K~ + n“vfi Beyond the Standard Model

We analyze the decay ~{L -+ ~“v~ in a model independent way. If lepton flavor is conserved the final state is (to a good approximation) purely CP even. In that case this decay mode goes mainly through CP violating interference between mixing and decay. Consequently, a theoretically clean relation between the measured rate and electroweak parameters holds in any given model. Specifically, I’(lf~ + mOVD)/I’(l{+ -+ m+vv) = sin29 (up to known isospin corrections), where 9 is the relative CP violating phase between the K – ~ mixing amplitude and the s j dv~ decay amplitude. The experimental bound on BR(K+ --+ r+vti) provides a model independent upper bound: BR(KL -+ ~“~fi) < 1.1x 10-8.In models with lepton flavor violation, the final state is not necessarily a CP eigenstate. Then CP conserving contributions can dominate the decay rate. Submitted to Phys. Lett. B -Research supported by the Department of Energy under contract DE-AC03-76SFO0515 In the Standard Model l{L + TOVUis dominantly a CP violating decay [1]. The main contributions come from penguin and box diagrams with an intermediate top quark and can be calculated with very little theoretical uncertainty [2,3]. It then provides a clean measurement of the Wolfenstein CP violating parameter q or, equivalently, of the Jarlskog measure of CP violation J and, together with 1{+ + T+vv, of the angle @ of the unitarity triangle [3]. The Standard Model predictions are BR(l{+ + T+vti) = (9.1 ~ 3.2) x 10-11 and BR(l{L + ~“vv) = (2.8 t 1.7) x 10–11 [4]. Such rates are within the reach of near future experiments [4]. The Standard Model contributions to the amplitude are fourth order in the weak coupling and proportional to small CKM matrix elements. Consequently, this decay can be sensitive to New Physics effects [5]. In this paper we study the 1{ + ~vfi decay in a model independent way. We are mainly interested in the question of what can be learned in general if a rate for l<L + ~“vti much larger than the Standard Model prediction is observed. We find that the information from a measurement of the rate is particularly clean and simple to interpret if lepton flavor is -. conserved. In this case the l{L + n“vv decay is dominated by CP violation in the interference between mixing and decay. The theoretical calculation of the decay rate is then free of hadronic uncertainties and allows the clean determination of CP violating parameters even in the presence of New Physics. Knowledge of neither magnitudes of decay amplitudes nor strong phases is required. Models with Z-mediated flavor changing neutral currents serve as an example of these points. In models with lepton flavor violation, the final ~“vti state is not necessarily a CP eigenstate. We show that in this case the CP conserving contributions can be significant and even dominant. The results are still informative but more complicated to interpret, as they depend on both CP violating and lepton flavor violating parameters. We give an explicit example of models with leptoquarks (or, equivalently, supersymmetry without R-parity). Our notation follows refs. [6,7]. We define the decay amplitudes A and A, A = (rOvfi\HIKO), A = (7r’%filHIIlo). (1)