 10 ;10 < 7 10 ;9 K +! + e + ; < 4:9 10 ;10 < 7 10 ;9 Liq. Xe Scintillation Detector Liq. Xe Scintillation Detector Muon Beam γ Thin Superconducting Coil Stopping Target γ Drift Chamber e + Timing Counter e + Drift Chamber 1m Figure 7. PSI R99-05 experimental setup. ichep2000: submitted to World Scientic on October 17,

11 experimental situation. On the rare K L decays side, most branching ratios and limits have been updated (KTEV, NA48, BNL E871), bringing no surprise but rather conrming models predictions. NA48 has started a K S program, which still needs approval to be continued. KLOE has started taking data and should provide complementary measurements in a near future. Many projects are in preparation to pursue the K! search beyond the BNL E787 and KTEV sensitivities : BNL E926 (KOPIO), BNL E949, FNAL CKM, FNAL KAMI, KEK E391a. They should provide clean independant constraints on the CKM matrix and complement measurements from the B sector. The search for CP or T violation outside the Standard Model is being pushed with K + (CERN NA48 proposal, KEK E246, BNL E923 project) and + decays (PSI P T, PSI P L, TRIUMF E614). Many new limits on lepton avor violation have been given (BNL E865, BNL E871, FNAL KTEV, LANL MEGA) and several projects are being launched (PSI R99-05, BNL MECO). They should reach sensitivities allowing, for example, the test of some supersymmetric extensions of the Standard Model. Progresses in light avor physics are steady. How much time will the Standard Model still resist? References 1. N. Cabbibo, Phys. Rev. Lett. 10, 531 (1963) M. Kobayashi and T. Maskawa, Progr. Theor. Phys. 49, 652 (1973) 2. M. Ciuchini et al., TUM-HEP , RM3-TH (2000) S. Bosch etal., Nucl. Phys. B565, 3 (2000) S. Bertolini et al., hep-ph/ (2000) T. Hambye et al., Nucl. Phys. B564, 391 (2000) 3. G.D. Barr et al., Phys. Lett. B317, 233 (1993) 4. L.K. Gibbons et al., Phys. Rev. Lett. 70, 1203 (1993) 5. A. Alavi-Harati et al., Phys. Rev. Lett. 83, 22 (1999) 6. V. Fanti et al., Phys. Lett. B465, 335 (1999) 7. A. Ceccucci, CERN seminar, February 29 th R. Batley et al., CERN/SPSC A. Alavi-Harati et al., Phys. Rev. Lett. 84, 408 (2000) 10. L.M. Sehgal and M. Wanninger, Phys.Rev. D46, 1035 (1992), ibid. D46, 5209(E) (1992) 11. V. Kekelidze, these proceedings 12. A. Alavi-Harati et al., Phys. Rev. Lett. 83, 917 (1999) 13. P. Heiliger and L.M. Sehgal, Phys. Rev. D47, 4920 (1993) 14. V. Kekelidze, these proceedings 15. R. Batley et al., CERN/SPSC V. Kekelidze, these proceedings 17. T. Yamanaka, XXXIVth Rencontres de Moriond, March 13-20, V. Kekelidze, these proceedings 19. A. Alavi-Harati et al., Fermilab-Pub- 00/225-E (2000), submitted to Phys. Rev. Lett. 20. A. Alavi-Harati et al., Fermilab-Pub- 00/023-E (2000), submitted to Phys. Rev. Lett. 21. A. Alavi-Harati et al., Phys. Rev. Lett. 84, 5279 (2000) 22. L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983) 23. D. Ambrose et al., Phys. Rev. Lett 81, 4309 (1998) D. Ambrose et al., Phys. Rev. Lett 84, 1389 (2000) 24. Yau W. Wah, these proceedings ichep2000: submitted to World Scientic on October 17,

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