On-shell renormalization of the mixing matrices in Majorana neutrino theories
Abstract We generalize a recently proposed on-shell approach to renormalize the Cabibbo–Kobayashi–Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism. An important property of this formulation is the gauge independence of both the renormalized and bare lepton mixing matrices. Also, the texture zero in the neutrino mass matrix is preserved.
Propagator mixing renormalization for Majorana fermions
We consider a mixed system of unstable Majorana fermions in a general parity-nonconserving theory and renormalize its propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. In contrast to the case of unstable Dirac fermions, the WFR matrices of the in and out states are uniquely fixed, while they again bifurcate in the sense that they are no longer related by pseudo-Hermitian conjugation. We present closed analytic expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions, as well as their expansions through two loops. In the case of stable Majorana fermions, the well-known one-loop results are recovered.
The Earth's Angular Momentum Budget on Subseasonal Time Scales
Irregular length of day (LOD) fluctuations on time scales of less than a few years are largely produced by atmospheric torques on the underlying planet. Significant coherence is found between the respective time series of LOD and atmospheric angular momentum (AAM) determinations at periods down to 8 days, with lack of coherence at shorter periods caused by the declining signal-to-measurement noise ratios of both data types. Refinements to the currently accepted model of tidal Earth rotation variations are required, incorporating in particular the nonequilibrium effect of the oceans. The remaining discrepancies between LOD and AAM in the 100- to 10-day period range may be due to either a common error in the AAM data sets from different meteorological centers, or another component of the angular momentum budget.