Implication of improved upper bounds on |1L| = 2 processes

We discuss implications of improved upper bounds on the |1L| = 2 processes (i) K+ → π−μ+μ+, from an experiment at BNL, and (ii) μ− → e+ conversion, from an experiment at PSI. In particular, we address the issue of constraints on neutrino masses and mixing, and on supersymmetric models with R-parity violation.  2000 Published by Elsevier Science B.V. PACS: 13.20.Eb; 14.60.Pq; 14.60.St; 14.80.Ly At present there are increasingly strong indications for neutrino oscillations and hence neutrino masses and lepton mixing from the solar neutrino deficiency and atmospheric neutrino anomaly [1]. The existence of lepton mixing means that lepton family number is not a good symmetry. Majorana neutrino masses occur generically, and violate total lepton number L by |1L| = 2 units. However, so far, in contrast to the data suggesting lepton mixing, experimental searches for the violation of total lepton number have only set limits. Among these are searches for the |1L| = 2 processes (i) neutrinoless double beta (0ν2β) decay of nuclei and (ii) μ− → e+ conversion in the field of a nucleus. A third class of |1L| = 2 processes includes the decays K+ → π−`+`′+, where `+`′+ = e+e+, μ+e+, or μ+μ+ [2,3]. In a previous work we considered these decays and, from a retroactive data * Corresponding author. E-mail addresses: [email protected] (L.S. Littenberg), [email protected] (R. Shrock). 1 On sabbatical leave from Yang Institute for Theoretical Physics, State University of New York, Stony Brook. analysis, set the first upper limit on one of them, namely [4,5], (1) BR(K+→ π−μ+μ+) < 1.5× 10−4 (90% CL). In [4] we also noted that rare K decay experiments at BNL could greatly improve this limit and proposed a search for K+ → π−μ+μ+ [6]. Among these experiments was BNL E865, which was searching for, and has now set a stringent upper limit on, the decay K+ → π+μ+e− [7]. This experiment has also recently obtained the 90% CL upper limit [8] (2) BR(K+→ π−μ+μ+) < 3.0× 10−9. In the present paper we discuss the implications of this limit. In the context of current bounds on neutrinoless double beta decay and μ− → e+ conversion, we shall also consider the implications of two other 90% CL limits on |1L| = 2 decays from E865 [8]: (3) BR(K+→ π−e+e+) < 6.4× 10−10