The status of rare kaon decay experiments is reviewed. With the current
generation of experiments now finishing, several exciting new results are
available. New limits in the search for Lepton Flavor Violation (LFV) will be
discussed, as will new limits and measurements of the CKM matrix parameters.
The next generation of rare kaon decay experiments and their contribution to
determination of CKM parameters will also be discussed.Comment: 7 pages, 2 figures, LaTeX, to be published in the Proceedings of the
  Workshop on Strange Quarks in Hadrons, Nuclei, and Nuclear Matter; Athens,
  Ohio, May 12-13, 200

Kettell, S.

English

arXiv

KETTELL,ST.

UNT (University of North Texas) Digital Library

. .BNL-67589-OO/08-REV.Rare Kaon Decay Experiments *Steve KettellBrookhauen National LaboratoryUpton, NY 11973AbstractThe current status of rare kaon decay experiments is reviewed. A large number ofnew results are available from several very sensitive experiments at BNL, FNAL andCE;RN. New limits in the search for Lepton Flavor Violation are discussed, as are newmeasurements of the CKM matrix.1 Introductic)nThe study of rare kaon decays has played a key role in the development of the standardmcldel (S M), and the field continues to have significant impact. Several recent reviewsof the field are or will be soon available [1]. The two areas of greatest import are thedetermination of fundamental standard-model parameters, such as CKM [2] mixing andCl’ violation, and the search for physics beyond the standard model (BSM) throughthe search for lepton flavor ..violating (LFV) decays.2 Lepton Flavor Violating DecaysThere is solid experimental evidence for the exact conservation of an additive quantumnumber for each family of charged leptons. While there is no SM mechanism for LFV(non-zero m. induces LFV in the charged lepton sector at a level that is too small toobserve), there is no underlying gauge symmetry preserving lept on flavor; and manyextensions to the SM predict LFV. Observation of L,FV would be unambiguous evidencefor physics beyond the SM.Due to the relatively long kaon lifetime, copious production at fixed target protonaccelerators, and very sophisticated experimental techniques, the mass scale probedby rare kaon decay experiments is quite high. This can be seen by comparing theK}, + pe decay. through a hypothetical LFV vector boson with coupling gx and massM;K to the conventional KPZ decay (g and Mw): Mx > 200 TeV/c2 x gx /g x1’4 For current experimental sensitivities at the level of 10–12,[1(1-’2/B(K~ +~e )] .mass scales in excess of 100 TeV are explored (for the usual electroweak coupling).The E871 experiment at BNL, a search for K; -+ pe , has been completed, with twolor.g runs during 1995–961. The )3871 analysis of the data set used a ‘blind ar,alysis’teclmique, in which selection criteria were devised and backgrounds measured on the*To be published in the Proceedings of the Workshop on Strange Quarks in Hadrons, Nuclei, and NuclearMatter; Athens, Ohio, May 12-13, 200@ Ed. K. Hicks1>.data outside of an exclusion region. These selection criteria were then applied to theremaining data and background measurements were compared to the actual numberof events. No events were seen in the signal region (see Fig. 1), with an expectedbackground of 0.1 events and the 90% CL limit on this decay is B(iY~ + pe ) <4..7 x400-.300 =--Cu~~ ~--~a+ Exclusion Box100Signal Box-0 Ic, ,485 490 495 500 505 510M we (MeV/c2)Figure 1: Final E871 data sample after all cuts, with no events in the signal region. Theexclusion box was used to set cuts in an unbiased way on data far- from the signal region.The shape of the signal box was optimized to maximize signal/background.10–12 [3]. There are no plans to pursue this decay further.The E865 experiment at BNL, designed to search for the decay K+ -+ n+p+e- ,an ana,logto~;+pewhich is sensitive to LFV interactions with different quantumnumbers, collected data during 1995, 1996 and 1998. The 90’3’oCL limits on this modefrom the 1995 and 1996 runs are B(K+ +n+p+e- ) <2.1 x 10–10 and <3.9 x 10–11respect ively. Combining these results with that oft he predecessor experiment E777, the90’ZOCL limit is B(K+ + r+p+e- ) <2.8 x 10-11 [4]. The final sensitivity, including1998 data, is expected to be N3 times better. There are no plans to continue thissearch.The current 90% CL limit for K; + rope is from E799-I [5] at FNAL, with B(K; + fi”pe )<3.1 x 10–9. This measurement has very little background, so E799-11 (KTeV) willbe able to substantially improve upon this limit, reacklng sensitivities close to E865.3 CKM MatrixThe K+ TVP modes: K{”+ T+V2 and K; -+ X“VV , are the ‘golden modes’ for deter-mining CKM matrix parameters. Both of these modes can be very precisely calculatedfrom fundamental SM parameters. The K++ 7r+VD mode is sensitive to the magni-tude of the poorly known & = Vt~Vtd and K;+ nOVD is purely direct- CP-violating andsensitive to lm(At).Two other modes for which it may be possible to extract fundamental CKM pa-+ – and K; -+ n“~+l– . However, in both cases, large long-rameters are K;+ p pdistance contributions limit the usefulness of these modes. Additional measurementsof some radiative kaon decays, as well as chiral perturbation theory (ChPT) work, areneeded to extract the short distance physics [6-10]. In the case of K~ + T“e+ e– andK;+ m“p+~– , there are also significant backgrounds... .The mode K;+ p+p– , whose small rate has played such an important role in thedevelopment of the SM (e.g. the GIM mechanism and the prediction of the charmquark [11] ), has now been measured (relative to Kj + T+x– ) to the unprecedentedprecision of 1.5%, with 6200 events observed by E871 [12].The decay K;+ p+p– is dominated by K;+ -y-y with the two real photons con-verting to a p+p– pair. This contribution is precisely calculated using QED from ameasurement of the K; –+ ~-y branching ratio. There is also a long distance diq,persivecontribution through off-shell photons, which has been calculated [6,7] although thereis some dispute as to the reliability y of these calculations [8,9]. Most interesting is theshort distance contribut,icm, through internal quark loops, dominated by the top quark.A measurement of this short distance contribution is sensitive to the real part of theAt or, equivalently, the Wolfenstein [13] parameter p [14]:BsD(K~ -+p+p- ) = 6.0 x 10-3[Re(At) --6.7 x 10-5]2 N 9 x 10-10 (1)The current measurement of the branching ratio B(K; + p+p- ) = (7.18+ O.17) x 10-9by the E871 collaboration [12] represents a factor of three improvement. This valueis only slightly above the unitarity bound from the on-shell two photon contributionof Ba~~(K~ + p+p– ) = (7.07 + 0.18) x 10–9 and leaves very little room for a shortdistance contribution. Using estimates of the long distance dispersive contribution [6],a 90% CL limit of p > –().33 is obtained [12].The decay K~ + e e+ – is predominantly through two off-shell photons, making thisdecay less interesting for extracting SM parameters. However, the recent observationof four events by E871 [15], with B(K} + e+e– ) = (8.7~~:~) x 10–12 is consistentwit h ChPT predictions [7,8] and is the smallest branching ratio ever measured for anyelement ary part icie decay.The K;+ T“r?+l– modes can proceed via the direct- CP-violating processes.short-distance contributicm is given by [14]BsD(K~ + mOe+e- ) = 2.5X 10-4[1m(~J]2 w 5 X 10-’2.This(2)The muon mode, K;+ T“p+p– , is expected to be five times smaller. Unfortu-nately, the decay K; + m(’e+e– can occur in two other ways: an indirect- CP-violatingcontribution (which can be determined from measurement of Kg+ no e+ e– ) and aCl’-conserving contribution (which may be calculated from the K; + m“~~ rate atlow invariant ~-y mass). These contributions may be comparable to or larger thanthe direct- CP-violating contribution. Even more formidable is the background fromKj~ + /?+1–~~ , as pointed out by Greenlee [16]. The KTeV experiment at FNAL, an-alyzing data from 1997, has significant ly improved the limit on K;+ To e+ e– . Twoevents, consistent with the expected background of 1.1 events, were found in the sig-nal region [17], giving a 90% CL limit of B(K~ + r“e+e– ) < 5.6 x 10–lO. A similaranalysis oft he related muon mode resulted in two events, consistent with the expectedbackground of 0.9 + 0.2 events, in the signal region [18], and a slightly smaller upperlimit, B(K; -+ n“p+p- ) <3.4 x 10-10 (90% CL). Improvement in limits on both ofthese modes will be slow due to the presence of background.There is a wealth of other new measurements in the kaon system reported recentlyfrom BNL, FNAL and CERN [1,19]. Many of these are useful for understanding long-distance effects in K:+ ,U+p– or K;+ n“l+l– and for determining the backgroundto K; +Tol+l– . These measurements are substantially improved over previous val-ues and even larger improvements will be obtained when the complete data sets areanalyzed.33.2 Golden ModesThe K++ n+ vu and K;+ n“ v~ decays are the ‘golden modes’ for measuring CKMparameters; and, along with the other golden mode ~~ + T)~~ and perhaps the ratioof the mixing frequencies of 13s and B~ mesons, provide the best opportunity to over-constrain the unit zry triangle and to search for new physics. The most powerful testsof our understanding of CP-violation and quark mixing will come from comparison ofthe results from B meson and kaon decays with little theoretical ambiguity. The twopremier tests are expected to be:,... Comparison of the angle D from the ratio B(KE + T“VD )/B(K+ + m+ vu ) andthe CP asymmetry in the decay B; --+?/-JK~ [20,21].. Comparison of the magnitude IVtd\from K+ + n+ VU and the ratio of the mixingfrequencies of ~$ to ~d mesons [22].The unitarity of the CKM matrix can be expressed asV:.vud + vc~vcd + Vt:vtd = ~. + & + At = O (3)with the three vectors ~a s Vij Vzd converging to form a very elongated triangle inthe complex plane. The first vector AU = v~~v.d is well determined from the decayK+ -+ n“e+ve (Ke3). The height can be measured by K; --+n“vti and the third sideAt = V: Vtd will be measured by K++ T+ VU . The decay K;+ m“v~ offers the bestopportunity for measuring the Jarlskog invariant JCP (23]. The K + mv~ decays aresensitive to the magnitude and imaginary part of At. Measurements oft hese two modes,along with Ke3, will then completely determine the unitarity triangle.The theoretical uncertainty in K+ -+ T+VD (w7Yo) is small and even smaller inK& -+ n“v~ (N2%); in both cases the hadronic matrix element is extracted from B(K.3).The branching ratios have been calculated to next-to-leading-log approximation [24],complete with isospin violation corrections [25] and two-loop-electroweak effects [26].Based on current understandings of SM parameters, the branching ratios can be ex-pressed as [22]:B(K++m+VD ) =~+c12B(Ke3), x Imt + X:AC1227r2sin4 OwlVU. [ ~= 3.6 x 10-4( [Re(At) – 1.4 x 10-4]2 +“[1m(&)]2)= (0.82+ 0.32) x 10-10(4)(5)= 1.6 X 10-3[1m(At)]2 = (3.1+ 1.3) X 10-11,where K are the ismpin corrections and the Inami-Lim functions [27], X~, are func-tions of Z~ ~ Lf~/IM~ where lkf~ is the mass of the quark q; these contain QCDcorrections. In addition , it is possible to place a theoretically unambiguous upperlimit on K++ T+W from the current limit on B, – ~$ mixing, B(K+ -+ T+vfi ) <1.67 X 10-10 [22].3.2.1 K++ T+vDThe E787 experiment at BNL has recently publishedsample [28]: one clean K+ + m+vu event lies in the4an analysis of the 1995–97 datasignal box (see Fig. 2), with a....E <MeV)Figure 2: Final E787 data sample from the 1995–!37 data set after all cuts. One cleanK+ -+ 7r+vv event is seen in the box. The remaining events are K+ -+ X+m” background.measured background of 0.08 + 0.02 events. Based on this one event the branchingratio is B(K+ + m+v~ ) =: 1.5~~:~ x 10–lO. From this measurement, a limit of 0.002<lu,~[ <0.04 is determined; in addition, the following limits on & R ~~~~ can be set:[Im(A,)\ <1.22 x 10-3, –1.10 x 10–3 < Re(At) < 1.39 x 10-3, and 1.07 x 10--4 <IAt <1.39 x 10-3. The final sensitivity of the E787 experiment, based on data from1905-98, should reach a factor of two further, to the SM expectation for K++ n+ VD .A new experiment, E!149, is under construction and will run in 2001–03. Takingadvantageof the very large AGS proton flux and the experience gained with the E787detector, E949 with modest upgrades should observe 0(10) SM events in a two yearrurl. The background is well-understood and is ~lOYO of the SM signal.A proposal for a further factor of 10 improvement has been initiated at FNAL. TheCKM experiment (E905) plans to collect 100 SM events, with N1O background events,in ii two year run starting after 2005. This experiment will use a new technique, withK+ decay-in-flight and momentum/velocity spectrometers.3.2.2 K; +7T0V~The current best direct limit [29] on Kf, -+ n0vi7 comes from the KTeV run in 1997:B(K} +7f0V~ ) <5.9 X 10-7 (90% CL).An even more stringent limit can be derived in a model independent way [21] fromthe E787 measurement of K+ -+ T+VD :B(K~+nOVD ) < 4.4 x B(K++n+VD ) (6)< 2.6 X 10-9 (90% CL)The next generation of K; -+ nOVD experiments will start with E391a at KEK,which hopes to achieve a sensitivity of w 10–10. Although the reach of E391a isnot sufficient to observe a signal at the standard model level, the experiment willbe able to rule out large BSM enhancements and learn more about how to do thisdiflicult experiment. This experiment would eventually move to the JHF and aim fora sensitivity of 0(10–14).Two other experiments propose to reach sensitivities of 0(10-13): E926 (KO-PIO/RSVP) at BNL and E804 (KAMI) at FNAL. KAMI plans to reuse the excellentCsl calorimeter from KTeV and to operate at high kaon momentum to achieve goodphoton energy resolution and efficiency. It will take advantage of the large flux avail-able from the Main Injector. KOPIO follows a different strategy; the kaon center of5mass will be reconstructed using a bunched proton beam and a very low momentumKL beam. This gives two independent criteria to identifi background: photon vetoand kinematics — allowing background levels to be directly measured from the data— and gives further confidence in any observed signal. The necessary flux will by ob-tained from the very high AGS proton current. The low energy beam also substantiallyreduces backgrounds horn neutrons and hyperons. After three years of running, 65 SMevents are expected with a S/B 2 2:1.4 Conclusions and Future ProspectsThe unprecedented sensitivities of rare kaon decay experiments in setting limits onLFV have constrained many extensions of the SM. The discovery of K++ n+v~ hasopened the doors to measurements of the unitarity triangle completely within the kaonsystem. Significant progress in the determination oft he fundamental CKM parameterswill come from the generation of experiments that is now starting. Comparison withthe B-system will then over-constrain the triangle and test the SM explanation of CPviolation.AcknowledgmentsI would like to thank members of several experiments for access to data and for usefuldiscussions, in particular, I would like to thank Bill Molzon, Bob Tschirhart, TonyBarker and Hong Ma. This work was supported under U.S. Department of Energycontract #DE-AC02-98CH10886.References[1][2][3][4][5][6][7][8][9][10][11]A.R. Barker and S.H. Kettell, Ann. Rev. Nucl. Part. Sci. 50, 249 (2000); L. Lit-tenberg, Proc. Rencontres de ~oriond, Les Arcs, France, March, l?OO~ S. Kettell,PTOC. 3r’d Int. Conf. B Phys. and C’P Violation, Taipei, Taiwan, Dec. 1999, alsohep-ex/0002011; W. Molzon, Proc. XIX Int. Symp. Lepton and Photon Interact.,Stanford, August 1999., also hep-ex/OOO1024; PTOC. Chicago Conf. Kaon Phys.,June 1999, also http: //hep.uchicago. edu/kaon99/.N. Cabibbo, Phys. Rev. Lei!t. 10, 531 (1963); M. Kobayashi, T. Maskawa ?rog.Theo?’. Phys. 46, 652 (1973).D. Ambrose, et al., Phys. Rev. Lett. 81, 5734 (1998).R. Appel, et al., Phys. Rev. Lett. In press; also hep-ex/0005016 (2000).K. Arisaka, et al., Phys. Lett. B432, 230 (1998).G. D’Ambrosio, et al., Phys. Lett. B423, 385 (1998).D.G. Dumm and A. Pith, Phys. Rev. Lett. 80, 4633 (1998).G. Valencia, Nucl. Phys. B517, 339 (1998).M. Knecht, et al., Phys. Rev. Lett. 83, 5230 (1999).J.F. Donoghue, F. Gabbiani, Phys. Rev. D51, 2187 (1995).S.L. Glashow, J. Iliopoulos, L. Maiani, Phys. Rev. D2, 1285 (1970); M.K. Gaillard,B.W. Lee Phys. Rev. D1O, 897 (1974).6[q[13][14][15][16][17][18][19][20][2:L][22][23][24][25][26][27][28][29]D. Ambrose, et al., .Phys. Rev. Lett. 84, 1389 (2000).L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983).A. Buras, et al., Nucl. Phys. 13566, 3 (2000).D. Ambrose, et al., .Phys. Rev. Lett. 81, 4301 (1998).H.B. Greenlee, Phys. Rev. D42, 3724 (1990).T. Yamanaka, Proc. Rencontres de Moriond, Les Arcs, France, March 1999.A. Alavi-Harati, et al., Phys. Rev. Lett. 84, 5279 (2000).S. Kettell, Proc. 3rd DA@NE Work. Phys. and Det., Frascati, Italy, Nov. 1999,also hep-ex/0002@09.G. Bucahalla and A. Bums, Phys. Lett. B333, 221 (1994); G. Bucahalla andA. Buras, Phys. Rev. D54, 6782 (1996); Y. Nir and M.P. Worah, Phys. Lett.B423, 319 (1998); S. Bergmann and G. Perez, hep-ph/OO07170.Y. Grossman and Y. Nir, Phys. Lett. B398, 163 (1997).G. Bucahalla and A Buras, Nucl. Phys. B548, 309 (1999)C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985),G. Buchalla and A. Buras, NucZ. Phys. B412, 106 (1994).W.J. Marciano and Z. Parsa, Phys. Rev. D53, R1 (1996).G. Bucahalla and A Buras, Phys. Rev. D57, 216 (1998).A. Buras, hep-ph/9806471; T. Inami and C.S. Lim, Prog.(1981).S. Adler, et al., Phys. Rev. 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RARE KAON DECAY EXPERIMENTS.

BNL-6 7589 July 1,200o Rare Kaon Decay Experiments * Steve Ket.tell Brookhaven National Laboratory Uptolz, NY 12973 Abstract The current status of rare kaon decay experiments is reviewed. A large number of new results are available from several very sensitive experiments at BNL, FNAL and CEBN. New limits in the search for Lepton Flavor Violation are discussed, as are new measurements of the CKM matrix. 1 Introduction The study of rare kson decays has played a key role in the development of the standard model (SM), and the field continues to have significant impact. Several recent reviews of the field are or will be soon available [l]. The two areas of greatest import are the determination of fundamental standard-model parameters, such as CKM [2] mixing and CP violation, and the search for physics beyond the standard model (BSM) through the search for lepton flavor violating (LFV) decays. 2 Lepton Flavor Violating Decays There is solid experimental evidence for the exact conservation of an additive quantum number for each family of charged leptons. While there is no SM mechanism for LFV (non-zero m, induces LFV in the charged .lepton sector at a level that is too small to observe), there is no underlying gauge symmetry preserving lepton flavor; and many extensions to the SM predict_ LFV. Observation of LFV would be unambiguous evidence for physics beyond the SM. Due to the relatively long kaon lifetime, copious production at fixed target proton accelerators, and very sophisticated experimental techniques, the mass scale probed by rare kaon decay experiments is quite high. This can be seen by comparing the K~+,cL~ decay, through a hypothetical LFV vector boson with coupling gx and mass Mx to the conventional Kc12 decay (g and Mw): Mx > 200 TeV/c2 x gx/g x [10-l~/B(K;+~e )]lj4. For current experimental sensitivities at the level of 10-12, mass scales in excess of 100 TeV are explored (for the usual electroweak coupling). ‘To be published in the Proceedings of the Workshop on Strange Quarks in Hadmns, Nuclei, and Nuclear Matter; Athens, Ohio, May 12-13, 2000; Ed. K. Hicks The E871 experiment at BNL, a search for Ki+pe , has been completed, with two long runs during 1995-96. The E871 analysis of the data set used a ‘blind analysis’ technique, in which selection criteria were devised and backgrounds measured on the data outside of an exclusion region. These selection criteria were then applied to the remaining data and background measurements were compared to-the actual number of events. No events were seen in the signal region (see Fig. l), with an expected background of 0.1 events and the 90% CL limit on this decay is B(KE + pe ) < 4.7 x 300 200 100 0 485 490 495 500 505 510 M Ile (MeV/c*) Figure 1: Final E871 data sample after all cuts, with no events in the signal region. The exclusion box was used to set cuts in an unbiased way on data far from the signal region. The shape of the signal box was optimized to maximize signal/background. lo-r2 [3]. There are no plans to pursue this decay further. The E865 experiment at BNL, designed to search for the decay K’ +7rir+p+e- , an analog to Ki +pe which is sensitive to LFV interactions with different quantum numbers; collected data during 1995, 1996 and 1998. The 90% CL limits on this mode from the 1995 and 1996 runs are B(K+,+rr+p+e- ) < 2.1 x lo-” and < 3.9 x 10-l’ respectively. Combing these results with that of the predecessor experiment E777, the 90% CL limit is B(K+ +7r+p+e- ) < 2.8 x lo-l1 [4]. The final sensitivity, including 1998 data, is expected to be -3 times better. There are no plans to continue this SE?Xh. The current 90% CL limit for P$ + rope is fromE799-I [S] at FNAL, with B(Kz + rope ) < 3.1 x lo-‘. This measurement has very little background, so E799-II (KTeV) will be able to substantially improve upon this limit, reaching sensitivities close to E865. 3 CKM Matrix The K +~rv~ modes: K’ + n+z@ and KE +TPUP , are the ‘golden modes’ for deter- mining CKM matrix parameters. Both of these modes can be very precisely calculated from fundamental SM parameters. The K+ +&UP mode is sensitive to the magni- tude of the poorly known Xt E VGVa and Ki + #vi7 is purely direct-CP-violating and sensitive to 1m(&). Two other modes for which it may be possible to extract fundamental CKM pa- rameters are Ki + ,u+p- and KE + ~~~.k’l- . However, in both cases, large long- distance contributions limit the usefulness of these modes. Additional measurements of some radiative lraon decays, as well as chiral perturbation theory (ChPT) work, are needed to extract the short distance physics [6-lo]. In the case of Ki+7r”e+e- and K;: + “O/X+/L- , there are also significant backgrounds. 2 3.1 Ki -+p+p- and Ki +.n”~!?+l? The mode Ki-+p”+pu- whose small rate has played such an important role in the development of the SM’ (e.g. the GIM mechanism and the prediction of the charm quark [ll]), h as now been measured (relative to Ki --+~T+x- ) to the unprecedented precision of 1.5%, with 6200 events observed by E871 [12]. The decay Ki + #p- is dominated by Ki + yy with the two real photons con- verting to a P+/.L- pair. This contribution is precisely calculated using QED from a measurement of the Kj, -+ yy branching ratio. There is also a long distance dispersive contribution through off-shell photons, which has been calculated [6,7] although there is some dispute as to the reliability of these calculations [8,9]. Most interesting is the short distance contribution, through internal quark loops, dominated by the top quark. A measurement of this short distance contribution is sensitive to the real part of the Xt or, equivalently, the Wolfenstein [13] parameter p [14]: &&$+/J+I_L- ) = 6.0 x 10-3[Re(Xt) - 6.7 x 1O-5]2 N 9 x 10-l’ (I) The current measurement of the branching ratio B(Ki +p+pL- ) = (7.18f0.17) x lo-’ by the E871 collaboration [12] represents a factor of three improvement. This value is only slightly above the unitarity bound from the on-shell two photon contribution of Babs(Ki -+p+p- ) = (7.47 f 0.18) x lo-’ and leaves very little room for a short distance contribution. Using estimates of the long distance dispersive contribution [6], a 90% CL limit of p > -0.33 is obtained [12]. The decay Ki + ese- is predominantly through two off-shell photons, making this decay less interesting for extracting SM parameters. However, the recent observation of four events by E871 [15], with B(Ki+e+e- ) = (8.7’2::) x lo-l2 is consistent with ChPT predictions [7,8] and is the smallest branching ratio ever measured for any elementary particle decay. The Ki -+ +‘@2- modes can proceed via t,he direct- CP-violating processes. This short-distance contribution is given by [14] BsD(K~-++‘e+e- ) = 2.5 x 10-4[Im(Xt)]2 - 5 x 10-12. (2) The muon mode 1 Ki +&‘p+p- , is expected to be five times smaller. Unfortu- nately, the decay Ki -+ r’e+e- can occur in two other ways: an indirect-CP-violating contribution (which can be determined from measurement of Ki -+~~~e~e- ) and a CP-conserving contribution (which may be calculated from the Ki --+r”yy rate at low invariant yy mass). These contributions may be comparable to or larger than the direct- CP-violating contribution. Even more formidable is the background from Ki -+&?yy , as pointed out by Greenlee [16]. The KTeV experiment at FNAL, an- alyzing data from 1997, has significantly improved the limit on KL + r’e+e- . TWO events, consistent with the-expected background of 1.1 events, were found in the sig- nal region [17], giving a 90% CL limit of B(Ki--+7r”ese- ) < 5.6 x 10-lo. A similar analysis of the related muon mode resulted in two events, consistent with the expected background of 0.9 f 0.2 events, in the signal region [18], and a slightly smaller upper limit, B(Ki + r”p+pL- ) < 3.4 x 10-l’ (90% CL). Improvement in limits on both of these modes will be slow due to the presence of background. There is a wealth of other new measurements in the kaon system reported recently from BNL, FNAL and CERN [1,19]. Many of these are useful for understanding long- distance effect,s in Ki +p+p- or Ki +~~l+!- and for determining the background to K” -+ r”l?+l- . These measurements are substantially improved over previous val- L ues and even larger improvements will be obtained when the complete data sets are analyzed. 3 3.2 Golden Modes The K+ +7rTsv~ and Ki -+n”vv decays are the ‘golden modes’ for measuring CKM parameters; and, along with the other golden mode Bj --+$Kg and perhaps the ratio of the mixing frequencies of B, and Bd mesons, provide the best opportunity to over- constrain the unitary triangle and to search for new physics. The most powerful tests of our understanding of CP-violation and quark mixing will come from comparison of the results from B meson and kaon decays with little theoretical ambiguity. The two premier tests are expected to be: l Comparison of the angle p from the ratio B(Ki -+#vv )/B(K+ -+7r+~V ) and the CP asymmetry in the decay Bz -+ $K’i$ [20,21]. l Comparison of the magnitude [V&l from KS +n+vF and the ratio of the mixing frequencies of B, to Bd mesons [22]. The unitarity of the CKM matrix can be expressed as V,*,Vud + V,*,Vcd + v,*, v&d = A, + Jb + A = cl (3) with the three vectors Xi = VizVid converging to form a very elongated triangle in the complex plane. The first vector A, = V&l&d is well determined from the decay K+ --+r”e+ve (Ke3). The height can be measured by Ki +T”VV and the third side At = VtzVtd will be measured by K+ + T+UV . The decay Ki +TT”VF offers the best opportunity for measuring the Jarlskog invariant Jcp [23]. The K + TTVV decays are sensitive to the magnitude and imaginary part of X t. Measurements of these two modes, along with Ke3, will then completely determine the unitarity triangle. The theoretical uncertainty in KS -+msvt7 (-7%) is small and even smaller in K; +&‘vV (-2%) . in both cases the hadronic matrix element is extracted from B(K,s). The branching ratios have been calculated to next-to-leading-log approximation [24], complete with isospin violation corrections [25] and two-loop-electroweak effects [26]. Based on current understandings of SM parameters, the branching ratios can be ex- pressed as [22]: B(K+-m+zc ) = r;+a2B(Ke3) c IX& + x$i,12 27~~ sin4 OWIV,,~~ [ = 3.6 x 10W4([Re(Xt) - 1.4 x 10V412 + [rrr~(X,)]~) = (0.82 f 0.32) x 10-l’ (4) (5) = 1.6 x 10-3[lm(At)]2 = (3.1 f 1.3) x 10-rl, where K are the isospin corrections and the Inami-Lim functions [27], X,, are func- tions of X~ = Mi/M& where Mq is the mass of the quark q; these contain QCD corrections. In addition, it is possible to place a theoretically unambiguous upper limit on KS --+T+vv from the current limit on B, - B, mixing, mB(K+ -+r+vV ) < 1.67 x 10-l’ [22]. 3.2.1 K+ + r+uY The E787 experiment at BNL has recently published an analysis of the 1995-97 data sample [28]: one clean Kf +n+vP event lies in the signal box (see Fig. 2), with a 4 ULLLI_II_IU 90 100 110 120 130 140 150 E(lWeV) Figure 2: Final E787 data sample from the 1995-97 data set after all cuts. One clean KS +7r+vJ event is seen in the box. The remaining events are Kt + ~$71’ background. measured background of 0.08 f 0.02 events. Based on this one event the branching ratio is B(K+ +7rr+vV ) = 1.5$;:; x 10-lo. From this measurement, a limit of 0.002 < ]I&] < 0.04 is determined; in addition, the following limits on Xt E &:I& can be set: ]rm(xt)] < 1.22 x 10-3, -1.10 x 10Y3 < Re(Xt) < 1.39 x 10p3, and 1.07 x 10e4 < ]Xt] < 1.39 x lo- 3. The final sensitivity of the E787 experiment, based on data from 1995-98, should reach a factor of two further, to the SM expectation for K+ --+&vi? . A new experiment, E949, is under construction and will run in 2001-03. Taking advantage of the very large AGS proton flux and the experience gained with the E787 detector, E949 with modest upgrades should observe c)(lO) SM events in a two year run. The background is well-understood and is ~10% of the SM signal. A proposal for a further factor of 10 improvement has been initiated at FNAL. The CKM experiment (E905) pl ans to collect 100 SM events, with -10 background events, in a two year run starting after 2005. This experiment will use a new technique, with Kt decay-in-flight and momentum/velocity spectrometers. 3.2.2 K; -+ n”vV The current best direct limit [29] on Ki -+~~OVV comes from the KTeV run in 1997: B(K;+#vv ) < 5.9 x 1O-7 (90% CL). An even more stringent limit can be derived in a model independent way [21] from the E787 measurement of K+ +7r+vV : B(I(; + 7r0vv ) < 4.4 x B(K+ + 7r+zX? ) (6) < 2.6 x lo-’ (90% CL) The next generation of- Ki -+~~‘zYv experiments will start with E391a at KEK, which hopes to achieve a sensitivity of N 10-l’. Although the reach of E391a is not sufficient to observe a signal at the standard model level, the experiment will be able to rule out large BSM enhancements and learn more about how to do this difficult experiment. This experiment would eventually move to the JHF and aim for a sensitivity of O(lO-14). Two other experiments propose to reach sensitivities of 0(10-13): E926 (KO- PIO/RSVP) at BNL and E804 (KAMI) at FNAL. KAMI plans to reuse the excellent CsI calorimeter from KTeV and to operate at high kaon momentum to achieve good photon energy resolution and efficiency. It will take advantage of the large flux avail- able from the Main Injector. KOPIO follows a different strategy; the kaon center of 5 mass will be reconstructed using a bunched proton beam and a very low momentum KL beam. This gives two independent criteria to identify background: photon veto and kinematics - allowing background levels to be directly measured from the data - and gives further confidence in any observed signal. The necessary flux will by ob- tained from the very high AGS proton current. The low energy beam also substantially reduces backgrounds from neutrons and hyperons. After three years of running, 65 SM events are expected with a S/B > 2:l. 4 Conclusions and Future Prospects The unprecedented sensitivities of rare kaon decay experiments in setting limits on LFV have constrained many extensions of the SM. The discovery of K+ +7r+v~ has opened the doors to measurements of the unitarity triangle completely within the kaon system. Significant progress in the determination of the fundamental CKM parameters will come from the generation of experiments that is now starting. Comparison with the B-system will then over-constrain the triangle and test the SM explanation of CP violation. Acknowledgments I would like to thank members of several experiments for access to~data and for useful discussions, in particular, I would like to thank Bill Molzon, Bob Tschirhart, Tony Barker and Hong Ma. This work was supported under U.S. Department of Energy contract #DE-AC02-98CH10886. References [l] A.R. Barker and S.H. Kettell, Ann. Rev. Nucl. Part. Sci. 50, 249 (2000); L. Lit- tenberg, Proc. Rencontres de Moriond, Les Arcs, France, March 2000; S. Ket- tell, Proc. 3rd Int. Conf. B Phys. and CP Violation, Taipei, Taiwan, Dec. 1999; W. Molzon, Proc. XIX Int. Symp. Lepton and Photon Interact., Stanford, August 1999.; Proc. Chicago Conf. Kaon Phys., June 1999. [2] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963); M. Kobayashi, T. 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Rare Kaon Decay Experiments

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