Abstract
We discuss lepton number violation in three units. From an effective field theory point of view, $\Delta L=3$ processes can only arise from dimension 9 or higher operators. These operators also violate baryon number, hence many of them will induce proton decay. Given the high dimensionality of these operators, in order to have a proton half-life in the observable range, the new physics associated to $\Delta L=3$ processes should be at a scale as low as 1 TeV. This opens up the possibility of searching for such processes not only in proton decay experiments but also at the LHC. In this work we analyze the relevant $d=9,11,13$ operators which violate lepton number in three units. We then construct one simple concrete model with interesting low- and high-energy phenomenology.
Highlights
The standard model conserves baryon (B) and lepton (L) number perturbatively
The only dimension 5 (d 1⁄4 5) operator, the famous Weinberg operator associated to Majorana neutrino masses, violates lepton number by two units
Proton decay searches concentrate on final states such as p → eþπ0 or p → Kþν
Summary
The standard model conserves baryon (B) and lepton (L) number perturbatively. this is no longer true for nonrenormalizable operators [1] which might be generated in ultraviolet completions of the theory. At d 1⁄4 6 there are various 4-fermion operators which violate baryon and lepton number by one unit [1,2,3], inducing proton decay to two-body final states. This implies that neutrinos must be Dirac particles, as Majorana mass terms would require violation of lepton number in two units Another immediate consequence of this hypothesis is that proton decay final states must be at least three-body, while an unambiguous experimental signal establishing ΔL 1⁄4 3 requires three charged leptons: p → π−π−eþeþeþ, i.e., a 5-body decay. For such high-dimensional operators, an observable rate of proton decay is achieved for a new physics scale in the (1–100) TeV range, depending on the dimension of the operator under consideration This opens up the possibility to observe violation of lepton number in three units at the LHC. SuperK has recently published some limits on 3-body decays [12]: τðp → eþννÞ > 1.7 × 1032 and τðp → μþννÞ > 2.2 × 1032 at 90% confidence level, but gives no limits
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