Rare K-decays as crucial tests for unified models with gauged baryon number

In the grand-unified models based on SU(15) and SU(16) in which the quarks and leptons are un-unified at the intermediate stages, we show that BR (KL → μe) ≤ 10−14 and BR (K → πμe) ≤ 10−14 despite the presence of leptoquark gauge bosons. Thus, the observation of these processes in the ongoing or upcoming experiments will rule out the models. PACS numbers: 12.10.Dm, 13.20.Eb, 11.30.Hv Experiments to observe the processes KL → μe and K → πμe are underway at Brookhaven [1]. When completed, they will probe a branching ratio as small as 10 for each process. If the processes are not seen at that level, it will mean bad news to a lot of theoretical models beyond the standard model. Here, on the contrary, we point out a class of grand-unified models which will definitely be ruled out if the processes are observed – not only by the Brookhaven experiment, but with any branching ratio larger than about 10. We have in mind the grand unified models based on SU(15) [2, 3] and SU(16) [4], which have baryon number as part of its gauge symmetry. In the recent literature, there has been a lot of discussion [2, 3, 5, 6, 7] that such models can have some chains of symmetry breaking where renormalization group analysis yields very low unification scale, as low as 10 GeV, without any conflict with the known bounds on proton lifetime [8, 6, 7]. It has also the pleasant feature that the monopole problem vanishes in such models with low unification scales [9]. Before proceeding, let us discuss why grand unification models based on these groups deserve attention. The gauge groups for these models are not just any group to play with. SU(15) is the maximal group for unification for all known fermions in a single generation, just as SU(16) is if a right handed neutrino is needed to make the fermion spectrum left-right symmetric [4]. Just as the minimal grand unification group SU(5) is interesting for its special status, so are these groups. Secondly, in all known physics, the fermions transform as fundamental representations of the non-abelian gauge groups. Quarks transform as the fundamental representation of the color group SU(3), left-handed fermions are fundamental representations of the electroweak SU(2). Thus, it is intriguing to check the idea that all fermions transform like the fundamental representation of the grand unified gauge group. Lastly, baryon number and lepton number are known symmetries of low energy physics. It is interesting to entertain the possibility that these are gauge symmetries at high energy. We now begin our argument by briefly describing the SU(15) model. All known left-chiral fermions of a single generation transform like the fundamental representation of this group: ΨL ≡ ( urubuy drdbdy ûrûbûy d̂rd̂bd̂y νee e )