Effective approach to lepton observables: the seesaw case

Abstract

In the absence of direct evidence of new physics, any ultraviolet theory can be reduced to its specific set of low-energy effective operators. As a case study, we derive the effective field theory for the seesaw extension of the Standard Model, with sterile neutrinos of mass $M>m_W$. We systematically compute all Wilson coefficients generated at one loop. Hence, it becomes straightforward to (i) identify the seesaw parameters compatible with the smallness of neutrino masses; (ii) compute precision lepton observables, which may be sensitive to scales as large as $M\sim 10^3$ TeV; and (iii) establish sharp correlations among those observables. We find that the flavour-conserving Wilson coefficients set an upper bound on the flavour-violating ones. The low-energy limits on $\mu \to e$ and $\tau \to e,\mu$ transitions suppress flavour violation in $Z$ and Higgs decays, as well as electric dipole moments, far beyond the experimental reach. The precision measurements of $G_F$, $m_W$, and $Z$ partial decay widths set more stringent bounds than present and future limits on $\tau \to e,\mu$ transitions. We also present a general spurion analysis, to compare the seesaw with different models, thus assessing the discriminating potential of the effective approach.

v4: Eq. 6 and Fig. 1 corrected, a few other minor corrections, phenomenology unchanged

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• Two portals to GeV sterile neutrinos : dipole versus mixing
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• Low-scale Leptogenesis with Minimal Lepton Flavour Violation
• The General One-loop Structure for the LFV Higgs Decays $H_r\to l_a{l}_b$ in multi-Higgs Models with Neutrino Masses
• Modified lepton couplings and the Cabibbo-angle anomaly
• Lessons from LHC on the LFV Higgs decays $h\to {\ell }_a{\ell }_b$ in the Two-Higgs Doublet Models
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