II*

SLAC-Pirj-aim April K^a fr/E) Tkcoftttltnl Porcpccttaea* o» Strata Phyal=c ' JOHN ELLIS* Sttnford Linttr Aettltrtttr Ctnltr Sltnfpri Onivtriiit, Stanford, Ctlijorni* 9J30S MASTI 1, Genera! Qnrrlnv are beiTjr enough to have an interesting range of decay modes avail­ able them, and light enough (o be produced in efficient numbers to explore rire node* with sstjsrying stttotics. Kaoni inJ their 4c:ijs bavo provided at least two major breakthroughs in our knowledge ot fiiDduaeatal phyaka. They have revealed to as CP violation,1 end their lick of fiimh>changingneutra l interac­ tions warned Of to expect ehann.3 In addition, /f° — R mixing baa provided us with one of our most etegut and sensitive laboratories for testing quantum mechanics,3 There is every reason to expect that future generations of kson experiments with intense sources would add further to our knowledge of funda­ mental physics. This talk attempts to set future experiments in * general theoretical context, tad indicate how they may bear mpon fundamental theoret­ ical issues, Figure I eosapsulates some important trends in elementary physics. Two major philosophical approaches can be distinguished. The •onioa-skic" philosophy emphasises the search for more elementary constituents of as previous levels ere shown to be composite. Many authors believe4 that the present "elementary" such as , , possibly gauge ud maybe Him fields ere In fact composites of underlying preens oo a distance scale £ 0(10 '*) cm, The unification merchants, on the other band, emphasise* the common origin and form of the different fundamental forces. H now seem established that the weak and electromagnetic interaction* are at least partkaily unified in the Glashow-SeJam-Weinberg (GSW) model," and that the nuclear forces ate complicated manifestations of an underlying gauge theory QCD7 which Is conceptually dose to the GSW model. Together they constitute the '* of elementary particles. Their family resemblance leads naturally to the hypothesis8 of a grand unified theory of all gauge interactions. If this exists, its grand symmetry must be broken at a very high energy scale0 within a few orders of magnitude of the Planck mass of O(1O10) GeV. Al that scale there may be a fins! "superunifloatiou* with gravity. The provocative prefix 'super* refi«ta tny belief that aucb a Goal unification probably employs aupersymmetry (SUSV) in some form,10 It may well be that SUSY makes an earlier appearance oa th> stage of unification. As we will see later, technical difficulties with GUTa would be alleviated if SUSY was effectively restored at an energy scale os low os 1 TeV.

*Work supported by the Department of Energy, contract DE-AC03-78SF00515. Invited talk presented at the Theoretical Symposium on Intense Medium Energy Sources of Strangeness

l)«lv*r*ity ot California., Santa Ctui, California, 16-20 March 1083 (

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Fig. 1. A genera) overview of the "oaten ttkifi" ud unification trends in elementary . The different theoretical ideas introduced above are developed la greater de­ tail in Sec. 2 of this talk. Then Mows a survey of different experiments which would be done with an Intense Medium En«gy Source of Strangeness, Including rue K decays, probes or the nature of CP isolation, ft decays, bypeton dec'/s and physics. Each experiment will be assessed (or its interest u a test oi* the different theoretical ideas reviewed in Sec. i. Section 3 concludes v/itb • personal list yf priorities for IMESS experiments. That terminates the physics content of this talk, and leaves us with two short sections of wariness, Section 4 discusses why and how quantum mechanics might be violated, find how nn« might test this in the K° - R° system. Finally, Sec. 5 asks the Unas table question: how best should one proceed to explore strange physics in the futuret

2. Surrey of Different Theories:

2.1 THE STANDARD MODEL By this name we denote the gauge theory based on the group £1/(3) (for the stung interactions) XSV{2) x U(l) (for the weak and electromagnetic is* teractioos), with just 3 for perhaps S > 3) identical generations oi quarks and leptons, and with spontaneous gauge symmetry breaking furnished by a tingle doublet of Higgs fields.11 As mandated by th • suppression of flsvor-ehangtaeneu ­ tral interactions of kaons, the Standard Model incorporate* the GIM mechanism3 so that neutral currents conserve flavora t the tree level, and flavor-changing neu­ tral interactions at the one-loop level are suppressed by 0(o mj/m^r). The GIM mechanism is an automatic consequence of any theory12 in which all quarks of the same charge and helicity have the same weak isoapin and get theif masses from the same Biggs doublet. The Standard Model provides not only 1 qualitative but also a quantitative explanation of the magnitudes of flavor-changing neutral interactions. For example, the magnitude of the AS « 2 K** - R mass mixing was used19 to give an experimentally verified upper limit ofl the •sass of the

NOTICE MS GF TlilS 8EP0RT ARE rlUGIBLE/ 2 been reproduced Iron the best •e copy lo permit the broadest e availability. $mmm v it* wxm & m*my\ etaratd qaark, ud tht c qiufe coatribatton to the AS -1 *• -• »+nr decay tutrix element ii small taongh13 to b* oamptswlt with tnatfiMbt." Wt will ( lata* tatbtjt eakvlatioo* lb thto-ojnatk KebeyaibVMaattw*1* attention oftht original <4-oaarh GIM modd.* They win provide at with atefal constraints oo tbt ugtea e\ (j M 1,9,3) chnteetfristog tbt charged weak bteractiona or qanrla,1' ae wri) at on tb» mm of tbt 1park" ud thereby eoaatet with the ofctM* which »titiokwMte of CP»W»tiMiJ»tki8UadMdMod«l Ttew b u loom tot antic adriag aaglae between leptew to tha Standard Modd, ml thtOtntrino»ma»|>po»cdtopenn »« Tab incau that tha nrobtril^ of tbt deferent Upton pneratfou ate eheolaltty toaiemd, •» thai #/»*?, If0 /»»*, etc Bttft if tht awftfto miMi an MMOO, appef fimita"o n their Ttlw tapprese At p*" 0 reactions to vanbmnMy tow rate* ofltaae thetaboonM phytic* beyond the Standard Modd. 2,2 MoBEtTsORMiOasT It • natural to utertab tht ponribUity of extending the weak pap group ot tbt Standard Modd, pethaaa by making U mow tgrrunttife; SU(3) x 1/(1) becomes A/pfe X SUMR X &|l| with paritj broken spoatsneoaity, or perhaps by makingU moraistkd: SU[%)iXV[i)bteoiaeiStrftkort In tbtabetactof uy attractive unified wsak iatcrtttfaa noddt tbt uifi era* have pat on to pud naificatioa* at a leale £ 0(10") GeV.• Uft-righttymmetric modeb are still *«y ratch with «« u evidenced by dhewrioni in tht CF-Ttolatton taction of thb meeting.19 They predict two mow \f^ beyond tbt two H*J already disMrsrfid, ud two LMIIHI Z° bosons. LefUriajhl symmetric modeb abo expect & right- buded neutrino Bdd ud non-ieto neutrino nmw, Thi right-handed neutrino cu acquire u SU{i)i x U[U innriut Majorua mui and may will bt rather heavy. Tbert art eonitriinta30 on tbe mamas of Wjf bowu ud tndr muiog wttb Wj beaut which an considerably mora restrictive i] tba I//J »lighter ihuakaoa.*9 Why not ban toon Hnjp boaouT Thty m atedtd ii tburita wltb Urpr po|« pupa, ud enld caaily be incorporated to tht uiaimal SU(l)iX.U{l) tbt- ory. With two Hjfgi doublets oseeu imptauent83 a global C/(l)«ymin«try which wo«U *ahr« ttt acahlea^f «tioa« CP Tkirtioa is $CI> Aioap (ht I parameter.*4 SUSY theories actually reqoin aa tfts tonibet of rfigp doublets to order to oaocd ottt tsomafies and gira auaaea to aO ojMtha and leptoa«.tt Aattber nwairatim tor mM/h Wgpn waa to pt u tMttioMl eo«M* of CP viohtrW* aa dbMOfaed in fha CP twUtioa tauion at thb aMettog.19 However, to modeb with a C/(l) cymmatry and fai SUSV tbeorke witb two N^pooobkii. At qwarka of «barge + 3/3 pt their maam from est Higp doublet and tbe ooarke of cbsrp - 1/3 from another. Thua tbeta modab incorporate ihv GIM roeebubn,3 the neutral Higp coapliap eouem flaror, and then b oo extra. Higp aoureeM of CP violation- la general, theories with t'>« Higp doublet* contain two charged barest H* ud tbrea ntntrab toelodu.t* two aeabua H° and ifl and oat pawdoiealar « wbieh baennet the tight uion if a thbal l/(i) aupenymnietry* b implemented.

S 3.3 DYNAMICAL SYMMETRY BREAKING Muy people regard Hjgga Bddi as as onaitractivtwart on the fata of gauge theory which they would prefer lo burn out. On suggestion37 b thai HUM an in fact composites of fermlou bound together by HW new technicolor" pap Interaction which confine* them within * rang* of (Ajp — OjlTW)]-1. The rolt of the jpofitueotu ayumetry breaking ffwifoudy associated with the vae- nam expectation of elementary Higgs ffeMa • now nanrpcdbydytiejaiealeyjnmfr- toy hvenkng associated with coadensatea <0|^Ftt>of4henat«ehn9ennkns.# Thto mechanisa gives maase* to the vector * in • vary economical way, bat »»icytkefaor6^t€>«^intjeeetoo>td»ane1leplo»». Offttpmi •"was to intradvte new 'extended technicolor* (ETC) toteracMoos ti inFig. *. Fig. ?- f» A tBgp-/? vertex metamorphoses into (b) • composite ,\ 4 A ^ ^v/^ f\ A M J_ se*larfr-//vertex which roqniNa .>"— t/" A. ,/V"U .JP- ? (c)fcfofr.fermioayerteithtid!ir '' ^ fe, w> 6 be ceoerated either by jd)ecalar w W w w JJ» exchange or (•) vector ETC (B) *** exchange. Tfae convention*! elementary Higp-n vertex b lepbeed by the composite Htgga-9f vertex which embodies a foar-ttnxuoo QQQf interaction generated by the exchange of mantra ETC gauge boaona. One then haa and masses """lb "» enabting the ETC bora masse* to be eatfanated in terms of the knows Tension mu> spectrum, b a favored ets*»w of ETC oodeb there b one tecboiganentioa IU,D,B, /V) of tecbstauarki and ieptosi In parallel to the conventional gener­ ations («, J, t,v\ etc. They are coupled to the convanUonal fermkmi by ssveral different classes of ETC bosons, namely at leut one per feneration at indicated in Fig. 3a, In addition to these gang* boaona, a non-Abdiaa gauge theory of ETC tmnt contain boaona coupling the different conventional generations to one another aa eeea i* Fig, 36. These 'tariaontat" ETC bosons have the same prop­ erties as the boriaootaj gauge bosons oftee postulated in the absence of aa ETC motivation. However, m ETC theoria the masses of these horizontal boaona are similar to throe of the ETC basona a*d can be estimated* sang lot* mula(lk There are other deniteoa of thotcchaieolor too, com* of whose masse* an less tightly constrained. The theory contains39 many "technlpions" which ere partneis of the composite Higgs that escape being eaten by the IK* and Z°. They include color triplet bound states of tcchnie,tiaras and techntleptotts called ptieudoaceJar leptoquarka PIQ whose masses tire expected9 to be 0(150) GeV. There are also color singlet charged psetidoseslara P* which should31 have mauea 0(5 to U) GeV and have not been seen at FEP or PETRA,** to the em­ barrassment of technicolor tbcorbta, There should abo be even lighter neutral

4 o«.

-1/3 Pig. 3. (a) Askelrb of the 0 group structure of the simplest extended techni­ color theories., and (b| a typical flavor-changing neu­ tral interaction mediated by horizontal i:TC boson Ho-io-itm exchange

bosons P°'z whose masses can only33 eonw from other interactions tbml we hare, not yet mentioned. One candidate31 b vector leptoquwk interactions of tbe Pati- Salam34 type. These are ex peeled3136 to yield

and tbe n»H-oli*er*atiou of K* — fr*/*0'3 decay tells* as that Mpot > O(3S0) MeV (3)

which suggests vj3 )vq. (2) an upper bound on mr*c of order 3000 TeV in such extended ETC theories. Tliese vector Ivptoquarks will be met again in tbe dis­ cussion of rare K aad E decays, along with the pseudoscalar (eptoquarks. Befon- leaving ETC theories, we should emphasize that models of the type described have severe problems with flavor-changing neutral interactions, espe­ cially tbe magnitude of the t\S = 2 interaction responsible for K° — R mixing, and the absence so Tar of o. AC = 2 interaction leading to D° —D mixing. These problem-j ran In- traced3"-38,37 to the failure of ETC theories to satisfy tbe usual conditions'"' f»( natural flavor cnnJervjtioo. People have not abandoned hope or solving thene problems.38 IT and when a full solution is found, it may well affect some of ihi- order of magnitude estimates of rare A' decays that we make later. However, tln->r estimates do apply to the models ,:l7 with partial solutions that do exist.

5 2.4 SUPERSVMMETRY This is another response to the puzzles posed by Higgs fields. In order for the IV* and Z° bosons to have required masses of 0(100) GeV, there must be at least some Higgs bosons with comparable masses. However, elementary scalar fields are believed lo receive contributions to their masses Sntff = 0\mp ~ lu10 GeV) when propagating (Fig. 4a) through the space-time foam that is believed to constitute the quantum gravitational vacuum.**9 More prosaically, they acquire c"m// = 0("*x — 101S GeV) from interactions (Fig. 4b) witb other Higgses in the grand uniGed theory vacuum.10

{ (oom J

(ol Kig. 4. A scalar 5eld acquires large mass by propagating either through (a) space-time foam or (b( through the GUT vacuum. 9"

(b)

Even if these contributions to the light Htggs mass were to vanish or cancel miraculously, there would be radiative corrections as in Fig. $a which would give bmy = 0(al2)(mj. or ml). These must be cancelled out through 0(o12), which requires some quite powerful magic. This can be provided cither by "dissolving" Higgses so that they become composite on distance scales < OJlTeV-1), as in technicolor theories,37 or else by imposing superaymmetry (SUSY), la SUSY theories10 there are bosons and with similar couplings. . .ince their quantum loops have opposite signs as indicated in Fig. Sb, fermions and bosons lend to cancel so that _ A--rnjr or m/, ^

ID order for im^ to be less than the required Higgs masses 0(100 GeV) we sec from Eq. (4) that one needs [m%-m\)< 0{\ TeV2) . (5)

fl (ill v Fig. S. (a) Diagrams reticrmaliiing c~ J -• the scalar mass, tod (b) the diagrams I*I--V^— (-)--<_>- which almost cancel them in a SUSY theory, with sUjns indicated in (b) parentheses. t-)

Thus the unseen SUSY partners of known particles cannot be very heavy. The basic building blocks of the simplest SUSY theories10 are supermultiplets con­ taining pain of particles differing in belicity by ± 1/2: AWuge boson A\ quark 4 , leptone* , shiggsW 1 \l) ' \0/ iquark q , elepton £ , Higgs H ] ' Of this zoo of DEW particles, tbe tightest gaugino is likely to be the 7, while there may Mso be light neutral shiggs particles H 41 The same flavor-changing neutral interactions that were the Nemesis30 nf technicolor theories also impose strong constraints on SUSY theories.*2 The tree level couplings of all the new neutral particles must conserve flavor, and loop contributions to AF /£ 0 interactions must be very small. The first requirement implies that tbe squark aad slepton mass eigenstates must be spartnera of pure quark and lepton mass eigenstates, and hence that the SUSY analogues of tbe Cabibbo-Kobayaaht-Mukswa charged weak current mixing angles must' >e iden­ tical with tbe familiar quark mixing angles. Tbe suppression of loop marrams requires 3 super-GIM mechanism, for example in the super-box diagram of Fig. 6 which U of order

only if

mf or mi \mfa) At first blush, these AF ^ 0 neutral interaction conditions may seem difficult to satisfy, but in foci they emerge naturally in models with SUSY broken sponta­ neously. There all the squarks acquire universal m? of order (30 GeV)2 or more, while all differences Am? in squared masses are

7 Fig. 6. A typical super-box diagram contributing *" to AF ?£ 0 neutral interactions in a SUSY theory which requires a super-GIM cancellation. i <__

There are also SUSY models which have additional sources of symmetry vi­ olation beyond those in the Standard Model. For example, there exbt possible additional sources of CP violation.47 There is also the possibility of spontaneous lepton number violation due to vacuum expectation values for the spin-zero part­ ners if , whose effects are currently heing investigated. Indeed, we cannot even be sure that the photino and gluioo couplings conserve flavor at the tree level. This is strongly suggested by the phenomenological constraints,*4'45'*' but it can be argued49 that one should t^ka a more agnostic phenomenological viewpoint. 2.5 It seems natural to suppose that the particles we currently regard as fun­ damental and elementary are in fact composite.4 We have already removed so many layers or the onion — why not one more? Moreover, we now know such an untidy profusion of quark and lepton flavors that it is very appealing to seek a simpler description of nature with fewer fundamental elements. We have already loyed with the idea of composite Higgs fields, so perhaps Quarks, leptons and even gauge bosons are composite also on a distance scateO(A-*) which may be as large as 0[\ TeV-1). Suppose for example that the only preoos are fermionic, with quarks and leptons containing at least three, while bosons contain two preons. Then one can visualize the observed interactions as being due to exchange forces as in Fig. 7, with the dominant forces of longest range occurring in channels corresponding to the lightest bosooic bound states with masses in <£ A. This is similar to the way IT exchange is important in nuclear interactions because mt <£ 1 GeV. We would expect there to be additional forces in other channels corresponding to the exchanges of other bosons with masses m = 0[A) analogous to the p, w and tensor exchanges of tbe conventional strong interactions.

Ftg 7. An exchange diagram which yields >> new effective interaction in a theory. This analogy with the conventional strong interactions is too glib and glosses over many technical puzzles.1 Why are the lightest bound states fermions with m « O(A), whereas the fermionic bound stales of QCD, the , are heavy with masses 0(1 GeVJT The underlying dynamic? must obey consistency condi­ tions50 which are very difficult So satisfy. Why are there light bosons of spin 1, whereas the only light bosons in QCD have spin 0? It b very difficult to see how light gauge bosons would emerge unless the underlying dynamics already possessed the corresponding gauge icvariance. If we suspend our disbelief for a moment, we might expect that the exchanges of heavy bosons, or other dynamics on a scale of 0(1 TeV*1] might generate all manner of novel interactions:

and more generally 0(1nm) „- -fnBm [Mb) In general, we would not expect these new interactions to conserve conventional quantum numbers such as lepton Dumber L, number B, etc., since pre­ sumably differeot quark and lepton flavors share some preonic constituents in common, though some of the interactions (9) might be suppressed by some ap­ proximate cbiral symmetry. The low-energy phenomenology of preon theories may in many ways resemble that of ETC theories, since observable new interac­ tions of the form (9) probably involve the transformation of horizontal generation quantum numbers or the exchange of quantum numbers.

3. Survey of Experimental Probe*

3.1 RARE AT DECAYS There has been a lot of discussion40 at this meeting of the whole gamut of rare K decays. Hei e I will only select a few possible experiments and concentrate on a subset of theories, treating composite model* only cursorily and models with multiple gauge or Higgs bosons not at all. Each experiment will be discussed in turn for its interest within different frameworks, and the results are summarized in a table expressing my personal assessments. 3,1.1 K% —• fie and iY* —* **(it These two decays do not occur at all in the Standard Model, because it conserves separately both and muou 'eptcn

numbers Lc and b$. The same is also true in most SUSY models, though there is a possible escape route. IT any of the spin-zero sneutrino fields require a vacuum expectation value the corresponding violation of lepton number would conceivably have repercussions in K decay, though the details are stili being worked out.18

0 In contrast, K [[ -* (te and K"* —• ir^/ie are mainstream pn»-ubilities in tech­ nicolor theories, where there are many possible contributions to these decays. In the direct channel one can exchange a horizontal ETC as in Fig. 8a. From the experimental upper limit ' $fe& <"•*»* one deduce34 a lower limit on the squared mass of the corresponding gauge bosons:

3 m%it >(3S00, 170) TeV (11) which is exceedingly close to the estimates30 obtained by using the formula (1). Therefore this mechanism should yield K% —• pt decay at a rate very close to the experimental limit (10). Another contribution to Kjj -» fie decay could come from the exchange of a Pati-Salam35 vector teptoquark boson in the crossed channel as in Fig. fib. In this case the limit (10) tells m34 that mps > 0(300) TeV (12) whereas we deduced earlier from the nonobscrration of AT* -»ir±P0'3 decay that mP0A > 0(350) MeV (3) and hence mpg < O(3C00) TeV. Hence this mechanism should give rise to K? -* (ie decay at a rate within at most 0( 10™*) of the present experimental upper limit (10). The exchanges of paeudoscalar bosons can also contribute to K® -* (te decay. For example, the light pseudoscalars F03 can be exchanged in the direct channel as is Fig. 8c, and the upper limit (10) tells us30 that m^ > 2 X lOV1 GeV2 (13) where the 9 are some Af* ?£ 0 mixing angles. Since the P°<3 are expected on the basis of Eqs. (2) and (12) to weigh less than 3 GeV, the constraint (13) means that the mixing angles 6 must be very small indeed. This possibility is not excluded within the ETC framework.3* A contribution to /f£ -* fie which is less easy to suppress is crossed channel paeudoscalar teptoquark [PLQ) eschanga as in Fig. 8d. The upper limit (10) tells us34 that

mPu) > O(lhO) GeV (H)

(cl Idl

Fig. 8. Contributions to /T{J -• fie decay front (a) direct channel HETC ex­ change, (b) cross channel Patj-Salam gauge boson exchange, (c) direct channel P0,3 exchange and (d) crossed channel pseudoscalar teptoquark exchange.

10 **.icta coincides with the best estimates29-38 of the mn ot tb* Pf^. Therefore ETC theories would also expect Jf£ -»pe via, this mechanism to occur very close to the present experimental upper limit (10). Thb contribution is difficult to avoid because there is DO way or preventing technileptoaa and techniquarks from binding to form the PIQ, its mass is simply related by seating to the *+ - ir° mass difference, and the a ~* ft and d -*• c transitions are cot expected to be suppressed by any small angle factors. The above contributions all have analogues in the decays if* -+ **/«. The only difference is that the present experimental limit52

b * weaker constraint than the /f£ —• fie limit (10). For example, it means30 that a m%d > 0(200) TeV (16) to be compared with the more stringent boand (11). However, the bound (15) is logically independent, since K£ -* pe proceeds via a pseudoscalai coupling to the quarks, whereasfC* -» itc proceeds via a rector or scalar coupling. Therefore in principle one decay could occur and not the other, though in practice models'" predict comparable values for the ratios (10, 15). Searches far the decay K% -* fit and also for K+ -. x+pe would be very interesting and topical from the point of view of technicolor theories or dynamical symmetry breaking.29 These decays could abo occur in preon models, but the rates are much more difficult to pin down. However, as we see .'aitr they may be the best ways to test preon models in rare K decays. 3 1.2 K* — X* + Higgs A parenthetic ramal of this decay a appropriate here since an experiment to look for K+ -* t+pt deeay could also be a useful Hicgs sewch experiment. In tbe Standard Model there is just one physical neutral Higgs w'jich should weigh more than 10 GeV.11 However, there could be a lighter neutral Higgs in models with multiple Higgs doublets, suci as superaytnmetric models for example. We expect10 tbe following to be the dominant decay modes of light neutral Higgs bosons: H —*e+e or *n 2me < ttiff < 2mp

2mp < inn < 2m, (17) 2m, < rrtff < 2m^f H - p+fi- or ir+iT , rV

2mx < tjifj < 2mr

11 10 63 excludes mH < 0(1S) MeV. There b a claim that the ab­ sence of a Higgs peak io rf -* 7 + ft* ft' excludes m// < 0(400) MeV, but the experimental vper limit is not far below the calculation51 of the 17* -* «j + H decay rate which is Dot very reliable. The range m« < m// < 2mn a almost excluded by a search in the K+ -» T+ + *+t~ decay.55 There is DO informa­ tion about lighter Higgses because of background problems, and heavier Higgses would have decayed into ii+f~ end could not hare been seen in this experiment. It would be interesting to perform sensitive searches for Higgses as spikes in K* —• K+ + (e+e~ and p "*>"). which coold be byproducts of K+ -* x+fit experiments. 3.1.3 K+ -* ** + Nothing "Nothing' comes in many varieties of unobserved neutrals, including the following: K * -» x+ + This is a two-body decay for which the experimental upper iimit57 is to be compared with a theoretical rat*58 whieh b generally > Higgs boson mass, but it seems very difficult to suppress the decay rate below the upper limit (!8). This is pst one of the many reasons why the conventional axion should be dead. However, its Frankenstein refuses to accept5' the mortality of his creature: perhaps it is u andead zombie which still awaits the silver stake of another experiment to be driven through its heart? K * -» IT* + familoti Wilciek60 has invented another light pseudoscala* for you, this time the exactly massless famikm /, a Goldatone boson of % conjectured family or generation symmetry. He estimates*0 the branching ratio

BtK+-x+ + /) = O(i0'<)(^)S (W) where F is an analogue of the decay constant /»• Cosmology01 telb us that F < O(1012) GeV, whereas present experiment* (18) tell us that F > 5 X 1010 GeV. This small gap could be closed by as experiment sensitive to a branching ratio of O(10~'°). Here is a theory which could be excluded by a forthcoming rare K decay experiment. K* -L*+ S|- Vj Dj The experimental upper limit*7 on this three-body decay is

r(/c^r,+E,(,,p,) r{K+ - all) ^ x ' The GIM loop diagrams42 of the Standard Model give for each neutrino flavor 1

B[K+ -» w+Ui p^ = O.ft X HT* i^L X QCD factor (21)

12 with

la these formulae, tbe QCD correction factor is reasonably well known, the U^ denote Cabtbbo-Kobayasbt-Maskwva. mixing matrix elements, sod the />,• uc known01 kinematic functions of the quark and leptoa masses. As can be seen in Pig. 6, & vanishes when the mass of tbe lepton associated with u, is 0(1 to 3) X iti^. The Cabibbc-Kebayaslii-Maskawa muring angle factors and tbe unknown / quark mass are constrained by other &F ?* 0 amplitudes53 such as K£ -•/i+p" which give!) an upper bound17 on the K* ~* x+ -t-v, P, decay rate44 as seen in Fig. 10. The known amount of K° — R mixing provides44 a lower bound on + + the A' -* r + V{&\ (for light associated charged leptons, tt) which can also be seen in Fig. 10. Indicated explicitly in Fig. 10 is the uncertainty in the K°-k9 mixing constraint arising from our ignorance of the AS = 2 operator matrix clement < R, Kldl'lff" >• usually expressed as a coefficient R times the value obtained by inserting tbe vacuum intermediate state.

"".0 (",/IGlVJ

There was a recent advance64 oo this point when it was realized that this matrix clement would be related by Sl/(&) sud PCAC to the known Al = 3/2 K+ — ir+TT° demy amplitude, yielding R = 0,33 with perhaps a (30 to 60)% uncertainty indicated by tlic dashed linen in Fig. 10. Another potential uncertainty arises in the A,'J> — fi+fi' constraint, la contrast to the AS — 2 operator, it can get significant contributions from SUSY ruper-loop diagrams,4365 which could lift

tbe bound fur a given value of m(, I,' we take conservatively the solid lines in Fig, 10 corresponding to rV = 1 aud no SUSY contribution to K\ — (i+f~, we 44 find they arc only compatible for mt < 60 GeV, the Buras'* bound. We get the absoluti- upper bound £B[K+ - ir+ + »v»i)

13 Fit 10- Upper and lower bounds on the + K~* —• ir 1>, yr decay rate Tor different values of W|. The numbers refer to the matrix element factor R.

frwn AM* J 1 I 1 ' ' • 20 40 60 90 in m, (OiVI on the decay rate Mid a lower bound** £B(tf+ - r+ + »,-»,>) -> /\tf*M X 1.4 X KT10 (24) where Nl!iH denotes the number of neutrinos whose associated leptons are light. The numbers (13,14) neglect the contributions of the heavier quarks to the G1M loop diagrams. Because of the K% -* |i+|*~ and K9 - R° mixing constraints, they can only slightly increase the upper bound on the K* -• »+ + p,- P; decay rate.** However, the lower bound can be destroyed by cancellations between the t quark and the 8th quark, though this cannot** happen if the 8th quark mixing angles are in the hierar hial ratio

If we ignore all this uncertainty, the bound (24) can be used to establish an upper bound on the number or neutrinos whose associated charged Itptou do not have masses too close to the W mass as seen in Fig, 11. The curve was plotted using the conservative value ft = l for the AS » 8 matrix element. Our conclusion is that the decay K* -* t+ + unobserved neutrals is very interesting in the context of the Standard Model. If the branching ratio is signif­ icantly larger iban the upper limit of 3.3 x 10"* (S3) this would be a signal for new physics: perhaps more t'jfto three neutrinos ©i ! Paradoxically, a branch­ ing ratio significantly lower than 4.2 X 10~,D (84) could also be a signal for new physics, perhaps a cancellation between third and fourth generation quarks, or

14 2000 r T"

\ 1500

Fif. 11. Tta promt appcf botUHl \ «atMeoQdMr«fentdno*fton m00 22 K+ — *• + ***< decay « a \| faoetton of the onss raj of the charged leptoa associated wftb «%. 900

o J I I L_ H 0 I B S « S '••» l»»'iwi f!*+ -• r+ + VjDjjii So far we hare conceatnted oo proteases where the out- going ncutriDCf ana antiaentriiio hire the sane Savor. ETC theories ud preon models could also give neutrinos ud aatlaeubboa ef different flavors, by mech­ anisms similar to those by whteb lbs/ sin Jf+ -f I+JK. Unfortunately, since these deteya art earperinwatallj indiatinguhable horn K* -> *+ + i/;P„ th>/ will not b« identifl Jile anion their braaebiag ntics am above a few tinea I0_g, which seems unlikely la vtew or th« jifjj •-» fit boaad (10).

/f + -* i>+ + pbottow T or ihJgpca IT Tie lubt antra) particles expected in tha SUSY theories of Sao. 2.4 could also be pair-prodoeed ia K+ decays, either at tha tree level,4"'*' or more plausibly (!) via super-loop diagrams analogous to those for decays into vjG^ W« eiptct4**** decays into gravUino pairs to be fieglSgible, aad utt expect B(K* -•* M+ g»viti»)< JB(lf+-r++^+^ (2«j and it» probsMy much smaller aobss the seofe of SUSY breaking b surprisingly small, The pbotfoo patr-prndoetioa rate depends OB lb* qoknown spectrum of SUSY iMrttetesv bat ia geneta!*****

m«f+-»+ + 7+«5o{^)fl[Jr*-.»+ + ^P,) (27) ao ti^ U b anlia^ to pisA lb* tat* Tor ^ However, in tome theories the tfgfatest SUSY particles may be neutral >faiggsei H , and they eooW*1 be C4ir-Drodoced wfib Vrudunt; ratios comparable with those for a angle Deatriao Baton

IS wkcRvi itd »t ate tie «jcwuu eapwtaiioo voltes of the two Higgs doublets io SUSY theories, We expect «| 3; «& and a? o| < i* tin ratio (28)becofnesj 0.88 4 4 f«ml=20GeV.We£Otaelttdetliattftdet^lf ^ff + «othin8«aa«bobe interesting lor SUSY theories. 3.2 COMPARISONS My penoul aeMssmesta «t the interest of different ran K decay anerinieaU from the points of view of different theories ore shown io Table 1. Toe erases indicate frameworks where * given process does sot occur. This dots sot neces­ sarily mcu the* the experiment is sot interesting from the point of view of thet theory. As Sherlock Holmes has observed, the best clue Is often the dog that dues sot bwk! Teble 1. Testing Theories In fore K Decays

Theories Standard Super- Preon Mode) Technicolor Symmetry Models Experiments

*2-PC X •vW y/

K+ -r x+pe X vV v* ! yf 11 1 did not X occur y X

+ not hint; VP vVvW • X • SUSY particles X X vW X

The number of check* is each box correspond to the amount of interest I per­ sonally bare in confirming the non-ten pred$etH» of the corresponding theory lor tfa»t exp'rimeeL Do they correspond to the nnabcr of yeata of ao expert •nentabat's life that it »^M be worth daaotme: to that teat ot the theoryt The question marks denote caeca where th« theory fa not yet completely clear.

1ft Since Table 1 attaches considerable significance to A'+ -* *r+ + nothing experiments, it is worthwhile to make comparisons wiib other nothing production experiments, in which the existence of nothing U inferred by tagging the event with a pioo, , rx or whatever.

+ + rQ -«, Nothip.g Clearly one way of tagging this fa :n /C -» * +l*° -• nothing), and it has been discussed as a way of producing pairs of massive pbotinos6" or neutrinos. There was some discussion at the Workshop of mailing and taggiog the *° in another way, perhaps by »+ + d -* p+p+{r -• nothing), but it was concluded that background problems made this uncompetitive with K+ decay. Jfi> -* Nothing Thb b in principle a reliable way to count neutrinos, using the V' — Jfi> + it**~ decay lo tag J(^ -* nothing, but it a not very sensitive. From the expected87 decay rate

and the experimental upper limit03 of 1/10 on this ratio we can infer that

s Nv £ 5 X 10 . (30) The cosmologbts*9 with their upper limit of three or four neutrinos should be laughing at us particle physiciitst There ere constraints on Nt, from K+ -» *+ + nothinc*4 and from the late stages of stellar evolution70 are much more stringent than (30), even though somewhat uncertain. As fsr SUSY particles, the rate for Hi> -*^1 depends sensitively on the unknown t squark masses,71 and, in fact, requires a difference between the masses of partners of the left- and right-handed e squarks. T -* Nothing Many of the same remarks ap^Iy, except that the greater mass of the T means that one has better sensitivity thro (20), but experimentalists have not yet got aruurd to quoting an upper limit on T —» nothing. If they could establish that taia was < 0(1/IQ)B[T -» e+t~) then one would get a

limit: Nv < 0(5000), v. huh begins to be comparable with present limits from K* -+ JT+ + nothing decay. e*e~ -» Nothing This can be tagged72 by a brenustrahlung

17 Z° — Dolbing and e*e —• nothing a» \/« = 20 GeV both found an apparent "M>* > 3. would K+ ~* r+ + nothing tell us AT? = 3 in which ewe we would suspect the ex.:°*«nce of novel neutrals, probably with masses larger than ISO MeVT Or if we wei» satisfied from Z and e+e- —• nothing that Aft, = 3, we could use the rate for K+ -* JT+ + nothing as a probe or Standard Model dynamics. Either way, the decay A"*" -» f+ + nothing has an important role to play. The same probably cannot be said far the decay p — c+ nothing which can be probed at a * or K factory.70 One difficulty is that the dominant decay of the fj is u -* e + (nothing =» v l>), so that there is a big background. One does not usually expect Lt and Lp to he violated in spontaneously broken SUSY theories, Goji/^e+7 + 7, whereas the analogous /if+ -• x+ + 7 + 7 decay can occur at 0(1/10) or the K* -» ir+ + v + f> rate. For the same reason one does not expect p -* c + axion decay, whereas the absence of K+ -* »+ + axion has already been used to dispute the very existence of an axion. However, the two-body decay ft -» « + famiton could be interesting:

B(p - e + f) *t 0(10»)(^f (31) to be compared with the analogous K+ ~* T+ + f decay rate (10). For this reason a continued search for the two-body p -• e + nothing decay down to a limit or order 10-12 may still be vtduabte. 3.3 ANO DECAYS Now that ve have broached the subject of ALu j& 0 processes, it is -voribr while to make a systematic comparison of one with another, and also with the rate K decays that were the subject of Sec. 3.1.1. Table 2 is a compilation of limits from various rare processes7' on the possible masses of certain species of exotic beasts. It b adapted from a table developed by Sbanker78 which was presented earlier at this meeting by Wilciek.*0 It is always difficult to achieve a consensus on tbe couplings to be assumed for imaginary particles, and I have made somewhat different assumptions than 3hanker.7B These do not affect the ratios of different limits on the same particle from different experiments oo much as they affect the absolute values of the limits, especially for theories with many 78 Higgs doublets. Shanker assumed couplings to lentous uf order ft mTfmw and to quarks of order jfc mb/mW> whereas I have chosen values three orders of magnitude smaller. These values correspond more closely to the masses of the light quarks and leptons involved in the processes we art considering. If they appear loo small, recall that there are probably mixing angle factors which enter when we consider reactions that violate Lt and/or Lp, and probably also when one changes quark generation: t -* d. For this reason it is difficult to interpret directly the order-of-magnitude limit on tbe Higgs mass coming from processes violating L( and Lp. However, it probably b reasonable to interpret Table 2 as indicating that among such processes, multiple Higgs theories are most sorely tested by anomalous muon conversion pZ —» tZ, This need not be the case for other theories of Lt and Lp violation, which may well be more severely tested by (i -» n or /i -• cle searches.

18 Table 2. Comparison of Mass Limits Fnva Rare Processes

Multiple Pseudoscalar Vector Experimental Process Higgs Leptornjark Leptoquark Limit Bfp-n) 0.2 1.9 X 10-10 B\p-+elc) 0.4 — — 1.9 X 10~8 B(pZ -~ eZ) 11.0 0.1S X* 60 X8 7 X 10-11 BiKt^Vt) 7.0 0.18 03 2 X 10~g 4.7 o.i2 xe 62 XB 0 X 10-° B[Kl -* ee) 7.0 0.18 X 9 05 X* 2 X 10~* 8[K+ -> *+H 0.7 0.01 3.5 7 X 10~g 1S &mK ISO ~" ^ as 3.5 X 1Q- (CeV) mass limits mass limits mass limits inGeV inTeV inTeV

Table 2 features my personal guesses as to possible mixing angle factoni in leptoquark interactions which would arise if one makes the normal idtntifica'wos of lepton and quark generations: a *-» p, d w e. We see again that tbe best limits on leptoquark masses seem to come from the KJj -»(it decaf limit discussed in See. 3.1.1, with K+ — w+fte providing less stringent limits as we expected. We also see that the decays A'° ~* up and ee give less interesting limits because at mixing angle factors. Since the decay K9 —» p/i bas already been obs^/ved at a rate ek»e to the unitarity 'irait, after jf £ -» j»e tbe next moat interesting ot these leplonic K 4ecays to look for may be K% -* ee. Another decay which gives »ccess to similar physics is S —» ppe. Unfortu­ nately, it bas been estimated77 that the upper limit on K —» pe decay already suggests that

>I B(E-p^|

(32) as "an awful long ways to |o." K decays seem more se&sitive proves of Le and L„ violating physics. One point to be recalled in looking at Table 2 is tbat as the sensitivity to a rare decay *—.nching ratio B is increased, the sensitivity to heavy boson masses only inc-isc a3 "»A«,v,*Zri • (33) Thus an order of magnitude increase la sensitivity correspoii' .3 to a change in

the limit on mfcr(,t>y by less than a factor of two. Moreover, this change i'„ often

10 small compared with other uncertainties in the calculation, such as those in the values of coupling constants and of matrix elements. Progress will not be rapid, nor will its interpretation be unambiguous. 3.4 CP VIOLATION The discovery1 of CP violation in the neutral K° system has so far been one of the greatest contributions by kaons to our physical knowledge. Unfortunately, despite its cosmic significance79 this original manifestation or CP violation in the mass matrix is still the only CP violating phenomenon observed experi­ mentally. Table 3 presents a list of interesting CP violating observables together with the corresponding predictions of the theoretical frameworks introduced in Sec. 2. We see that four of the observables appear in K decays, while two involve hyperon decays. First ve have the fundamental K\ — K-i mass mixing parameter t. Its value can be fitted hut not predicted in the Standard Model where « CC s

•3 are both considerably smaller than ein6tl as would be the ease if the b quark lifetime turns out to be 0(1O-12) seconds, lu models with additional gauge bosons and left-right symmetric models in particular the value of t is related to the masses of the heavier gauge bosons. In multiple Higgs models the value of £ is related to the spectra and couplings of the Higgs bosons. Technicolor models tend to predict magnitudes of the CP-conserving real part of the AS = 2 K\-K2 mass mixing which are much too large, and give no understanding why t should be so small. The last column in Table 3 introduces the non-perturbative QCD OP-violating $ vacuum angle,24 which cannot contribute significantly to f because of the *ev«a upper limit of 0(IQ""9) oa & coming from the noft-observaUou80 of a electric dipole moment. Next we turn to model predictions for intrinsic CP violation i1 in the K -* 2x decay amplitude and the ratio c'/c. Figure J2 depicts a Penguin diagram, which plays a crucial role in calculations of this quantity. As reviewed by Wolfenslein,'* this meeting has witnessed considerable progress in the elucidation or the Standard Model*1 and multi-Higgs model83 predictions. The Standard Model predicts31 a definite sign (positive) aa well as a lower bound on the magnitude. Multiple Higgs models also predict82 « definite sign (negative) and a magnitude much larger than the Standard Model bound. These modeb are on the borderline of siierimental exclusion, but may not yet have crossed it- Left-right symmetric gauge modeb are unfortunately rather less specific in their predictions fot •'/(• The naive technicolor modeb seem63 to prtrtict too large a value for d/i, but ihb defect might also be rectified if one could cure38 the other flavor-changing neutral interaction problems30 of such theories.

20 Table 3 CP Violating Obaervabla and Model Predictions Standard Multiple Multiple Super- »QCD Model W H Tcchnicolor symmetry e fit ""•Hfe "mH too big? \ 0

«7« > 2 X IP-3 ~i

s Q+-0-V+- Off1) o|ur ) T iarge I as for 0 Standard Pit in K — ^u- 0 0 < 5 X 10"s 0 Modil 0

-Pl r ? T flfA-pl+flir 5 0

•fE^fe 1 -3^ f T T 0

2S 25 M'-™) <]o-M ~ 3 X I0"27 ~SX 10"2tt ~ »

very small J large ? large ? as for 0 Standard UDobservable t large 7 large? Model 0

too fit - unless fit - unlass =3 Universe small CPX CPX t/ possible large spontaneously spontaneously S? 1 i-»3 4941*13

The next row1" features predictions of the different models for intrinsic CP violation in the K —» 3ir decay amplitude. It is expected to be the order of magnitude as €* in the Standard Model, and *lso very small in a left-right sym­ metric gauge model, whereas the multiple-Higgs model prediction has not been uevdo).'*!. The muon transverse polarization P% a expected to be non-zero ealy in maltiple-Higgs models, but b not expected to be very large. For complete­ ness, two CP-violating observables in hyperon decay are listed, together with the Standard Model predictions for them which are both 0[t?), The lefi-.ighl gauge and multiple-Hig^j model predictions have not yet been developed. We now turn to CP violating observabtes beyond the ambit of the strange 5 physicist. The neutron electric dipole moment dn is expected * to De UQiVoserv- obly small in the Standard Model, but can be close to the present experimental limit80 of 6 X I0"25 e- cm in left-right gauge modeli,85 multiple-Htggs models,8* and in technicolor theories.87 Tbb is the only observable for which the QCD $ 88 1 vacuum parameter is likely to play a role, and the estimate dn ~ 3X10" 0 e— cm tails us that K2X HP9 (35) wbicb is j its Affects are not observable elsewhere. Observation c! o jeutron electric dip vie moment in the near future need not exclude *ii Standard Model of CP violation. Its prediction could have been augmented by a contribution from 8 close to the limit (35) which would "nt show up in any other pheoomenological situation. The election could also have an obsirvable80 electric dipole moment, wh'f-h can !>e comparable with that of the neutron in some SUSY models.00 It U natural to ask whether CP violation could oppe&r in the Da - D° or 3° - B systems in ways analogous to its manifestation in the K9-K system. According to thu Standard Model, e should be small in the D° system Nt could

22 be Urge in the B° system. The depends on the values of unknown Kobayasbi- Maskawa angles, but unfortunately Efl — B° mixing j expected to be suppressed in domains of the angles wuere t is large,"1 so it is unlikely that CP violation could actually be observed in the B° system if the Standard Model b correcl. Finally we come to the v.'aiverse. It b included here because of the idea79 that the observed btryon asymmetry in the Universe may have originated from CP and B violation in GUT reactions^ when the Universe was O(I0-35) sec­ onds old. Thb qualitative mechanism is not strong*5 enough in the Standard Model to produce the observed baryon-io-photon ratio of & few times 10_'°, but couli! * • fit in more complicated models containing more Hoggs muitiplets and/or i • .• pauge bosons. However, tbe connection with low energy physics is not clear, ouice the extra baryosynthetic structure need only appear at the GUT scale, and may not be light enough to 3how np in present-day accelerator experi­ ments. Also, it b important to note that in many cf these models with additional low energy structure CP is violated spontaneously, in which case no significant baryon asymmetry can be generated. For thb reason technicolor theories87 are not baryosynthetie. The OCD 6 parameter ^bo does not contribute directly to the baryon asymmetry,94 although one can argve that most theories which gen­ erate enough baryons and do not possess some additional symmT*™ such as a Peccei-Quinn33 U(l) or SUSY will also have a value of 6 close to the limit (35) and suggest a neutron electric dipole moment close to the present experimental Uinit.9^ Since cosroological CP violation may be the reason we exist, t thb meet­ ing, it provides a motivation for constructing a suitable extention of ti e Standard Model.

3.5 NEUTRINO PHYSICS The death of a kaon b often the birth or a neutrino -vhich can be used for high intensity and precision neutrino physics, as was discussed by a working 06 group at thb meeting. One can imagine detailed measurements of i>ft, Pp e and i/«e scattering which enable one to measure

2 Sm29 fa 140 GeV X 4(«n 0u/) (30) so that a determination of m^o with a precision of about 300 MeV would fix BirPfy with an error of ±0.002. It is not clear that one would gain from a more accurate value of trip, because of uncertainties in the one loop correction due to strongly interacting particles and because of higher order radiative corrections mass. Compare thb precision with the shift" in the apparent value or 3in~fl(v due to radiative corrections, which b O(0.012j. In thb context, a "precision" low energy determination of oina^ should mean an error <£ 0.01 and prcfci ably 0(0.002).

23 As discussed by Shrock at this meeting, another interesting class of low eue-gy neutrino experiments involves scarchesTOfor massive neutrinos v^. One may look for their production in ;r -+ pvfi, evjf and K -* ftv^j, evu decays via anomalous bump!' in the lepton energy spectrum, in which cases one is sensitive to l%i//|2 or lUtff)* respectively, where the Ugff are mixing matrix elements, as sees in Pig. 13. Another possibility ia to search for I>H decays, as was mentions 100 at this meeting by Ferro-Luzzi. One can look either for VJJ -* ut^t~ or for V H ~* V(Z*e~. and is generally sensitive to the product \Ut^0^1 or |t/tHil/MW|. Figure 13 is taken from a proposal'00 for such a decay experiment at CERN, and We see that Tery large ranges of mixing matrix elements are accessible to such an experiment. This range could be further improved using a more intense source, just as the (ior « spectrum bump-hunting experiments could also improve in sensitivity.

-r—i 1~ 1^-Chorm WBB W71S1N)

1 V-ITH1UMFI

Fig. 13. Actual and potential bounds on heavy neutrino couplings as func­ tions of their masses.

100 ZOO 300 400 500

m,H (MeV)

3.6 A PERSONAL PRIORITY LIST It b always dangerous to put something like this into print, as it is likely to be over-simplified and over-interpreted. However, several participants have urged tae to produce such a distillation, which I do not mind doing as long as everyone realizes it is just a personal opinion, and there is at lf>ast as many different opinions as there are theorists at this meeting. Top or my priorities would be a measurement of the CP violating parameter t'/(, because of the light it would cast on the mecbanism(s) of CP violation. Second would be K+ —»• r* + nothing experiments, because this is the last great frontier of AS jt 0 neutral interactions which will felt us a tot about the

24 Standard Model « well as expose us to a«w physio. N«t I come to the more speculative searches Tor new interactions, at the top of which list I would place K9 —* lie. This seems to be more sensitive and topical than the other searches such as /Y* -» *•*/«, £ -* ppe, and ftA -* eA, n -* c id ft -* e8c. At the bottom of my list come precision neutrino experimc n part because of my doubts whether the errors could be reduced sufficients be really exciting. Then there are many other experiments which get an ">" plete."

A. Beyond Physics The jiscussion or serious physics has terminated with the previous section. Now I would like to mention to you briefly a little philosophical speculation you may care to entertain: can one observe a violation of quantum mechanics? It has been noticed101 that black holes correspond to mixed thermal states with finite entropy associated to the existence of an event horizon across which information can be lost. Hawking102 has further observed that quantum effects cause black holes to radiate particles with * mixed thermal spectrum. These discoveries may not be of purely philosophical or astrophysics! significance in view of the old ide*103 that spaeetime may have a foamy structure at short distances, with 0(1) mini black hole or other topological structure (instanton!) in every Planck volume. Thus we may imagine that event horizons codstantly appear and disappear, and wonder whether this would have any implication for the purity of quantum mechanic*! wave functions. Hawking and collaborators39 have performed calculations suggesting that indeed gravitational instantons may cause initially pure states to evolve with time into mixed states, and Hawking104 has argued that the conventional laws of quantum mechanics should be modified as a consequence.

101 He entertains the possibility that au initial density matrix p_D may yield a final density matrix p*B:

P+fl=/flCi>f-D (37) where the superscattering operator Jf^c** does not factoriie into the product of an 5 matrix and its adjoint: /W*£4D (38) as in conventional quantum mechanics. If this is indeed the case, one might expectl0i a non-standard equation for the time evolution of the density matrix:

57=A(P) (38) where Jfi is a gener&l bermitian linear operator which does not take the standard form: /f=*i\p,H\+5JI : fi^ff^O (40) it is easy to check that pure states may evolve into mixed states if the JS operator does not factor as in Eq. (38), or if fl takes the non-canonical form (40). We

25 would expect100 the conventional rules of quantum mechanics to apply on time scales Si < \S fl\~x> but expect that if then violations of quantum mechanics may be observable. This general expect­ ation100 is indeed borne out by calculations in simple examples*"* of modified quantum mechanical systems. For example, one might expect that an initially pure K° state pioduced in a badTOD-L&dron collision could evolve into a mixed atmte which is approximately a Ki but with a small Kg admixture. This K$ component can come from a term 6 fi in (40) which produces a slow 'decay' of the Ki into the Kg, appearing as a continuous 'regeneration' of K§ 'n vacuo (precisely what one would expect if the definite phase relationship between the K° and R components of a Ki beam were to become mixed in some way). This contributes to the downstream 2T yield ia a way which is distinguishable from the usual CP impurity of the Ki, but this distinction requires a precise comparison ol the CP parameters |»j+-| — 18 |«|, ijJ+_, and S ~ 2/fce. Based on existing data this comparison gives \6JI\ <2xiO-31GeV . (42)

A constraint on |6 /71 for of similar magnitude can be deduced105-106 from the success of long baseline neutron interf eronwtry experiments. Since neu­ tral kaons are at the cutting edge of this issue, it might be'vorthwbil'j to consider how one mif'jt devise somewhat more sensitive tests ">f quantum mechanics in tbe K° - fir system.

S. A Question Figure 14 is an *rtist'a impression of tbe receiit past history of physics &nd its cousins which abo features some possible extrapolations into tbe future. Tbe horizontal lines depict Gelds of study which do not jet more fundamental as time elapses. Tbe diagonal line depicts the direction of elementary particle physics, including a few landmarks passed in tbe past as well as some possible landmarks of the future. As the diagonal and horizontal lines diverge, new fields of study open up between them. For example, tbe recent achievement of a consensus Standard Model or elementary particle physics bids fair to act as a node where a new line branches off horizontally. This may meet a new disgooel line branching off from traditional nuclear physics. The old pion factories were mainly motivated by nuclear physics but have turned out to give some help in elucidating the Standard Model. Kaon factories would surety be useful for Standard Model physics. We can ask ourselves whether they will have significant impact on ilic particle physics of the IQQO's. Assuming that they do, we should also ask our political masters whether we are playing in a lero-sum game. Would any significant fraction of the cost of a kaon factory be charged agaiogt the elementary particle physics account? If so, we particle physics chauvinists have to wonder whether kaon factories would be a ccst-effective means of pursuing our discipline.

2B The "weak" lobby gathered at this meeting is agreed that strange physics is great physics. Furthermore, there seems to he little transatlantic competition since we leant that there is to be no beam for charged kaon physics at CERN in the foreseeablefuture . One has the impression that a kind of Yalta philosophy may be at work, according to which CERN concentrates on p physics and leaves strange physics to accelerators in the United States Can the variety of strange physics we feel necessary be done "on the cheap" t

TIME

NUCLEAR PHYSICS

Eltmeniary POfticle Phytic*

Fig. N. A sketch of the past and possible future evolution of elementary particle physics and related disciplines.

Acknowledgements It is .1 pleasure to thank T. Coldman, H. Haber and J. Primack for their kind hospitality, and to thank S. J. Brodsky. M. K. Gaillard, J, S Hagelin, C. Heuscb and C. Sachr&jda for useful comments and discussions.

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