Naturalness redux: The case of the neutrino seesaw mechanism

The idea of naturalness, as originally conceived, refers only to the finite renormalization of the Higgs boson mass induced by the introduction of heavier states. In this respect, naturalness is still a useful heuristic principle in model building beyond the standard model whenever new massive states are coupled to the Higgs field. The most compelling case is provided by the generation of neutrino masses. In this paper, we confront this problem from a new perspective. The right-handed sector responsible for the seesaw mechanism—which introduces a large energy threshold above the electroweak scale—is made supersymmetric to comply with naturalness, while the standard model is left unchanged and nonsupersymmetric. Cancellations necessary to the naturalness requirement break down only at two loops, thus offering the possibility to increase the right-handed neutrino mass scale up to 1 order of magnitude above the usual values allowed by naturalness. If also the weak boson sector of the standard model is made supersymmetric, cancellations break down at three loops, and the scale of new physics can be further raised. In the type-I seesaw, this implementation provides right-handed neutrino masses that are natural and at the same time large enough to give rise to baryogenesis (via leptogenesis). The model contains a dark matter candidate and distinctive new physics in the leptonic sector.

Figure 1

One-loop cancellation among different contributions to the Higgs boson mass term in the setup outlined in Sec. 2a. We mark in red the heavy states with mass $M$.

Figure 2

Upper panel: representative two-loop corrections to the Higgs boson mass responsible for the quadratic correction proportional to $M^2$ in Eq. (29). The heavy states with mass $M$ are marked in red. Lower panel: representative three-loop corrections relevant if SUSY is extended also to the EW gauge sector of the SM (see the text for details).

Figure 3

Three loops double-bubble diagrams with the top on the external bubble.

Figure 4

LEP bound on the mass spectrum of the scalar doublet $\tilde{L}=({\tilde{L}}^0,{\tilde{L}}^{-}{)}^{\mathrm{T}}$. The gray region represents an indicative lower bound of the same order of the one set in the context of direct slepton searches [20]. The orange regions represent the 1- and 3-$\sigma$ exclusion limits obtained including Eqs. (38)–(40) in the fit of LEP-I and LEP-II data [32].

Figure 5

Representative Feynman diagrams (at the parton level) describing a typical monojet event with one hard jet and missing transverse energy in the final state (left panel) and with the additional presence of a disappearing track due to ${\tilde{L}}^{\pm }\to {\pi }^{\pm }{\tilde{L}}_0$ decay (right panel).