Comment on theK+→π+e+e

Abstract

The sectiori Cotnments arid Addenda is for vhort con~municatioris which arc not appropriate for regular nrtic1c.r It iriciudes onlv tiic fo!lowing /y/~e.s o f cut??municalions. ( 1 ) Comments of7 paper., r~reviously published in T l~e Physical Review vr Physical Review Letters ( 2 ) Addenda to papers previousiy pzrhlisl7etf in The Physical Review or Physical Review Letters, in which the adtiitionai injbrn~ation can be presented without the need for u1riting a complete article. Manuscripts intended for this section rnust be accornpanietl by a brief abstract for information-retrieval purposes. Acccpted marzuscripts follow the same publication schcdulc as articles in this journal. iir~tl pagcJ proofs are sent to authors.The neutral-current process K + +n'e +e -is reevaluated taking strong-~nteraction corrections into account. Reasonable agreement with experiment is found. Some time ago Gaillard and ~e e 'calculated neutral-c u r r e n t decays of kaons. T h e s e authors w e r e able to fit all decay r a t e s with a charmed quark with m a s s -1.5 GeV-a very successful prediction. All the calculations w e r e made, basically, with the free-quark model. When strong interactions w e r e taken into account2 the agreement remained and indeed improved.However, there is one decay for which the freequark model gives a r e s u l t not very compatible with experiment, namely, I(+--v'e'e-for which the branching r a t i o estimated in Ref. 1 i s -lomF, to b e compared with the experimental value"Z06 10.5) x 1 0 -~. Of necessity, the calculation of Ref. 1 was very rough; we have thought i t worthwhile to have another look at the p r o c e s s to verify whether a r efined calculation a g r e e s with experiment, o r 8 the The d i a g r a m s for the K'-7ife"e-p r o c e s s may b e split into two groups, external and internal b r e m sstrahlung [Figs. l ( a ) and 1 (b), respectively]. In the f i r s t , the K*.-.rr+ transition i s described by the amplitude A correspoudi.ng to the elementary diag r a m s of Fig. 2. It is not difficult to verify that we can w r i t e with bothA(0) a n d A f ( 0 ) of o(cx/M$). T h e r e f o r e , l f we neglect t e r m s of o r d e r G, " we may take A to be a constant. Then the contribution of the external bremsstrahlung (EB) [~i g , l(a)] is discrepancy i s maintained. Not surprisingly, our The internal-bremsstrahlung piece may again be refined estimate is in good agreement with experisplit illto two s u b c l a s s e s , corresponding to the ment. diagrams of Figs. l ( a ) and l ( b ) , respectively. Of t!lese, the f i r s t diagrams (radiation by the U7 line) contain two W propagators; since by virtue of the Glashow-liiopoolor-Maiani (GIM) mechanism4 they FIG. 1. Diagrams contributing to K*n +eie-. (a) External bremsstrahlung, (b) internal b r e m s s trnhlung.PIG. 2. Diagrams f o r the K*-1; " transition.

Unified theories with U(2) flavor symmetry

“…The measured values of the bottom quark and the τ lepton masses are compatible with their equality at a unification scale [2], establishing a nice consistency with the heaviness of the top quark in the case of a supersymmetric theory [3]. On the other hand, the interpretation of the light masses and of the mixing angles constitutes a formidable challenge.…”

“…If the approximate equality holds, then there are contributions to flavorchanging processes which are interesting -we call this the "1,2-3" signal [12]. On the contrary, in general there should be considerable degeneracy between the scalars of the first two generations: m sin φ m 300GeV (3) in the charge −1/3 sector, where φ is the relevant CP violating phase. In the lepton sector, the corresponding limit from µ → eγ and µ → e conversion is (m (m/100GeV) [13].…”

“…The interactions of (5), (6) and (7) are understood to include all possible SU(5) invariants. The second operator of (5) leads to the well-known SU(5) mass relation [2,3] …”

Is the stop mass below the top mass?

“…Unfortunately, for the light quarks the masses are uncertain, but the ratio of b-quark and τ -lepton masses can be correctly predicted by the radiative mass corrections [44,9,18,19,16,17].…”

Scalar Mass Universality, “Anomalous”U(1) andRSymmetries

“…However, being not the logical consequence of local supersymmetry, such an assumption may well be violated. Actually, many string-model calculations 7 ) show that the universality is violated by "moduli-dependent" contributions to scalar masses.…”